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styles__ConceptLeftRailCollapsibleContainer-sc-999edb8d-4 jYBMb" data-collapsible-container="true"><div class="styles__ConceptLeftRailTocContainer-sc-999edb8d-1 VPClm"><a href="#what-is-a-sinusoid" class="styles__ConceptLeftRailLink-sc-999edb8d-2 dXPsPe">What is a sinusoid?</a><a href="#what-is-phasor" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">What is phasor?</a><a href="#functions-of-sinusoids" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Functions of Sinusoids</a><a href="#benefits-of-sinusoids" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Benefits of sinusoids</a><a href="#function-of-phasors" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Function of Phasors</a><a href="#application-of-sinusoids-and-phasors" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Application of sinusoids and phasors</a><a href="#common-mistakes" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM"> Common Mistakes</a><a href="#context-and-applications" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Context and Applications</a><a href="#related-concepts" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Related Concepts</a><a href="#practice-problems" class="styles__ConceptLeftRailLink-sc-999edb8d-2 brAuCM">Practice Problems</a></div></div></div></div><div class="styles__AppLayoutMainContentMiddleRail-sc-ef9b07f2-11 gOBSIZ"><div class="styles__ConceptMiddleRailContainer-sc-19e4770b-2 eEviTx"><div id="CONCEPT_HTML_CONTAINER_ID" class="styles__ConceptMiddleRailHtml-sc-19e4770b-0 idfrjW"><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="what-is-a-sinusoid">What is a sinusoid?</h2><p>Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.</p></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="what-is-phasor">What is phasor?</h2><p>Phasor is defined as the complex number that is used to define the amplitude and phase domain of the sinusoids.</p></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="functions-of-sinusoids">Functions of Sinusoids</h2><p>Sinusoidal currents are typically referred to as alternating currents (AC). Currents of this kind are opposite at every intervals and changes with positive and negative values. Circuits that work on the sinusoidal voltage or current are referred to as AC circuits.</p><p>The sinusoidal wave have both transient response and steady-state response, similar to the step feature. The transient response dies out with time such that the most effective response that remains is the steady state response. The transient reaction has negligibly small time period in comparison with the steady-state response, and it can be considered that the circuit operates in sinusoidal steady-state.</p><p>Sinusoids are mathematical curves. They are in the form of cosine and sine functions. Sinusoids are used to represent the waveform of alternating current.</p><div class="wp-block-image"><figure class="aligncenter size-full is-resized"><img src="https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08105802/image-80.png" alt="A sinusoid is a sign that has a form of a sine wave. The shape of the supply voltage for power distribution is called a sinusoid as it resembles a sine or cosine wave shape." class="wp-image-57294" width="560" height="194"><figcaption>Sine wave <br>GNU Free Documentation License<strong> | </strong><a href="https://commons.wikimedia.org"><strong>https://commons.wikimedia.org</strong></a><strong> | </strong>Dave3457 </figcaption></figure></div><h3 class="wp-block-heading">What is an alternating current?</h3><p>Alternating current (AC) is the flow of charges that reverses its flow at a specific time period. AC waveform starts from zero and it increases to the average value and then decreases till zero after a specific period waveform continues in a reverse direction following the same manner and starts from zero then increases to maximum RMS value then decays to zero. The time required to complete one cycle including positive and negative waveform is known as the period. The same frequency is defined as the number of cycles per second. </p><h3 class="wp-block-heading">Sinusoidal circuit</h3><p>Sinusoidal currents are referred to as AC. Circuit which has sinusoidal voltage and current as its input and output is referred to as AC circuit. There are two types of the response generated by the sinusoidal circuit. One is a transient response and the other is a steady-state response.</p><h3 class="wp-block-heading">Transient and steady-state response</h3><p>Consider the example of starting off the ceiling fan. When we switch on the fan, the fan attains its maximum speed after a few seconds. The time required by the fan to reach its maximum speed is termed as transient time. After reaching the maximum speed fan continues to run at the same speed. Therefore, the time at which a fan runs at a steady speed is termed as steady time.</p><p>The transient response dies out after a certain amount of time and only steady-state remains. The time at which only steady-state remains is called sinusoidal steady state.</p></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="benefits-of-sinusoids">Benefits of sinusoids</h2><ul class="wp-block-list"><li>All the natural phenomenon we see around us the example: vibration of string, movement of a pendulum, etc. have sinusoidal characteristics.</li><li>Any practical periodic signal can be represented in the form of a sinusoidal function by the use of the Fourier series.</li><li>Sinusoidal functions are easier to calculate and operate.</li><li>Sinusoids can be easily transformed into phasors.</li><li>It saves time.</li></ul></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="function-of-phasors">Function of Phasors</h2><p>Phasors are used to define the amplitude and phase difference of sinusoidal function. Phasors are represented by vectors in a diagram. Phasors are generally a set of complex numbers in mathematical form.</p><h3 class="wp-block-heading">Complex numbers</h3><p>The complex numbers conjugate that contains both real and imaginary parts are termed as complex numbers. Complex numbers can be represented in two forms, one is a rectangular form which is defined as (a + bi) where the real axis part is represented by “a” and the imaginary part is represented by “I”. The second form is phasor form which is written as r<Φ where r represents the amplitude of sinusoidal function and Φ represents the phase of a sinusoidal function.</p><h3 class="wp-block-heading">Basics of a complex numbers</h3><p>Consider a complex number written in rectangular form.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>i</mi><mi>y</mi></math></p><p>Here, x represents the real part, y represents the imaginary part.</p><p>Z can also be represented in polar form as shown below.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Z</mi><mo>=</mo><mi>r</mi><mfenced><mrow><mi>cos</mi><mi>ϕ</mi><mo>+</mo><mi>i</mi><mi>sin</mi><mi>ϕ</mi></mrow></mfenced></math></p><p>Here, <em>r</em> represents amplitude which can be calculated as:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></msqrt></math></p><p>The <em>ϕ</em> represents the phase domain of sinusoidal that can be calculated as shown below:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfrac><mi>y</mi><mi>x</mi></mfrac></math></p><h3 class="wp-block-heading">Phasor representation</h3><p>Euler’s identity is given by:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>e</mi><mrow><mo>±</mo><mi>j</mi><mi>ϕ</mi></mrow></msup><mo>=</mo><mi>cos</mi><mi>ϕ</mi><mo>±</mo><mi>i</mi><mi>sin</mi><mi>ϕ</mi></math></p><p>Here, cos ϕ and sin ϕ are the real and imaginary parts of <em>e</em>.</p><p>Sinusoidal voltage can be represented in rectangular as well as phasor form. The phasor form representation is shown below:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><msub><mi>V</mi><mi>m</mi></msub><mi>cos</mi><mfenced><mrow><mi>ω</mi><mi>t</mi><mo>+</mo><mi>ϕ</mi></mrow></mfenced><mspace linebreak="newline"></mspace><mi>v</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>R</mi><mi>e</mi><mfenced><mrow><msub><mi>V</mi><mi>m</mi></msub><msup><mi>e</mi><mrow><mi>j</mi><mfenced><mrow><mi>ω</mi><mi>t</mi><mo>+</mo><mi>ϕ</mi></mrow></mfenced></mrow></msup></mrow></mfenced><mspace linebreak="newline"></mspace><mi>v</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>R</mi><mi>e</mi><mfenced><mrow><msub><mi>V</mi><mi>m</mi></msub><msup><mi>e</mi><mrow><mi>j</mi><mi>ω</mi><mi>t</mi></mrow></msup><msup><mi>e</mi><mrow><mi>j</mi><mi>ϕ</mi></mrow></msup></mrow></mfenced></math></p><p>Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mo>=</mo><msub><mi>V</mi><mi>m</mi></msub><msup><mi>e</mi><mrow><mi>j</mi><mi>ϕ</mi></mrow></msup></math></p><p>Therefore, the sinusoidal voltage will result in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mfenced><mi>t</mi></mfenced><mo>=</mo><mi>V</mi><msup><mi>e</mi><mrow><mi>j</mi><mi>ω</mi><mi>t</mi></mrow></msup></math>.</p><p>Hence, in this way the phasor representation can be found out for any signal including current and voltage.</p><h3 class="wp-block-heading">Explain Phasor Diagram?</h3><p>A pictorial representation of phasor representation including magnitude and phase domain is termed a phasor diagram. The phasor diagram contains voltage vector, current vector, and phase angle. With the help of the nature of phase angle, the behavior of the circuit can be determined that is whether it is lagging or leading.</p><div class="wp-block-image"><figure class="aligncenter size-full is-resized"><img src="https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08111548/image-81.png" alt="When current lags the voltage it can be said the circuit have lagging nature as shown in figure whereas if current leads the voltage, it can be said that nature of circuit is leading." class="wp-image-57315" width="373" height="264"><figcaption>Lagging Nature</figcaption></figure></div><div class="wp-block-image"><figure class="aligncenter size-full is-resized"><img src="https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08111744/image-82.png" alt="The leading power factor in an ac electric circuit is attained by way of the use of capacitive load inside the circuit. As inside the presence of a in basic terms capacitive load or mixture of resistive-capacitive load, the cutting-edge leads furnished voltage. This offers upward push to the strength element usually stated to be main in nature." class="wp-image-57320" width="385" height="266"><figcaption>Leading Nature</figcaption></figure></div><h3 class="wp-block-heading">Benefits of phasor diagram</h3><p>With the help of a phasor diagram, it is easier to represent waveform and carry out calculations involving ac waves. It can be used to determine the nature of the circuit whether it is lagging or leading. It can be used to determine the root mean square value.</p><p>When the circuit consists of only a resistor, the current and voltage will be in the same phase difference. When the circuit contains the inductor, the current will lag the voltage and the circuit will have lagging nature whereas when the circuit contains a capacitor, the current will lead the voltage, therefore, the circuit will have a leading nature.</p></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="application-of-sinusoids-and-phasors">Application of sinusoids and phasors</h2><p>The application of sinusoids and phasors to AC circuits are:</p><ul class="wp-block-list"><li>The motivation behind the use of sinusoids in the evaluation of AC circuits is that almost all the natural phenomena have sinusoidal characteristics.</li><li>Signals in the sinusoidal shape are simple to generate and transmit.</li><li>The usage of Fourier evaluation, any realistic periodic signal may be represented as a sum of sinusoids.</li><li>Mathematically, a sinusoid is easy for mathematical calculations.</li></ul></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="common-mistakes"> Common Mistakes</h2><p>Students may get confused between instantaneous value and the phasor representation. Following are the points to avoid those confusions.</p><ul class="wp-block-list"><li>v(t) represents the instantaneous value of sinusoidal voltage whereas V represents the phasor representation of sinusoidal voltage.</li></ul><ul class="wp-block-list"><li>The value of instantaneous voltage is time-dependent whereas a value of V is time-independent.</li></ul><ul class="wp-block-list"><li>Instantaneous voltage is always real whereas phasor representation is the complex plane.</li></ul><ul class="wp-block-list"><li>It may also be possible to get confused between the time domain and phasor representation. Note the following points to avoid mistakes.</li></ul><ul class="wp-block-list"><li>The time-domain function will be represented using small alphabets whereas phasor representation will be given by capital alphabet.</li></ul><ul class="wp-block-list"><li>Time-domain represents sinusoidal voltage as a function of time whereas phasor is independent of time.</li></ul></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="context-and-applications">Context and Applications</h2><p>Some applications of sinusoids and phasors are listed below.</p><ul class="wp-block-list"><li>Solving real-life practical problems.</li><li>Signal analysis.</li><li>Network theory.</li><li>Control theory</li><li>Fluid dynamics.</li><li>Determining the response of the system.</li><li>Analysis of bulk power system reliability.</li><li>Solving RLC circuits.</li><li>Trigonometry</li><li>Linear algebra.</li></ul><p>This subject matter is tremendous inside the expert exam for each undergraduate and graduate publication, mainly for:</p><ul class="wp-block-list"><li>Bachelor of Technology in the electrical and electronic department</li><li>Bachelor of Science Physics</li><li>Master of Science Physics</li></ul></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="related-concepts">Related Concepts</h2><p>Sinusoids and phasor involve the following concepts.</p><ul class="wp-block-list"><li>Euler’s identity</li><li>Trigonometry identities</li></ul></div></section><section class="styles__ConceptMiddleRailSection-sc-19e4770b-1 hUrBEb"><div><h2 class="wp-block-heading" class="wp-block-heading" id="practice-problems">Practice Problems</h2><p><strong>Question 1</strong>- Transform <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>5</mn><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mn>40</mn><mi>t</mi><mo>-</mo><mn>40</mn></mrow></mfenced></math> sinusoids into phasors.</p><ol style="list-style-type: lower-alpha;"><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mfenced><mrow><mo>∠</mo><mn>30</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mfenced><mrow><mo>∠</mo><mn>80</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mfenced><mrow><mo>∠</mo><mo>-</mo><mn>140</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mfenced><mrow><mo>∠</mo><mn>40</mn></mrow></mfenced></math></li></ol><p><strong>Correct answer:</strong> (c)</p><p><strong>Explanation:</strong> To find the phasor of the sinusoidal time domain using the magnitude and phase angle.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnspacing="0px" columnalign="right center left"><mtr><mtd><mn>5</mn><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mn>40</mn><mi>t</mi><mo>+</mo><mn>40</mn></mrow></mfenced></mtd><mtd><mo>=</mo></mtd><mtd><mn>5</mn><mo> </mo><mi>cos</mi><mo> </mo><mfenced><mrow><mn>40</mn><mi>t</mi><mo>+</mo><mn>40</mn><mo>-</mo><mn>180</mn></mrow></mfenced></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><mn>5</mn><mo>∠</mo><mfenced><mrow><mo>-</mo><mn>140</mn></mrow></mfenced></mtd></mtr></mtable></math></p><p> </p><p><strong>Question 2</strong>- Transform <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>3</mn><mi>sin</mi><mfenced><mrow><mn>30</mn><mi>t</mi><mo>-</mo><mn>50</mn></mrow></mfenced></math> into phasor.</p><ol style="list-style-type: lower-alpha;"><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mfenced><mrow><mo>∠</mo><mn>140</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mfenced><mrow><mo>∠</mo><mo>-</mo><mn>140</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mfenced><mrow><mo>∠</mo><mn>30</mn></mrow></mfenced></math></li><li>None of the above</li></ol><p><strong>Correct answer:</strong> (b)</p><p><strong>Explanation:</strong> Use identity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>A</mi><mo>=</mo><mi>cos</mi><mo> </mo><mfenced><mrow><mi>A</mi><mo>-</mo><mn>90</mn></mrow></mfenced></math></p><p>To find phasor use magnitude and phase angle.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnspacing="0px" columnalign="right center left"><mtr><mtd><mi>v</mi></mtd><mtd><mo>=</mo></mtd><mtd><mn>3</mn><mi>sin</mi><mfenced><mrow><mn>30</mn><mi>t</mi><mo>-</mo><mn>50</mn></mrow></mfenced></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><mn>3</mn><mi>cos</mi><mfenced><mrow><mn>30</mn><mi>t</mi><mo>-</mo><mn>50</mn><mo>-</mo><mn>90</mn></mrow></mfenced></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><mn>3</mn><mo>∠</mo><mfenced><mrow><mo>-</mo><mn>140</mn></mrow></mfenced></mtd></mtr></mtable></math></p><p> </p><p><strong>Question 3</strong>- Transform phasor <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>+</mo><mi>i</mi><mn>7</mn></math> into sinusoids.</p><ol style="list-style-type: lower-alpha;"><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mfenced><mrow><mo>∠</mo><mn>25</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>06</mn><mfenced><mrow><mo>∠</mo><mn>60</mn><mo>.</mo><mn>25</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mfenced><mrow><mo>∠</mo><mn>90</mn></mrow></mfenced></math></li><li><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mfenced><mrow><mo>∠</mo><mn>54</mn></mrow></mfenced></math></li></ol><p><strong>Explanation:</strong> Find magnitude and phase using the formula discussed earlier.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnspacing="0px" columnalign="right center left"><mtr><mtd><mi>i</mi></mtd><mtd><mo>=</mo></mtd><mtd><msqrt><msup><mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mn>7</mn></mfenced><mn>2</mn></msup></msqrt><mo>∠</mo><mfenced><mrow><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mrow><mo>-</mo><mn>7</mn></mrow><mn>4</mn></mfrac></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo></mtd><mtd><mn>8</mn><mo>.</mo><mn>06</mn><mo>∠</mo><mn>60</mn><mo>.</mo><mn>25</mn></mtd></mtr></mtable></math></p><p> </p><p><strong>Question 4-</strong> When current leads voltage the nature of the circuit is _____.</p><ol style="list-style-type: lower-alpha;"><li>Leading</li><li>Lagging</li><li>Unity</li><li>All of the above</li></ol><p><strong>Correct answer:</strong> (a)</p><p><strong>Explanation:</strong> When current leads voltage, the circuit is leading in nature.</p><p> </p><p><strong>Question 5-</strong> When voltage leads to the current the nature of the circuit is _____.</p><p>A. Lagging</p><p>B. Leading</p><p>C. Unity</p><p>D. 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The generator, driven at a…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/required-information-consider-the-given-circuit-where-5-ma.-an-ammeter-with-internal-resistance-r-is/4af3fe4e-40cc-4d4b-ba98-7e966c23eb2e" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: ! Required information Consider the given circuit where ₁ = 5 mA. An ammeter with internal…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/1.-laboratory-iask-descriptions-verification-of-rc-and-rl-transient-analysis-computations-for-this-l/39f1307c-ddbc-4c20-b54b-1cbf458a258c" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 1. Laboratory Iask Descriptions Verification of RC and RL transient analysis computations For this…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/practice-10.12-use-nodal-analysis-on-the-circuit-of-fig.-10.23-to-find-v-and-v2.-50-90-ma-1-j25-ms-m/e7bfff16-b0b0-4848-ae7c-ff5a5e2bab65" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: PRACTICE 10.12 Use nodal analysis on the circuit of Fig. 10.23 to find V₁ and V2. 50-90° mA 1 -j25…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/6.-find-the-thevenin-equivalent-to-the-left-of-the-a-b-terminals.-when-finding-rth-apply-a-1-v-volta/39e5fa22-b923-46d5-8c6f-50d3c16a6d9f" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Pen and Paper solution please</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/0.8-ns.-3.3-compiled-code-simulation-apply-logic-levelization-on-circuit-m-given-in-figure-3.38.-ass/58c751f8-e229-45d6-91ed-e17f844df44d" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 0.8 ns. 3.3 (Compiled-Code Simulation) Apply logic levelization on circuit M given in Figure 3.38.…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/8.-5-points-using-tables-or-the-definition-find-the-discrete-time-signal-n-whose-dtft-is-ae-jw-xew-1/081e2820-bbef-4f81-8af6-4a58e75c2be3" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 8. (5 points) Using Tables (or the definition) find the discrete time signal [n] whose DTFT is ae-jw…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/254-82-8-x-y-v-s-5-2-2-3-4-x-x-y-dz-dy-dx/1e63c0ab-728e-471d-84b0-e5fa2fc76d8a" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 254-82 8-x-y² v - s 5 2 -2 3 -√√4-x² x²+ y² dz dy dx</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/ww-c-vi-r-vo/4e07a9d8-5a21-4653-93e0-3ce35a378b2a" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: We want to design an IIR filter corresponding to the following analog filter with a cut-off…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/a-3-phase-14kvrms-line-to-line-10mva-60hz-2-pole-0.85-pf-lagging-star-connected-synchronous-generato/2c994e49-e382-47d8-9161-c0a12e6abade" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: A 3-phase, 14kVrms (line-to-line), 10MVA, 60Hz, 2-pole, 0.85 PF lagging star-connected, synchronous…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/3-r-d-ei/2eba3eb4-b6bb-42b8-b849-803de912b289" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: In the circuit of the figure, ε = 12.2 V, R = 7.34 Ω and L = 5.48 H. The battery is connected at t =…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/find-the-transfer-function-hw-from-the-magnitude-bode-plot-shown-below.-h-db-20-dbdecade-40-20-20-2-/33890f33-ea86-4772-a3dd-6ac5c7d0543e" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Find the transfer function H(w) from the magnitude Bode plot shown below. H (dB) -20 dB/decade 40 20…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/q1-compute-the-z-parameters-of-the-circuit-in-the-figure-below-50-ww-10-w-ww-411-10-20-w-ww/e6d1ad9b-b599-4975-9166-9de50055dbc4" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Q1: Compute the z parameters of the circuit in the figure below 50 ww 10 Ω ww 411 10 20 Ω ww</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/hw-a-15nc-point-charge-is-at-111-in-free-space.-calculate-v1-if-point-p1-is-located-p1-23-1-and-a-v0/4bc85f00-cce6-41e4-83fd-189d1099405a" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: HW: A 15nc point charge is at (1,1,1) in free space. Calculate V1 if point P1 is located P1(-2,3,-1)…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/close-switch-2-j-800-3-4-2-graded-2-state-whether-the-light-bulbs-below-are-a-in-series-b-in-paralle/1b5dc4c1-6be9-4881-80a6-02be51b834ae" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: No Chatgpt please</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/4.-given-the-following-active-filter-circuit-rf-ww-9k52-vin-sinut-r2-www-rt-mmm-ikul-lokr-c-1-001592/a3eea27a-87de-4e10-9008-96e19daf064b" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Check if this correct?</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/1-the-radiation-intensity-of-a-lossless-antenna-is-given-by-u-3-cos-wsr.-p-007-027.-find-2-a-the-rad/39fd32bf-b9ce-42ac-ac2d-62cc2b1e517b" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Please solve the second question (question 2) thaaannkssss siiirrr</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/chapter-3-d3.1.-given-a-60-mc-point-charge-located-at-the-origin-find-the-total-electric-flux-passin/70769f7e-34d6-46b1-8946-c6ca84a8611a" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Make the solution more detailed.</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/2-sketch-the-periodic-digital-signal-and-find-its-fourier-coefficients-ck-and-sketch-their-rea-and-i/f1c524d4-10d1-4924-83ae-9c53b5388741" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 2) Sketch the periodic digital signal and find its Fourier Coefficients Ck and sketch their rea and…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/show-how-to-make-a-state-diagram-for-a-mealy-machine-with-the-following-specifications-1.-has-one-in/23f81de0-0921-402c-a321-938307a0203b" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Show how to make a state diagram for a Mealy machine with the following specifications:1. Has one…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/q1a-mealy-synchronous-sequential-circuit-has-two-inputsx1x2-and-two-outputs-2122.the-first-output-of/61d48135-7e46-40f1-8100-afe32cb8a4ed" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Q1/A mealy synchronous sequential circuit has two inputs(X1,X2) and two outputs (21,22).The first…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/question-1-o-pts-you-are-given-an-npn-transistor-with-an-hfe-100-and-va-100-volts.-vbethreshold-0.7-/d029c452-7cdf-463f-9e09-dd540996217f" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Question 1 O pts You are given an NPN transistor with an hfe = 100 and VA = 100 Volts.…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/4.-determine-the-thevenin-equivalent-circuit-for-the-circuit-shown-in-figure-p4-below-as-seen-by-a-l/934d18ad-3f68-4c3a-ab85-cc43c97261e9" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: what is Voc and Isc</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/vs-a-w-rb-vout-a-1216-p.m.-for-the-following-circuit-find-the-transfer-function-hdvoutvs-using-imped/c2454a56-11ea-4aef-9ef6-a37595d1ac27" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Vs α w RB Vout a 12:16 p.m. For the following circuit, find the transfer function H(D)=Vout/Vs using…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/20-14.49-5-w-www-1.5-vcs-s-2-a/46628975-8f3b-4837-ab7d-9f2c864fbbbc" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Draw the s-domain equivalent of the circuit in Figure 14.49 and find the value of v(t) when i(0) is…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/fct-3-5/ec182bd2-1df3-4d2b-b21c-24ecaeb97aef" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Find the Fourier Transform F(w) for this function.</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/what-is-the-application-of-rectifiers-in-ups/038254dc-e6d4-447c-95aa-e3fed5fb6cf3" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: what is the application of rectifiers in UPS</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/3.-obtain-the-y-parameters-for-the-t-network-shown-in-fig.3-692-1842-ww-www-answer-30.3-ms-y22-45.47/0280964e-f462-4597-bd0d-6a1ae881edb0" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 3. Obtain the y parameters for the T network shown in Fig.3 692 1842 ww www Answer: -30.3 mS, y22 =…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/in-the-circuit-below-if-e20330-volt-and-frequency200hz-what-is-the-total-current-it-from-the-source-/9cdf9383-9218-40ae-83cb-010cdef42e20" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: In the circuit below if E=20+330 volt and frequency=200Hz; what is the total Current IT from the…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/draw-the-logic-circuits-that-can-achieve-the-following-truth-tables-a-b-c-output-a-b-c-output-0-0-0-/845b1a20-5678-481c-9b6f-2dc5b6162d85" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Don't use ai to answer I will report you answer</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/2.-for-the-following-circuits-a-find-the-impedance-zjw-of-circuit-a-as-a-function-of-win-rectangular/8c9edcb4-167a-4268-8b9c-2ebdcf459a2d" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 2. For the following circuits: (a) Find the impedance Z(jw) of circuit (a) as a function of win…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/determine-the-gain-vo-vs-of-the-given-transistor-amplifier-circuit-where-60.-10-2-kw-ww-4-kw-vs-4-kw/83abbe41-fe0c-461f-8cf7-ebfd54d400dd" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Determine the gain vo/ Vs of the given transistor amplifier circuit where /= 60/. 10 2 ΚΩ ww 4 ΚΩ…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/4.-for-the-nmos-amplifier-in-fig.-2-replace-the-transistor-with-its-t-equivalent-circuit-assume-20.-/b58f85ea-d58b-4243-ac1c-21fe7f53b65f" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: see fig 2 to answer</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/charged-particles-y-u-o-fr-qe-fe-e-aperture-particles-with-b-fm-qux-b-constant-velocity/3fcb9b01-13d1-4aee-ae68-6b87b9dd0175" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Consider a particle velocity filter. The uniform E and B fields are oriented perpendicular to each…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/problem-2-if-t-10cos-2t-find-it-xcos-2t-y-where-y-is-the-phase-in-radians.-find-x-and-y.-af-b-h-132-/915351b7-7da6-4a86-8839-e492d5481a79" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: NEED HANDWRITTEN SOLUTION DO NOT USE AI #A=1.2 #B=1.5</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/t-di-seele-d2-draw-out-put-voltage-and-determine-vagr-and-vrms/871c18dd-9b86-48b1-9850-8cb8911a9f86" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: T₂ Di seele D2 Draw out put voltage and Determine Vagr and Vrms?</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/1-using-the-equations-below-design-a-4x16-line-decoder-y-xx2x3x4-y5-xx2-x3-x4-y-xx2x3x4-y13x1x2x3x4-/ffffc427-6d62-4522-aef7-b949fb6125c7" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: 1) Using the equations below, design a 4X16 line decoder Y₁ = X₁X2X3X4 Y5 = X₁X2 X3 X4 Y₁ = X₁X2X3X4…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/in-a-particular-bjt-the-base-current-is-10ua-and-the-collector-current-is-800ua.-find-ss-and-a-for-t/6cdba8f9-f22a-45ef-9391-184a01f0f79c" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: In a particular BJT, the base current is 10uA, and the collector current is 800uA. Find ẞ and a for…</a></div><div class="styles__SingleQnaZippyContainer-sc-1935bbd8-2 NNa-DR"><a href="/questions-and-answers/an-rlc-series-circuit-has-an-impedance-of-83-and-a-power-factor-of-0.56-with-the-voltage-lagging-the/fc818c79-fb0e-48e1-8fae-e555938b4e50" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__SingleQnaZippyQuestionText-sc-1935bbd8-3 lVJhp">Q: Need handwritten and correct solution. Do not use AI please</a></div></div></div></div><div class="styles__ConceptRightRailContainer-sc-ea776dd9-0 gcvSJp"><div class="styles__CmsMarketingCtaContainerWrapper-sc-c493ab53-7 kCbpdi"><div class="styles__CmsMarketingCtaContainer-sc-c493ab53-0 bkoAA"><h3 class="styles__CmsMarketingCtaHeader-sc-c493ab53-1 fOINyA">Search. Solve. 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If another 100 ohm…","slug":"four-resistors-having-a-value-of-100-ohms-each-are-connected-in-parallel.-if-another-100-ohm-resisto","computed":{"hrefAndAs":{"href":"/my-questions?questionId=909a6c01-3d92-41b4-ab50-43bb389eb2e0","as":"/questions-and-answers/four-resistors-having-a-value-of-100-ohms-each-are-connected-in-parallel.-if-another-100-ohm-resisto/909a6c01-3d92-41b4-ab50-43bb389eb2e0"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"656b0c6e-24c0-4b4b-b230-99cc5131f6e3","questionText":"Exs / Find the complete response \u0026 and then\ni for 670 in the circad of sug (5)\nIH\nyr\nми это\nww\n12V…","slug":"exs-find-the-complete-response-and-and-then-i-for-670-in-the-circad-of-sug-5-ih-yr-mi-eto-ww-12v-22-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=656b0c6e-24c0-4b4b-b230-99cc5131f6e3","as":"/questions-and-answers/exs-find-the-complete-response-and-and-then-i-for-670-in-the-circad-of-sug-5-ih-yr-mi-eto-ww-12v-22-/656b0c6e-24c0-4b4b-b230-99cc5131f6e3"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"ede0b9a7-4d9a-42d8-b335-a3436f115d48","questionText":"2. A 3-phase, 75 MVA, 11-8 kV star-connected alternator with a solidly earthed neutral point has the…","slug":"2.-a-3-phase-75-mva-11-8-kv-star-connected-alternator-with-a-solidly-earthed-neutral-point-has-the-f","computed":{"hrefAndAs":{"href":"/my-questions?questionId=ede0b9a7-4d9a-42d8-b335-a3436f115d48","as":"/questions-and-answers/2.-a-3-phase-75-mva-11-8-kv-star-connected-alternator-with-a-solidly-earthed-neutral-point-has-the-f/ede0b9a7-4d9a-42d8-b335-a3436f115d48"}}},{"answer":"Computing Fourier Transforms Using EigenfunctionsUnderstanding the Problem:We're asked to compute…","id":"73aabca0-4374-44c7-8123-4741415f19a5","questionText":"Try to use eigenfunctions to solve please","slug":"1.-compute-the-fourier-transform-of-the-following-ct-signals-a-xt-b-e-3ortor-e-1-0.-3ortor-sin2t.-t-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=73aabca0-4374-44c7-8123-4741415f19a5","as":"/questions-and-answers/1.-compute-the-fourier-transform-of-the-following-ct-signals-a-xt-b-e-3ortor-e-1-0.-3ortor-sin2t.-t-/73aabca0-4374-44c7-8123-4741415f19a5"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"e4af2339-ae49-4870-a834-8fa95bf3d99d","questionText":"NEED HANDWRITTEN CORRECT ANSWER PLEASE","slug":"find-vct-for-tgreater0-in-the-circuit-in-fig.-p7.111-if-vc0-0.-1-10v-0-1kw-www-figure-p7.111-200-mh-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=e4af2339-ae49-4870-a834-8fa95bf3d99d","as":"/questions-and-answers/find-vct-for-tgreater0-in-the-circuit-in-fig.-p7.111-if-vc0-0.-1-10v-0-1kw-www-figure-p7.111-200-mh-/e4af2339-ae49-4870-a834-8fa95bf3d99d"}}},{"answer":"Step 1:","id":"2eb6d09b-c363-41e0-8f96-ec004eacc2ea","questionText":"(33pts)\n2. Use nodal analysis to find io in the following circuit\n259\n2A\nį, 402\nM\n200\n302\n20 V\n6 A","slug":"33pts-2.-use-nodal-analysis-to-find-io-in-the-following-circuit-259-2a-i-402-m-200-302-20-v-6-a","computed":{"hrefAndAs":{"href":"/my-questions?questionId=2eb6d09b-c363-41e0-8f96-ec004eacc2ea","as":"/questions-and-answers/33pts-2.-use-nodal-analysis-to-find-io-in-the-following-circuit-259-2a-i-402-m-200-302-20-v-6-a/2eb6d09b-c363-41e0-8f96-ec004eacc2ea"}}},{"answer":"","id":"4d97a06f-cab8-436d-825e-5957aed3426d","questionText":"Please solve it without artificial intelligence on paper and pen","slug":"2-22-241-www-eller-vict-20-determine-the-input-find-input-to-and-to-41016and-voltage-voct-41e-326-ju","computed":{"hrefAndAs":{"href":"/my-questions?questionId=4d97a06f-cab8-436d-825e-5957aed3426d","as":"/questions-and-answers/2-22-241-www-eller-vict-20-determine-the-input-find-input-to-and-to-41016and-voltage-voct-41e-326-ju/4d97a06f-cab8-436d-825e-5957aed3426d"}}},{"answer":"Step 1: Learning to sketch a signal from its expression and vice versa:Step 2: Using differentiation…","id":"e70dc946-195c-45e8-8ef0-a4c55a6d0752","questionText":"Find the Fourier transform of the following signals using differentiation property.\n2\nx(t)\nM\n-2\n-1\n1…","slug":"find-the-fourier-transform-of-the-following-signals-using-differentiation-property.-2-xt-m-2-1-1-2-f","computed":{"hrefAndAs":{"href":"/my-questions?questionId=e70dc946-195c-45e8-8ef0-a4c55a6d0752","as":"/questions-and-answers/find-the-fourier-transform-of-the-following-signals-using-differentiation-property.-2-xt-m-2-1-1-2-f/e70dc946-195c-45e8-8ef0-a4c55a6d0752"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"37a95dfe-4cf0-47bf-94be-45b759e5fc9b","questionText":"Problem 4: We want to design an IIR filter corresponding to the following analog filter\nwith a…","slug":"problem-4-we-want-to-design-an-iir-filter-corresponding-to-the-following-analog-filter-with-a-cut-of","computed":{"hrefAndAs":{"href":"/my-questions?questionId=37a95dfe-4cf0-47bf-94be-45b759e5fc9b","as":"/questions-and-answers/problem-4-we-want-to-design-an-iir-filter-corresponding-to-the-following-analog-filter-with-a-cut-of/37a95dfe-4cf0-47bf-94be-45b759e5fc9b"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"54fbed7a-a3b4-4fec-9d2f-a0247c2cf2e2","questionText":"Find Rf in kQ so that G;=-15 (current gain Gi = i₁/is) and RL = 8 kQ.\nRf\nYour Answer:\niL\nRS\nVo\nRL…","slug":"find-rf-in-kq-so-that-g-15-current-gain-gi-iis-and-rl-8-kq.-rf-your-answer-il-rs-vo-rl-answer-units","computed":{"hrefAndAs":{"href":"/my-questions?questionId=54fbed7a-a3b4-4fec-9d2f-a0247c2cf2e2","as":"/questions-and-answers/find-rf-in-kq-so-that-g-15-current-gain-gi-iis-and-rl-8-kq.-rf-your-answer-il-rs-vo-rl-answer-units/54fbed7a-a3b4-4fec-9d2f-a0247c2cf2e2"}}},{"answer":"","id":"87908708-bf09-4815-aaed-d0c363091e20","questionText":"Using the node voltage method, calculate the currents in the conductances of 1, 4 and 8 (S) siemens.…","slug":"2-a-2s-ww-20-02-10-www-4-s-8-s-ww-www-1s-v3-1-13-v","computed":{"hrefAndAs":{"href":"/my-questions?questionId=87908708-bf09-4815-aaed-d0c363091e20","as":"/questions-and-answers/2-a-2s-ww-20-02-10-www-4-s-8-s-ww-www-1s-v3-1-13-v/87908708-bf09-4815-aaed-d0c363091e20"}}},{"answer":"","id":"01c4e188-7706-49ef-9122-1df6b3edc1e7","questionText":"B. An electromechanical open-loop control system is shown in Figure (2). The generator,\ndriven at a…","slug":"b.-an-electromechanical-open-loop-control-system-is-shown-in-figure-2.-the-generator-driven-at-a-con","computed":{"hrefAndAs":{"href":"/my-questions?questionId=01c4e188-7706-49ef-9122-1df6b3edc1e7","as":"/questions-and-answers/b.-an-electromechanical-open-loop-control-system-is-shown-in-figure-2.-the-generator-driven-at-a-con/01c4e188-7706-49ef-9122-1df6b3edc1e7"}}},{"answer":"Step 1: Use of Source transformation where a parallel current source I with a resistance R can be…","id":"4af3fe4e-40cc-4d4b-ba98-7e966c23eb2e","questionText":"!\nRequired information\nConsider the given circuit where ₁ = 5 mA. An ammeter with internal…","slug":"required-information-consider-the-given-circuit-where-5-ma.-an-ammeter-with-internal-resistance-r-is","computed":{"hrefAndAs":{"href":"/my-questions?questionId=4af3fe4e-40cc-4d4b-ba98-7e966c23eb2e","as":"/questions-and-answers/required-information-consider-the-given-circuit-where-5-ma.-an-ammeter-with-internal-resistance-r-is/4af3fe4e-40cc-4d4b-ba98-7e966c23eb2e"}}},{"answer":"Step 1:\\","id":"39f1307c-ddbc-4c20-b54b-1cbf458a258c","questionText":"1. Laboratory Iask Descriptions\nVerification of RC and RL transient analysis computations\nFor this…","slug":"1.-laboratory-iask-descriptions-verification-of-rc-and-rl-transient-analysis-computations-for-this-l","computed":{"hrefAndAs":{"href":"/my-questions?questionId=39f1307c-ddbc-4c20-b54b-1cbf458a258c","as":"/questions-and-answers/1.-laboratory-iask-descriptions-verification-of-rc-and-rl-transient-analysis-computations-for-this-l/39f1307c-ddbc-4c20-b54b-1cbf458a258c"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"e7bfff16-b0b0-4848-ae7c-ff5a5e2bab65","questionText":"PRACTICE\n10.12 Use nodal analysis on the circuit of Fig. 10.23 to find V₁ and V2.\n50-90° mA\n1\n-j25…","slug":"practice-10.12-use-nodal-analysis-on-the-circuit-of-fig.-10.23-to-find-v-and-v2.-50-90-ma-1-j25-ms-m","computed":{"hrefAndAs":{"href":"/my-questions?questionId=e7bfff16-b0b0-4848-ae7c-ff5a5e2bab65","as":"/questions-and-answers/practice-10.12-use-nodal-analysis-on-the-circuit-of-fig.-10.23-to-find-v-and-v2.-50-90-ma-1-j25-ms-m/e7bfff16-b0b0-4848-ae7c-ff5a5e2bab65"}}},{"answer":"The Thevenin resistance (Rth) is the equivalent resistance of the entire network, seen from the…","id":"39e5fa22-b923-46d5-8c6f-50d3c16a6d9f","questionText":"Pen and Paper solution please","slug":"6.-find-the-thevenin-equivalent-to-the-left-of-the-a-b-terminals.-when-finding-rth-apply-a-1-v-volta","computed":{"hrefAndAs":{"href":"/my-questions?questionId=39e5fa22-b923-46d5-8c6f-50d3c16a6d9f","as":"/questions-and-answers/6.-find-the-thevenin-equivalent-to-the-left-of-the-a-b-terminals.-when-finding-rth-apply-a-1-v-volta/39e5fa22-b923-46d5-8c6f-50d3c16a6d9f"}}},{"answer":"Step 1: Logic Levelization of Circuit MLevelization refers to assigning a level number to each gate…","id":"58c751f8-e229-45d6-91ed-e17f844df44d","questionText":"0.8 ns.\n3.3 (Compiled-Code Simulation) Apply logic levelization on circuit M given in\nFigure 3.38.…","slug":"0.8-ns.-3.3-compiled-code-simulation-apply-logic-levelization-on-circuit-m-given-in-figure-3.38.-ass","computed":{"hrefAndAs":{"href":"/my-questions?questionId=58c751f8-e229-45d6-91ed-e17f844df44d","as":"/questions-and-answers/0.8-ns.-3.3-compiled-code-simulation-apply-logic-levelization-on-circuit-m-given-in-figure-3.38.-ass/58c751f8-e229-45d6-91ed-e17f844df44d"}}},{"answer":"","id":"081e2820-bbef-4f81-8af6-4a58e75c2be3","questionText":"8. (5 points) Using Tables (or the definition) find the discrete time signal [n] whose DTFT is\nae-jw…","slug":"8.-5-points-using-tables-or-the-definition-find-the-discrete-time-signal-n-whose-dtft-is-ae-jw-xew-1","computed":{"hrefAndAs":{"href":"/my-questions?questionId=081e2820-bbef-4f81-8af6-4a58e75c2be3","as":"/questions-and-answers/8.-5-points-using-tables-or-the-definition-find-the-discrete-time-signal-n-whose-dtft-is-ae-jw-xew-1/081e2820-bbef-4f81-8af6-4a58e75c2be3"}}},{"answer":"Step 2: Switching to cylindrical coordinatesIn cylindrical coordinates:Step 3: Solve the…","id":"1e63c0ab-728e-471d-84b0-e5fa2fc76d8a","questionText":"254-82 8-x-y²\nv - s 5\n2\n-2\n3\n-√√4-x² x²+ y²\ndz dy dx","slug":"254-82-8-x-y-v-s-5-2-2-3-4-x-x-y-dz-dy-dx","computed":{"hrefAndAs":{"href":"/my-questions?questionId=1e63c0ab-728e-471d-84b0-e5fa2fc76d8a","as":"/questions-and-answers/254-82-8-x-y-v-s-5-2-2-3-4-x-x-y-dz-dy-dx/1e63c0ab-728e-471d-84b0-e5fa2fc76d8a"}}},{"answer":"For part a. FOR PART B","id":"4e07a9d8-5a21-4653-93e0-3ce35a378b2a","questionText":"We want to design an IIR filter corresponding to the following analog filter with a cut-off…","slug":"ww-c-vi-r-vo","computed":{"hrefAndAs":{"href":"/my-questions?questionId=4e07a9d8-5a21-4653-93e0-3ce35a378b2a","as":"/questions-and-answers/ww-c-vi-r-vo/4e07a9d8-5a21-4653-93e0-3ce35a378b2a"}}},{"answer":"Step 1:Step 2:","id":"2c994e49-e382-47d8-9161-c0a12e6abade","questionText":"A 3-phase, 14kVrms (line-to-line), 10MVA, 60Hz, 2-pole, 0.85 PF lagging star-connected,\nsynchronous…","slug":"a-3-phase-14kvrms-line-to-line-10mva-60hz-2-pole-0.85-pf-lagging-star-connected-synchronous-generato","computed":{"hrefAndAs":{"href":"/my-questions?questionId=2c994e49-e382-47d8-9161-c0a12e6abade","as":"/questions-and-answers/a-3-phase-14kvrms-line-to-line-10mva-60hz-2-pole-0.85-pf-lagging-star-connected-synchronous-generato/2c994e49-e382-47d8-9161-c0a12e6abade"}}},{"answer":"","id":"2eba3eb4-b6bb-42b8-b849-803de912b289","questionText":"In the circuit of the figure, ε = 12.2 V, R = 7.34 Ω and L = 5.48 H. The battery is connected at t =…","slug":"3-r-d-ei","computed":{"hrefAndAs":{"href":"/my-questions?questionId=2eba3eb4-b6bb-42b8-b849-803de912b289","as":"/questions-and-answers/3-r-d-ei/2eba3eb4-b6bb-42b8-b849-803de912b289"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"33890f33-ea86-4772-a3dd-6ac5c7d0543e","questionText":"Find the transfer function H(w) from the magnitude Bode plot shown below.\nH (dB)\n-20 dB/decade\n40\n20…","slug":"find-the-transfer-function-hw-from-the-magnitude-bode-plot-shown-below.-h-db-20-dbdecade-40-20-20-2-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=33890f33-ea86-4772-a3dd-6ac5c7d0543e","as":"/questions-and-answers/find-the-transfer-function-hw-from-the-magnitude-bode-plot-shown-below.-h-db-20-dbdecade-40-20-20-2-/33890f33-ea86-4772-a3dd-6ac5c7d0543e"}}},{"answer":"Step 1:","id":"e6d1ad9b-b599-4975-9166-9de50055dbc4","questionText":"Q1: Compute the z parameters of the circuit in the figure below\n50\nww\n10 Ω\nww\n411\n10\n20 Ω\nww","slug":"q1-compute-the-z-parameters-of-the-circuit-in-the-figure-below-50-ww-10-w-ww-411-10-20-w-ww","computed":{"hrefAndAs":{"href":"/my-questions?questionId=e6d1ad9b-b599-4975-9166-9de50055dbc4","as":"/questions-and-answers/q1-compute-the-z-parameters-of-the-circuit-in-the-figure-below-50-ww-10-w-ww-411-10-20-w-ww/e6d1ad9b-b599-4975-9166-9de50055dbc4"}}},{"answer":"","id":"4bc85f00-cce6-41e4-83fd-189d1099405a","questionText":"HW: A 15nc point charge is at (1,1,1) in free space. Calculate V1 if point P1 is\nlocated P1(-2,3,-1)…","slug":"hw-a-15nc-point-charge-is-at-111-in-free-space.-calculate-v1-if-point-p1-is-located-p1-23-1-and-a-v0","computed":{"hrefAndAs":{"href":"/my-questions?questionId=4bc85f00-cce6-41e4-83fd-189d1099405a","as":"/questions-and-answers/hw-a-15nc-point-charge-is-at-111-in-free-space.-calculate-v1-if-point-p1-is-located-p1-23-1-and-a-v0/4bc85f00-cce6-41e4-83fd-189d1099405a"}}},{"answer":"if doubt arises please mention in the comments.","id":"1b5dc4c1-6be9-4881-80a6-02be51b834ae","questionText":"No Chatgpt please","slug":"close-switch-2-j-800-3-4-2-graded-2-state-whether-the-light-bulbs-below-are-a-in-series-b-in-paralle","computed":{"hrefAndAs":{"href":"/my-questions?questionId=1b5dc4c1-6be9-4881-80a6-02be51b834ae","as":"/questions-and-answers/close-switch-2-j-800-3-4-2-graded-2-state-whether-the-light-bulbs-below-are-a-in-series-b-in-paralle/1b5dc4c1-6be9-4881-80a6-02be51b834ae"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"a3eea27a-87de-4e10-9008-96e19daf064b","questionText":"Check if this correct?","slug":"4.-given-the-following-active-filter-circuit-rf-ww-9k52-vin-sinut-r2-www-rt-mmm-ikul-lokr-c-1-001592","computed":{"hrefAndAs":{"href":"/my-questions?questionId=a3eea27a-87de-4e10-9008-96e19daf064b","as":"/questions-and-answers/4.-given-the-following-active-filter-circuit-rf-ww-9k52-vin-sinut-r2-www-rt-mmm-ikul-lokr-c-1-001592/a3eea27a-87de-4e10-9008-96e19daf064b"}}},{"answer":"Step 1:Step 2:Step 3:Step 4:","id":"39fd32bf-b9ce-42ac-ac2d-62cc2b1e517b","questionText":"Please solve the second question (question 2) thaaannkssss siiirrr","slug":"1-the-radiation-intensity-of-a-lossless-antenna-is-given-by-u-3-cos-wsr.-p-007-027.-find-2-a-the-rad","computed":{"hrefAndAs":{"href":"/my-questions?questionId=39fd32bf-b9ce-42ac-ac2d-62cc2b1e517b","as":"/questions-and-answers/1-the-radiation-intensity-of-a-lossless-antenna-is-given-by-u-3-cos-wsr.-p-007-027.-find-2-a-the-rad/39fd32bf-b9ce-42ac-ac2d-62cc2b1e517b"}}},{"answer":"Problem StatementWe are given a point charge of 60 μC located at the origin. The task is to find the…","id":"70769f7e-34d6-46b1-8946-c6ca84a8611a","questionText":"Make the solution more detailed.","slug":"chapter-3-d3.1.-given-a-60-mc-point-charge-located-at-the-origin-find-the-total-electric-flux-passin","computed":{"hrefAndAs":{"href":"/my-questions?questionId=70769f7e-34d6-46b1-8946-c6ca84a8611a","as":"/questions-and-answers/chapter-3-d3.1.-given-a-60-mc-point-charge-located-at-the-origin-find-the-total-electric-flux-passin/70769f7e-34d6-46b1-8946-c6ca84a8611a"}}},{"answer":"","id":"f1c524d4-10d1-4924-83ae-9c53b5388741","questionText":"2) Sketch the periodic digital signal and find its Fourier Coefficients Ck and sketch their rea\nand…","slug":"2-sketch-the-periodic-digital-signal-and-find-its-fourier-coefficients-ck-and-sketch-their-rea-and-i","computed":{"hrefAndAs":{"href":"/my-questions?questionId=f1c524d4-10d1-4924-83ae-9c53b5388741","as":"/questions-and-answers/2-sketch-the-periodic-digital-signal-and-find-its-fourier-coefficients-ck-and-sketch-their-rea-and-i/f1c524d4-10d1-4924-83ae-9c53b5388741"}}},{"answer":"To create a state diagram for a Mealy machine that processes blocks of three input bits and produces…","id":"23f81de0-0921-402c-a321-938307a0203b","questionText":"Show how to make a state diagram for a Mealy machine with the following specifications:1. Has one…","slug":"show-how-to-make-a-state-diagram-for-a-mealy-machine-with-the-following-specifications-1.-has-one-in","computed":{"hrefAndAs":{"href":"/my-questions?questionId=23f81de0-0921-402c-a321-938307a0203b","as":"/questions-and-answers/show-how-to-make-a-state-diagram-for-a-mealy-machine-with-the-following-specifications-1.-has-one-in/23f81de0-0921-402c-a321-938307a0203b"}}},{"answer":"1. State Diagram:* Define States: Create states to represent the different stages of the input…","id":"61d48135-7e46-40f1-8100-afe32cb8a4ed","questionText":"Q1/A mealy synchronous sequential circuit has two inputs(X1,X2) and two\noutputs (21,22).The first…","slug":"q1a-mealy-synchronous-sequential-circuit-has-two-inputsx1x2-and-two-outputs-2122.the-first-output-of","computed":{"hrefAndAs":{"href":"/my-questions?questionId=61d48135-7e46-40f1-8100-afe32cb8a4ed","as":"/questions-and-answers/q1a-mealy-synchronous-sequential-circuit-has-two-inputsx1x2-and-two-outputs-2122.the-first-output-of/61d48135-7e46-40f1-8100-afe32cb8a4ed"}}},{"answer":"To find RC such that the gain AV is approximately -10, we can use the following relationships for a…","id":"d029c452-7cdf-463f-9e09-dd540996217f","questionText":"Question 1\nO pts\nYou are given an NPN transistor\nwith an hfe = 100 and VA = 100\nVolts.…","slug":"question-1-o-pts-you-are-given-an-npn-transistor-with-an-hfe-100-and-va-100-volts.-vbethreshold-0.7-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=d029c452-7cdf-463f-9e09-dd540996217f","as":"/questions-and-answers/question-1-o-pts-you-are-given-an-npn-transistor-with-an-hfe-100-and-va-100-volts.-vbethreshold-0.7-/d029c452-7cdf-463f-9e09-dd540996217f"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"934d18ad-3f68-4c3a-ab85-cc43c97261e9","questionText":"what is Voc and Isc","slug":"4.-determine-the-thevenin-equivalent-circuit-for-the-circuit-shown-in-figure-p4-below-as-seen-by-a-l","computed":{"hrefAndAs":{"href":"/my-questions?questionId=934d18ad-3f68-4c3a-ab85-cc43c97261e9","as":"/questions-and-answers/4.-determine-the-thevenin-equivalent-circuit-for-the-circuit-shown-in-figure-p4-below-as-seen-by-a-l/934d18ad-3f68-4c3a-ab85-cc43c97261e9"}}},{"answer":"","id":"c2454a56-11ea-4aef-9ef6-a37595d1ac27","questionText":"Vs\nα\nw\nRB\nVout\na\n12:16 p.m.\nFor the following circuit, find the transfer function\nH(D)=Vout/Vs using…","slug":"vs-a-w-rb-vout-a-1216-p.m.-for-the-following-circuit-find-the-transfer-function-hdvoutvs-using-imped","computed":{"hrefAndAs":{"href":"/my-questions?questionId=c2454a56-11ea-4aef-9ef6-a37595d1ac27","as":"/questions-and-answers/vs-a-w-rb-vout-a-1216-p.m.-for-the-following-circuit-find-the-transfer-function-hdvoutvs-using-imped/c2454a56-11ea-4aef-9ef6-a37595d1ac27"}}},{"answer":"","id":"46628975-8f3b-4837-ab7d-9f2c864fbbbc","questionText":"Draw the s-domain equivalent of the circuit in Figure 14.49 and find the value of v(t) when i(0) is…","slug":"20-14.49-5-w-www-1.5-vcs-s-2-a","computed":{"hrefAndAs":{"href":"/my-questions?questionId=46628975-8f3b-4837-ab7d-9f2c864fbbbc","as":"/questions-and-answers/20-14.49-5-w-www-1.5-vcs-s-2-a/46628975-8f3b-4837-ab7d-9f2c864fbbbc"}}},{"answer":"","id":"ec182bd2-1df3-4d2b-b21c-24ecaeb97aef","questionText":"Find the Fourier Transform F(w) for this function.","slug":"fct-3-5","computed":{"hrefAndAs":{"href":"/my-questions?questionId=ec182bd2-1df3-4d2b-b21c-24ecaeb97aef","as":"/questions-and-answers/fct-3-5/ec182bd2-1df3-4d2b-b21c-24ecaeb97aef"}}},{"answer":"A rectifier is an electrical device that converts alternating current (AC), which periodically…","id":"038254dc-e6d4-447c-95aa-e3fed5fb6cf3","questionText":"what is the application of rectifiers in UPS","slug":"what-is-the-application-of-rectifiers-in-ups","computed":{"hrefAndAs":{"href":"/my-questions?questionId=038254dc-e6d4-447c-95aa-e3fed5fb6cf3","as":"/questions-and-answers/what-is-the-application-of-rectifiers-in-ups/038254dc-e6d4-447c-95aa-e3fed5fb6cf3"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"0280964e-f462-4597-bd0d-6a1ae881edb0","questionText":"3. Obtain the y parameters for the T network shown in Fig.3\n692\n1842\nww\nwww\nAnswer:\n-30.3 mS, y22 =…","slug":"3.-obtain-the-y-parameters-for-the-t-network-shown-in-fig.3-692-1842-ww-www-answer-30.3-ms-y22-45.47","computed":{"hrefAndAs":{"href":"/my-questions?questionId=0280964e-f462-4597-bd0d-6a1ae881edb0","as":"/questions-and-answers/3.-obtain-the-y-parameters-for-the-t-network-shown-in-fig.3-692-1842-ww-www-answer-30.3-ms-y22-45.47/0280964e-f462-4597-bd0d-6a1ae881edb0"}}},{"answer":"","id":"9cdf9383-9218-40ae-83cb-010cdef42e20","questionText":"In the circuit below if E=20+330 volt\nand frequency=200Hz; what is the total\nCurrent IT from the…","slug":"in-the-circuit-below-if-e20330-volt-and-frequency200hz-what-is-the-total-current-it-from-the-source-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=9cdf9383-9218-40ae-83cb-010cdef42e20","as":"/questions-and-answers/in-the-circuit-below-if-e20330-volt-and-frequency200hz-what-is-the-total-current-it-from-the-source-/9cdf9383-9218-40ae-83cb-010cdef42e20"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"845b1a20-5678-481c-9b6f-2dc5b6162d85","questionText":"Don't use ai to answer I will report you answer","slug":"draw-the-logic-circuits-that-can-achieve-the-following-truth-tables-a-b-c-output-a-b-c-output-0-0-0-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=845b1a20-5678-481c-9b6f-2dc5b6162d85","as":"/questions-and-answers/draw-the-logic-circuits-that-can-achieve-the-following-truth-tables-a-b-c-output-a-b-c-output-0-0-0-/845b1a20-5678-481c-9b6f-2dc5b6162d85"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"8c9edcb4-167a-4268-8b9c-2ebdcf459a2d","questionText":"2. For the following circuits:\n(a) Find the impedance Z(jw) of circuit (a) as a function of win…","slug":"2.-for-the-following-circuits-a-find-the-impedance-zjw-of-circuit-a-as-a-function-of-win-rectangular","computed":{"hrefAndAs":{"href":"/my-questions?questionId=8c9edcb4-167a-4268-8b9c-2ebdcf459a2d","as":"/questions-and-answers/2.-for-the-following-circuits-a-find-the-impedance-zjw-of-circuit-a-as-a-function-of-win-rectangular/8c9edcb4-167a-4268-8b9c-2ebdcf459a2d"}}},{"answer":"Step 1: Step 2: Step 3: Step 4:","id":"83abbe41-fe0c-461f-8cf7-ebfd54d400dd","questionText":"Determine the gain vo/ Vs of the given transistor amplifier circuit where /= 60/.\n10\n2 ΚΩ\nww\n4 ΚΩ…","slug":"determine-the-gain-vo-vs-of-the-given-transistor-amplifier-circuit-where-60.-10-2-kw-ww-4-kw-vs-4-kw","computed":{"hrefAndAs":{"href":"/my-questions?questionId=83abbe41-fe0c-461f-8cf7-ebfd54d400dd","as":"/questions-and-answers/determine-the-gain-vo-vs-of-the-given-transistor-amplifier-circuit-where-60.-10-2-kw-ww-4-kw-vs-4-kw/83abbe41-fe0c-461f-8cf7-ebfd54d400dd"}}},{"answer":"Step 1:Step 2:Step 3:","id":"b58f85ea-d58b-4243-ac1c-21fe7f53b65f","questionText":"see fig 2 to answer","slug":"4.-for-the-nmos-amplifier-in-fig.-2-replace-the-transistor-with-its-t-equivalent-circuit-assume-20.-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=b58f85ea-d58b-4243-ac1c-21fe7f53b65f","as":"/questions-and-answers/4.-for-the-nmos-amplifier-in-fig.-2-replace-the-transistor-with-its-t-equivalent-circuit-assume-20.-/b58f85ea-d58b-4243-ac1c-21fe7f53b65f"}}},{"answer":"a) Calculating the Magnetic Field (B): To pass through the electric (E) and magnetic (B) fields…","id":"3fcb9b01-13d1-4aee-ae68-6b87b9dd0175","questionText":"Consider a particle velocity filter. The uniform E and B fields are oriented perpendicular to each…","slug":"charged-particles-y-u-o-fr-qe-fe-e-aperture-particles-with-b-fm-qux-b-constant-velocity","computed":{"hrefAndAs":{"href":"/my-questions?questionId=3fcb9b01-13d1-4aee-ae68-6b87b9dd0175","as":"/questions-and-answers/charged-particles-y-u-o-fr-qe-fe-e-aperture-particles-with-b-fm-qux-b-constant-velocity/3fcb9b01-13d1-4aee-ae68-6b87b9dd0175"}}},{"answer":"The problem is asking us to find the amplitude X and phase Y of a cosine function that represents a…","id":"915351b7-7da6-4a86-8839-e492d5481a79","questionText":"NEED HANDWRITTEN SOLUTION DO NOT USE AI \n#A=1.2\n#B=1.5","slug":"problem-2-if-t-10cos-2t-find-it-xcos-2t-y-where-y-is-the-phase-in-radians.-find-x-and-y.-af-b-h-132-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=915351b7-7da6-4a86-8839-e492d5481a79","as":"/questions-and-answers/problem-2-if-t-10cos-2t-find-it-xcos-2t-y-where-y-is-the-phase-in-radians.-find-x-and-y.-af-b-h-132-/915351b7-7da6-4a86-8839-e492d5481a79"}}},{"answer":"","id":"871c18dd-9b86-48b1-9850-8cb8911a9f86","questionText":"T₂\nDi\nseele\nD2\nDraw out put voltage and Determine\nVagr and Vrms?","slug":"t-di-seele-d2-draw-out-put-voltage-and-determine-vagr-and-vrms","computed":{"hrefAndAs":{"href":"/my-questions?questionId=871c18dd-9b86-48b1-9850-8cb8911a9f86","as":"/questions-and-answers/t-di-seele-d2-draw-out-put-voltage-and-determine-vagr-and-vrms/871c18dd-9b86-48b1-9850-8cb8911a9f86"}}},{"answer":"","id":"ffffc427-6d62-4522-aef7-b949fb6125c7","questionText":"1) Using the equations below, design a 4X16 line decoder\nY₁ = X₁X2X3X4\nY5 = X₁X2 X3 X4\nY₁ = X₁X2X3X4…","slug":"1-using-the-equations-below-design-a-4x16-line-decoder-y-xx2x3x4-y5-xx2-x3-x4-y-xx2x3x4-y13x1x2x3x4-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=ffffc427-6d62-4522-aef7-b949fb6125c7","as":"/questions-and-answers/1-using-the-equations-below-design-a-4x16-line-decoder-y-xx2x3x4-y5-xx2-x3-x4-y-xx2x3x4-y13x1x2x3x4-/ffffc427-6d62-4522-aef7-b949fb6125c7"}}},{"answer":"Step 1: Definitions: (i). β (current gain) is the ratio of the collector current IC to the base…","id":"6cdba8f9-f22a-45ef-9391-184a01f0f79c","questionText":"In a particular BJT, the base current is 10uA, and the collector current is 800uA. Find ẞ and a for…","slug":"in-a-particular-bjt-the-base-current-is-10ua-and-the-collector-current-is-800ua.-find-ss-and-a-for-t","computed":{"hrefAndAs":{"href":"/my-questions?questionId=6cdba8f9-f22a-45ef-9391-184a01f0f79c","as":"/questions-and-answers/in-a-particular-bjt-the-base-current-is-10ua-and-the-collector-current-is-800ua.-find-ss-and-a-for-t/6cdba8f9-f22a-45ef-9391-184a01f0f79c"}}},{"answer":"Step 1:","id":"fc818c79-fb0e-48e1-8fae-e555938b4e50","questionText":"Need handwritten and correct solution. Do not use AI please","slug":"an-rlc-series-circuit-has-an-impedance-of-83-and-a-power-factor-of-0.56-with-the-voltage-lagging-the","computed":{"hrefAndAs":{"href":"/my-questions?questionId=fc818c79-fb0e-48e1-8fae-e555938b4e50","as":"/questions-and-answers/an-rlc-series-circuit-has-an-impedance-of-83-and-a-power-factor-of-0.56-with-the-voltage-lagging-the/fc818c79-fb0e-48e1-8fae-e555938b4e50"}}}],"qnaSampleAnswerHrefAndAs":{"href":"/my-questions?questionId=0009473c-2ab5-4aaf-a1ab-9b02d8d0baf6","as":"/questions-and-answers/the-openloop-gain-of-an-amplifier-is-a-5-and215-10-4-.-if-the-openloop-gain-decreases-by-10-percent--trt/0009473c-2ab5-4aaf-a1ab-9b02d8d0baf6"},"rightRail":{"tags":{"subjects":{"parent":{"title":"Engineering","short_name":"engineering"},"child":{"title":"Electrical Engineering","short_name":"electrical-engineering"}},"topics":["Electric Circuits and Networks","AC analysis","Sinusoids and phasors"]},"cta":{"loggedout_cta":{"heading":"Search. Solve. Succeed! ","content":"\u003cp style=\"text-align: center\"\u003eStudy smarter access to millions of step-by step textbook solutions, our Q\u0026A library, and AI powered Math Solver. Plus, you get 30 questions to ask an expert each month.\u003c/p\u003e","button_text":"Try bartleby learn now"},"loggedin_cta":{"image":"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2022/03/03214209/narrow-question-component.png","heading":" Q \u0026 A","sub_heading":"Stuck on your homework?","content":"Ask a question and get an expertly curated answer in as fast as 30 minutes.*","button_text":"Ask a Question","disclaimer":"*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers."}}},"leftRail":{"content":[{"name":"What is a sinusoid?","link":"what-is-a-sinusoid"},{"name":"What is phasor?","link":"what-is-phasor"},{"name":"Functions of Sinusoids","link":"functions-of-sinusoids"},{"name":"Benefits of sinusoids","link":"benefits-of-sinusoids"},{"name":"Function of Phasors","link":"function-of-phasors"},{"name":"Application of sinusoids and phasors","link":"application-of-sinusoids-and-phasors"},{"name":" Common Mistakes","link":"common-mistakes"},{"name":"Context and Applications","link":"context-and-applications"},{"name":"Related Concepts","link":"related-concepts"},{"name":"Practice Problems","link":"practice-problems"}]},"middleRail":{"id":57028,"status":"publish","slug":"sinusoids-and-phasors","title":"Sinusoids And Phasors","subjects":{"parent":{"title":"Engineering","short_name":"engineering"},"child":{"title":"Electrical Engineering","short_name":"electrical-engineering"}},"description":"","content":"\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"what-is-a-sinusoid\"\u003eWhat is a sinusoid?\u003c/h2\u003e\u003cp\u003eSinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.\u003c/p\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"what-is-phasor\"\u003eWhat is phasor?\u003c/h2\u003e\u003cp\u003ePhasor is defined as the complex number that is used to define the amplitude and phase domain of the sinusoids.\u003c/p\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"functions-of-sinusoids\"\u003eFunctions of Sinusoids\u003c/h2\u003e\u003cp\u003eSinusoidal currents are typically referred to as alternating currents (AC). Currents of this kind are opposite at every intervals and changes with positive and negative values. Circuits that work on the sinusoidal voltage or current are referred to as AC circuits.\u003c/p\u003e\u003cp\u003eThe sinusoidal wave have both transient response and steady-state response, similar to the step feature. The transient response dies out with time such that the most effective response that remains is the steady state response. The transient reaction has negligibly small time period in comparison with the steady-state response, and it can be considered that the circuit operates in sinusoidal steady-state.\u003c/p\u003e\u003cp\u003eSinusoids are mathematical curves. They are in the form of cosine and sine functions. Sinusoids are used to represent the waveform of alternating current.\u003c/p\u003e\u003cdiv class=\"wp-block-image\"\u003e\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003cimg src=\"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08105802/image-80.png\" alt=\"A sinusoid is a sign that has a form of a sine wave. The shape of the supply voltage for power distribution is called a sinusoid as it resembles a sine or cosine wave shape.\" class=\"wp-image-57294\" width=\"560\" height=\"194\"/\u003e\u003cfigcaption\u003eSine wave \u003cbr\u003eGNU Free Documentation License\u003cstrong\u003e | \u003c/strong\u003e\u003ca href=\"https://commons.wikimedia.org\"\u003e\u003cstrong\u003ehttps://commons.wikimedia.org\u003c/strong\u003e\u003c/a\u003e\u003cstrong\u003e | \u003c/strong\u003eDave3457 \u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\u003ch3 class=\"wp-block-heading\"\u003eWhat is an alternating current?\u003c/h3\u003e\u003cp\u003eAlternating current (AC) is the flow of charges that reverses its flow at a specific time period. AC waveform starts from zero and it increases to the average value and then decreases till zero after a specific period waveform continues in a reverse direction following the same manner and starts from zero then increases to maximum RMS value then decays to zero. The time required to complete one cycle including positive and negative waveform is known as the period. The same frequency is defined as the number of cycles per second. \u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eSinusoidal circuit\u003c/h3\u003e\u003cp\u003eSinusoidal currents are referred to as AC. Circuit which has sinusoidal voltage and current as its input and output is referred to as AC circuit. There are two types of the response generated by the sinusoidal circuit. One is a transient response and the other is a steady-state response.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eTransient and steady-state response\u003c/h3\u003e\u003cp\u003eConsider the example of starting off the ceiling fan. When we switch on the fan, the fan attains its maximum speed after a few seconds. The time required by the fan to reach its maximum speed is termed as transient time. After reaching the maximum speed fan continues to run at the same speed. Therefore, the time at which a fan runs at a steady speed is termed as steady time.\u003c/p\u003e\u003cp\u003eThe transient response dies out after a certain amount of time and only steady-state remains. The time at which only steady-state remains is called sinusoidal steady state.\u003c/p\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"benefits-of-sinusoids\"\u003eBenefits of sinusoids\u003c/h2\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eAll the natural phenomenon we see around us the example: vibration of string, movement of a pendulum, etc. have sinusoidal characteristics.\u003c/li\u003e\u003cli\u003eAny practical periodic signal can be represented in the form of a sinusoidal function by the use of the Fourier series.\u003c/li\u003e\u003cli\u003eSinusoidal functions are easier to calculate and operate.\u003c/li\u003e\u003cli\u003eSinusoids can be easily transformed into phasors.\u003c/li\u003e\u003cli\u003eIt saves time.\u003c/li\u003e\u003c/ul\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"function-of-phasors\"\u003eFunction of Phasors\u003c/h2\u003e\u003cp\u003ePhasors are used to define the amplitude and phase difference of sinusoidal function. Phasors are represented by vectors in a diagram. Phasors are generally a set of complex numbers in mathematical form.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eComplex numbers\u003c/h3\u003e\u003cp\u003eThe complex numbers conjugate that contains both real and imaginary parts are termed as complex numbers. Complex numbers can be represented in two forms, one is a rectangular form which is defined as (a + bi) where the real axis part is represented by “a” and the imaginary part is represented by “I”. The second form is phasor form which is written as r\u0026lt;Φ where r represents the amplitude of sinusoidal function and Φ represents the phase of a sinusoidal function.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eBasics of a complex numbers\u003c/h3\u003e\u003cp\u003eConsider a complex number written in rectangular form.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eZ\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, x represents the real part, y\u0026nbsp;represents the imaginary part.\u003c/p\u003e\u003cp\u003eZ can also be represented in polar form as shown below.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eZ\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003er\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, \u003cem\u003er\u003c/em\u003e\u0026nbsp;represents amplitude which can be calculated as:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003er\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsqrt\u003e\u003cmsup\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmsup\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/msqrt\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eThe \u003cem\u003eϕ\u003c/em\u003e\u0026nbsp;represents the phase domain of sinusoidal that can be calculated as shown below:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmi\u003etan\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmfrac\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mfrac\u003e\u003c/math\u003e\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003ePhasor representation\u003c/h3\u003e\u003cp\u003eEuler’s identity is given by:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e±\u003c/mo\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003cmo\u003e±\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, cos ϕ and sin ϕ are the real and imaginary parts of \u003cem\u003ee\u003c/em\u003e.\u003c/p\u003e\u003cp\u003eSinusoidal voltage can be represented in rectangular as well as phasor form. The phasor form representation is shown below:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003cmspace linebreak=\"newline\"\u003e\u003c/mspace\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eR\u003c/mi\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003cmspace linebreak=\"newline\"\u003e\u003c/mspace\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eR\u003c/mi\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eTherefore, the sinusoidal voltage will result in \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/math\u003e.\u003c/p\u003e\u003cp\u003eHence, in this way the phasor representation can be found out for any signal including current and voltage.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eExplain Phasor Diagram?\u003c/h3\u003e\u003cp\u003eA pictorial representation of phasor representation including magnitude and phase domain is termed a phasor diagram. The phasor diagram contains voltage vector, current vector, and phase angle. With the help of the nature of phase angle, the behavior of the circuit can be determined that is whether it is lagging or leading.\u003c/p\u003e\u003cdiv class=\"wp-block-image\"\u003e\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003cimg src=\"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08111548/image-81.png\" alt=\"When current lags the voltage it can be said the circuit have lagging nature as shown in figure whereas if current leads the voltage, it can be said that nature of circuit is leading.\" class=\"wp-image-57315\" width=\"373\" height=\"264\"/\u003e\u003cfigcaption\u003eLagging Nature\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\u003cdiv class=\"wp-block-image\"\u003e\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003cimg src=\"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08111744/image-82.png\" alt=\"The leading power factor in an ac electric circuit is attained by way of the use of capacitive load inside the circuit. As inside the presence of a in basic terms capacitive load or mixture of resistive-capacitive load, the cutting-edge leads furnished voltage. This offers upward push to the strength element usually stated to be main in nature.\" class=\"wp-image-57320\" width=\"385\" height=\"266\"/\u003e\u003cfigcaption\u003eLeading Nature\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\u003ch3 class=\"wp-block-heading\"\u003eBenefits of phasor diagram\u003c/h3\u003e\u003cp\u003eWith the help of a phasor diagram, it is easier to represent waveform and carry out calculations involving ac waves. It can be used to determine the nature of the circuit whether it is lagging or leading. It can be used to determine the root mean square value.\u003c/p\u003e\u003cp\u003eWhen the circuit consists of only a resistor, the current and voltage will be in the same phase difference. When the circuit contains the inductor, the current will lag the voltage and the circuit will have lagging nature whereas when the circuit contains a capacitor, the current will lead the voltage, therefore, the circuit will have a leading nature.\u003c/p\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"application-of-sinusoids-and-phasors\"\u003eApplication of sinusoids and phasors\u003c/h2\u003e\u003cp\u003eThe application of sinusoids and phasors to AC circuits are:\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eThe motivation behind the use of sinusoids in the evaluation of AC circuits is that almost all the natural phenomena have sinusoidal characteristics.\u003c/li\u003e\u003cli\u003eSignals in the sinusoidal shape are simple to generate and transmit.\u003c/li\u003e\u003cli\u003eThe usage of Fourier evaluation, any realistic periodic signal may be represented as a sum of sinusoids.\u003c/li\u003e\u003cli\u003eMathematically, a sinusoid is easy for mathematical calculations.\u003c/li\u003e\u003c/ul\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"common-mistakes\"\u003e\u0026nbsp;Common Mistakes\u003c/h2\u003e\u003cp\u003eStudents may get confused between instantaneous value and the phasor representation. Following are the points to avoid those confusions.\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003ev(t) represents the instantaneous value of sinusoidal voltage whereas V represents the phasor representation of sinusoidal voltage.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eThe value of instantaneous voltage is time-dependent whereas a value of V is time-independent.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eInstantaneous voltage is always real whereas phasor representation is the complex plane.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eIt may also be possible to get confused between the time domain and phasor representation. Note the following points to avoid mistakes.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eThe time-domain function will be represented using small alphabets whereas phasor representation will be given by capital alphabet.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eTime-domain represents sinusoidal voltage as a function of time whereas phasor is independent of time.\u003c/li\u003e\u003c/ul\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"context-and-applications\"\u003eContext and Applications\u003c/h2\u003e\u003cp\u003eSome applications of sinusoids and phasors are listed below.\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eSolving real-life practical problems.\u003c/li\u003e\u003cli\u003eSignal analysis.\u003c/li\u003e\u003cli\u003eNetwork theory.\u003c/li\u003e\u003cli\u003eControl theory\u003c/li\u003e\u003cli\u003eFluid dynamics.\u003c/li\u003e\u003cli\u003eDetermining the response of the system.\u003c/li\u003e\u003cli\u003eAnalysis of bulk power system reliability.\u003c/li\u003e\u003cli\u003eSolving RLC circuits.\u003c/li\u003e\u003cli\u003eTrigonometry\u003c/li\u003e\u003cli\u003eLinear algebra.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThis subject matter is tremendous inside the expert exam for each undergraduate and graduate publication, mainly for:\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eBachelor of Technology in the electrical and electronic department\u003c/li\u003e\u003cli\u003eBachelor of Science Physics\u003c/li\u003e\u003cli\u003eMaster of Science Physics\u003c/li\u003e\u003c/ul\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"related-concepts\"\u003eRelated Concepts\u003c/h2\u003e\u003cp\u003eSinusoids and phasor involve the following concepts.\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eEuler’s identity\u003c/li\u003e\u003cli\u003eTrigonometry identities\u003c/li\u003e\u003c/ul\u003e\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"practice-problems\"\u003ePractice Problems\u003c/h2\u003e\u003cp\u003e\u003cstrong\u003eQuestion 1\u003c/strong\u003e- Transform \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e sinusoids into phasors.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e80\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (c)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e To find the phasor of the sinusoidal time domain using the magnitude and phase angle.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmtable columnspacing=\"0px\" columnalign=\"right center left\"\u003e\u003cmtr\u003e\u003cmtd\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 2\u003c/strong\u003e- Transform \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e50\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e into phasor.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003eNone of the above\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (b)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e Use identity \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003eA\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003eA\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eTo find phasor use magnitude and phase angle.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmtable columnspacing=\"0px\" columnalign=\"right center left\"\u003e\u003cmtr\u003e\u003cmtd\u003e\u003cmi\u003ev\u003c/mi\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e50\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e50\u003c/mn\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 3\u003c/strong\u003e- Transform phasor \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eI\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/math\u003e into sinusoids.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e25\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e06\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e25\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e54\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e Find magnitude and phase using the formula discussed earlier.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmtable columnspacing=\"0px\" columnalign=\"right center left\"\u003e\u003cmtr\u003e\u003cmtd\u003e\u003cmi\u003ei\u003c/mi\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmsqrt\u003e\u003cmsup\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmsup\u003e\u003cmfenced\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/mfenced\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/msqrt\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmsup\u003e\u003cmi\u003etan\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmfenced\u003e\u003cmfrac\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/mrow\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mfrac\u003e\u003c/mfenced\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e06\u003c/mn\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e25\u003c/mn\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 4-\u003c/strong\u003e When current leads voltage the nature of the circuit is _____.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003eLeading\u003c/li\u003e\u003cli\u003eLagging\u003c/li\u003e\u003cli\u003eUnity\u003c/li\u003e\u003cli\u003eAll of the above\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (a)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e When current leads voltage, the circuit is leading in nature.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 5-\u003c/strong\u003e When voltage leads to the current the nature of the circuit is _____.\u003c/p\u003e\u003cp\u003eA. Lagging\u003c/p\u003e\u003cp\u003eB. Leading\u003c/p\u003e\u003cp\u003eC. Unity\u003c/p\u003e\u003cp\u003eD. None of these\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (a)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation: \u003c/strong\u003eWhen current lags voltage, the circuit is lagging in nature.\u003c/p\u003e","bottom_cta":{"loggedin_cta":{"heading":"Have your own electrical engineering question?","button_text":" Ask a Question","disclaimer":"*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers."},"loggedout_cta":{"heading":"Want more help with your electrical engineering homework?","content":"We've got you covered with step-by-step solutions to millions of textbook problems, subject matter experts on standby 24/7 when you're stumped, and more.","button_text":"Get Started","sample_text":"Check out a sample electrical engineering Q\u0026A solution here!","disclaimer":"*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers."}},"youtubeLicense":[],"computed":{"splitContent":["\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"what-is-a-sinusoid\"\u003eWhat is a sinusoid?\u003c/h2\u003e\u003cp\u003eSinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.\u003c/p\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"what-is-phasor\"\u003eWhat is phasor?\u003c/h2\u003e\u003cp\u003ePhasor is defined as the complex number that is used to define the amplitude and phase domain of the sinusoids.\u003c/p\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"functions-of-sinusoids\"\u003eFunctions of Sinusoids\u003c/h2\u003e\u003cp\u003eSinusoidal currents are typically referred to as alternating currents (AC). Currents of this kind are opposite at every intervals and changes with positive and negative values. Circuits that work on the sinusoidal voltage or current are referred to as AC circuits.\u003c/p\u003e\u003cp\u003eThe sinusoidal wave have both transient response and steady-state response, similar to the step feature. The transient response dies out with time such that the most effective response that remains is the steady state response. The transient reaction has negligibly small time period in comparison with the steady-state response, and it can be considered that the circuit operates in sinusoidal steady-state.\u003c/p\u003e\u003cp\u003eSinusoids are mathematical curves. They are in the form of cosine and sine functions. Sinusoids are used to represent the waveform of alternating current.\u003c/p\u003e\u003cdiv class=\"wp-block-image\"\u003e\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003cimg src=\"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08105802/image-80.png\" alt=\"A sinusoid is a sign that has a form of a sine wave. The shape of the supply voltage for power distribution is called a sinusoid as it resembles a sine or cosine wave shape.\" class=\"wp-image-57294\" width=\"560\" height=\"194\"\u003e\u003cfigcaption\u003eSine wave \u003cbr\u003eGNU Free Documentation License\u003cstrong\u003e | \u003c/strong\u003e\u003ca href=\"https://commons.wikimedia.org\"\u003e\u003cstrong\u003ehttps://commons.wikimedia.org\u003c/strong\u003e\u003c/a\u003e\u003cstrong\u003e | \u003c/strong\u003eDave3457 \u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\u003ch3 class=\"wp-block-heading\"\u003eWhat is an alternating current?\u003c/h3\u003e\u003cp\u003eAlternating current (AC) is the flow of charges that reverses its flow at a specific time period. AC waveform starts from zero and it increases to the average value and then decreases till zero after a specific period waveform continues in a reverse direction following the same manner and starts from zero then increases to maximum RMS value then decays to zero. The time required to complete one cycle including positive and negative waveform is known as the period. The same frequency is defined as the number of cycles per second. \u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eSinusoidal circuit\u003c/h3\u003e\u003cp\u003eSinusoidal currents are referred to as AC. Circuit which has sinusoidal voltage and current as its input and output is referred to as AC circuit. There are two types of the response generated by the sinusoidal circuit. One is a transient response and the other is a steady-state response.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eTransient and steady-state response\u003c/h3\u003e\u003cp\u003eConsider the example of starting off the ceiling fan. When we switch on the fan, the fan attains its maximum speed after a few seconds. The time required by the fan to reach its maximum speed is termed as transient time. After reaching the maximum speed fan continues to run at the same speed. Therefore, the time at which a fan runs at a steady speed is termed as steady time.\u003c/p\u003e\u003cp\u003eThe transient response dies out after a certain amount of time and only steady-state remains. The time at which only steady-state remains is called sinusoidal steady state.\u003c/p\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"benefits-of-sinusoids\"\u003eBenefits of sinusoids\u003c/h2\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eAll the natural phenomenon we see around us the example: vibration of string, movement of a pendulum, etc. have sinusoidal characteristics.\u003c/li\u003e\u003cli\u003eAny practical periodic signal can be represented in the form of a sinusoidal function by the use of the Fourier series.\u003c/li\u003e\u003cli\u003eSinusoidal functions are easier to calculate and operate.\u003c/li\u003e\u003cli\u003eSinusoids can be easily transformed into phasors.\u003c/li\u003e\u003cli\u003eIt saves time.\u003c/li\u003e\u003c/ul\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"function-of-phasors\"\u003eFunction of Phasors\u003c/h2\u003e\u003cp\u003ePhasors are used to define the amplitude and phase difference of sinusoidal function. Phasors are represented by vectors in a diagram. Phasors are generally a set of complex numbers in mathematical form.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eComplex numbers\u003c/h3\u003e\u003cp\u003eThe complex numbers conjugate that contains both real and imaginary parts are termed as complex numbers. Complex numbers can be represented in two forms, one is a rectangular form which is defined as (a + bi) where the real axis part is represented by “a” and the imaginary part is represented by “I”. The second form is phasor form which is written as r\u0026lt;Φ where r represents the amplitude of sinusoidal function and Φ represents the phase of a sinusoidal function.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eBasics of a complex numbers\u003c/h3\u003e\u003cp\u003eConsider a complex number written in rectangular form.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eZ\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmi\u003ey\u003c/mi\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, x represents the real part, y\u0026nbsp;represents the imaginary part.\u003c/p\u003e\u003cp\u003eZ can also be represented in polar form as shown below.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eZ\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003er\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, \u003cem\u003er\u003c/em\u003e\u0026nbsp;represents amplitude which can be calculated as:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003er\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsqrt\u003e\u003cmsup\u003e\u003cmi\u003ex\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmsup\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/msqrt\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eThe \u003cem\u003eϕ\u003c/em\u003e\u0026nbsp;represents the phase domain of sinusoidal that can be calculated as shown below:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsup\u003e\u003cmi\u003etan\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmfrac\u003e\u003cmi\u003ey\u003c/mi\u003e\u003cmi\u003ex\u003c/mi\u003e\u003c/mfrac\u003e\u003c/math\u003e\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003ePhasor representation\u003c/h3\u003e\u003cp\u003eEuler’s identity is given by:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e±\u003c/mo\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003cmo\u003e±\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, cos ϕ and sin ϕ are the real and imaginary parts of \u003cem\u003ee\u003c/em\u003e.\u003c/p\u003e\u003cp\u003eSinusoidal voltage can be represented in rectangular as well as phasor form. The phasor form representation is shown below:\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003cmspace linebreak=\"newline\"\u003e\u003c/mspace\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eR\u003c/mi\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003cmspace linebreak=\"newline\"\u003e\u003c/mspace\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eR\u003c/mi\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eHere, \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmsub\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmi\u003em\u003c/mi\u003e\u003c/msub\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eϕ\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eTherefore, the sinusoidal voltage will result in \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmfenced\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mfenced\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003eV\u003c/mi\u003e\u003cmsup\u003e\u003cmi\u003ee\u003c/mi\u003e\u003cmrow\u003e\u003cmi\u003ej\u003c/mi\u003e\u003cmi\u003eω\u003c/mi\u003e\u003cmi\u003et\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003c/math\u003e.\u003c/p\u003e\u003cp\u003eHence, in this way the phasor representation can be found out for any signal including current and voltage.\u003c/p\u003e\u003ch3 class=\"wp-block-heading\"\u003eExplain Phasor Diagram?\u003c/h3\u003e\u003cp\u003eA pictorial representation of phasor representation including magnitude and phase domain is termed a phasor diagram. The phasor diagram contains voltage vector, current vector, and phase angle. With the help of the nature of phase angle, the behavior of the circuit can be determined that is whether it is lagging or leading.\u003c/p\u003e\u003cdiv class=\"wp-block-image\"\u003e\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003cimg src=\"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08111548/image-81.png\" alt=\"When current lags the voltage it can be said the circuit have lagging nature as shown in figure whereas if current leads the voltage, it can be said that nature of circuit is leading.\" class=\"wp-image-57315\" width=\"373\" height=\"264\"\u003e\u003cfigcaption\u003eLagging Nature\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\u003cdiv class=\"wp-block-image\"\u003e\u003cfigure class=\"aligncenter size-full is-resized\"\u003e\u003cimg src=\"https://cms-media.bartleby.com/wp-content/uploads/sites/2/2021/12/08111744/image-82.png\" alt=\"The leading power factor in an ac electric circuit is attained by way of the use of capacitive load inside the circuit. As inside the presence of a in basic terms capacitive load or mixture of resistive-capacitive load, the cutting-edge leads furnished voltage. This offers upward push to the strength element usually stated to be main in nature.\" class=\"wp-image-57320\" width=\"385\" height=\"266\"\u003e\u003cfigcaption\u003eLeading Nature\u003c/figcaption\u003e\u003c/figure\u003e\u003c/div\u003e\u003ch3 class=\"wp-block-heading\"\u003eBenefits of phasor diagram\u003c/h3\u003e\u003cp\u003eWith the help of a phasor diagram, it is easier to represent waveform and carry out calculations involving ac waves. It can be used to determine the nature of the circuit whether it is lagging or leading. It can be used to determine the root mean square value.\u003c/p\u003e\u003cp\u003eWhen the circuit consists of only a resistor, the current and voltage will be in the same phase difference. When the circuit contains the inductor, the current will lag the voltage and the circuit will have lagging nature whereas when the circuit contains a capacitor, the current will lead the voltage, therefore, the circuit will have a leading nature.\u003c/p\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"application-of-sinusoids-and-phasors\"\u003eApplication of sinusoids and phasors\u003c/h2\u003e\u003cp\u003eThe application of sinusoids and phasors to AC circuits are:\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eThe motivation behind the use of sinusoids in the evaluation of AC circuits is that almost all the natural phenomena have sinusoidal characteristics.\u003c/li\u003e\u003cli\u003eSignals in the sinusoidal shape are simple to generate and transmit.\u003c/li\u003e\u003cli\u003eThe usage of Fourier evaluation, any realistic periodic signal may be represented as a sum of sinusoids.\u003c/li\u003e\u003cli\u003eMathematically, a sinusoid is easy for mathematical calculations.\u003c/li\u003e\u003c/ul\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"common-mistakes\"\u003e\u0026nbsp;Common Mistakes\u003c/h2\u003e\u003cp\u003eStudents may get confused between instantaneous value and the phasor representation. Following are the points to avoid those confusions.\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003ev(t) represents the instantaneous value of sinusoidal voltage whereas V represents the phasor representation of sinusoidal voltage.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eThe value of instantaneous voltage is time-dependent whereas a value of V is time-independent.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eInstantaneous voltage is always real whereas phasor representation is the complex plane.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eIt may also be possible to get confused between the time domain and phasor representation. Note the following points to avoid mistakes.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eThe time-domain function will be represented using small alphabets whereas phasor representation will be given by capital alphabet.\u003c/li\u003e\u003c/ul\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eTime-domain represents sinusoidal voltage as a function of time whereas phasor is independent of time.\u003c/li\u003e\u003c/ul\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"context-and-applications\"\u003eContext and Applications\u003c/h2\u003e\u003cp\u003eSome applications of sinusoids and phasors are listed below.\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eSolving real-life practical problems.\u003c/li\u003e\u003cli\u003eSignal analysis.\u003c/li\u003e\u003cli\u003eNetwork theory.\u003c/li\u003e\u003cli\u003eControl theory\u003c/li\u003e\u003cli\u003eFluid dynamics.\u003c/li\u003e\u003cli\u003eDetermining the response of the system.\u003c/li\u003e\u003cli\u003eAnalysis of bulk power system reliability.\u003c/li\u003e\u003cli\u003eSolving RLC circuits.\u003c/li\u003e\u003cli\u003eTrigonometry\u003c/li\u003e\u003cli\u003eLinear algebra.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThis subject matter is tremendous inside the expert exam for each undergraduate and graduate publication, mainly for:\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eBachelor of Technology in the electrical and electronic department\u003c/li\u003e\u003cli\u003eBachelor of Science Physics\u003c/li\u003e\u003cli\u003eMaster of Science Physics\u003c/li\u003e\u003c/ul\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"related-concepts\"\u003eRelated Concepts\u003c/h2\u003e\u003cp\u003eSinusoids and phasor involve the following concepts.\u003c/p\u003e\u003cul class=\"wp-block-list\"\u003e\u003cli\u003eEuler’s identity\u003c/li\u003e\u003cli\u003eTrigonometry identities\u003c/li\u003e\u003c/ul\u003e","\u003ch2 class=\"wp-block-heading\" class=\"wp-block-heading\" id=\"practice-problems\"\u003ePractice Problems\u003c/h2\u003e\u003cp\u003e\u003cstrong\u003eQuestion 1\u003c/strong\u003e- Transform \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e sinusoids into phasors.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e80\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (c)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e To find the phasor of the sinusoidal time domain using the magnitude and phase angle.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmtable columnspacing=\"0px\" columnalign=\"right center left\"\u003e\u003cmtr\u003e\u003cmtd\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmn\u003e40\u003c/mn\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e180\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 2\u003c/strong\u003e- Transform \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003ev\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e50\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e into phasor.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e30\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003eNone of the above\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (b)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e Use identity \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmi\u003eA\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmo\u003e\u0026#160;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmi\u003eA\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003eTo find phasor use magnitude and phase angle.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmtable columnspacing=\"0px\" columnalign=\"right center left\"\u003e\u003cmtr\u003e\u003cmtd\u003e\u003cmi\u003ev\u003c/mi\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmi\u003esin\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e50\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmi\u003ecos\u003c/mi\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmn\u003e30\u003c/mn\u003e\u003cmi\u003et\u003c/mi\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e50\u003c/mn\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e140\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 3\u003c/strong\u003e- Transform phasor \u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmi\u003eI\u003c/mi\u003e\u003cmo\u003e=\u003c/mo\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmi\u003ei\u003c/mi\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/math\u003e into sinusoids.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e7\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e25\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e06\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e25\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e90\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003cli\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e54\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/math\u003e\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e Find magnitude and phase using the formula discussed earlier.\u003c/p\u003e\u003cp\u003e\u003cmath xmlns=\"http://www.w3.org/1998/Math/MathML\"\u003e\u003cmtable columnspacing=\"0px\" columnalign=\"right center left\"\u003e\u003cmtr\u003e\u003cmtd\u003e\u003cmi\u003ei\u003c/mi\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmsqrt\u003e\u003cmsup\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003cmo\u003e+\u003c/mo\u003e\u003cmsup\u003e\u003cmfenced\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/mfenced\u003e\u003cmn\u003e2\u003c/mn\u003e\u003c/msup\u003e\u003c/msqrt\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmfenced\u003e\u003cmrow\u003e\u003cmsup\u003e\u003cmi\u003etan\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmfenced\u003e\u003cmfrac\u003e\u003cmrow\u003e\u003cmo\u003e-\u003c/mo\u003e\u003cmn\u003e7\u003c/mn\u003e\u003c/mrow\u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/mfrac\u003e\u003c/mfenced\u003e\u003c/mrow\u003e\u003c/mfenced\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmo\u003e=\u003c/mo\u003e\u003c/mtd\u003e\u003cmtd\u003e\u003cmn\u003e8\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e06\u003c/mn\u003e\u003cmo\u003e\u0026#8736;\u003c/mo\u003e\u003cmn\u003e60\u003c/mn\u003e\u003cmo\u003e.\u003c/mo\u003e\u003cmn\u003e25\u003c/mn\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 4-\u003c/strong\u003e When current leads voltage the nature of the circuit is _____.\u003c/p\u003e\u003col style=\"list-style-type: lower-alpha;\"\u003e\u003cli\u003eLeading\u003c/li\u003e\u003cli\u003eLagging\u003c/li\u003e\u003cli\u003eUnity\u003c/li\u003e\u003cli\u003eAll of the above\u003c/li\u003e\u003c/ol\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (a)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation:\u003c/strong\u003e When current leads voltage, the circuit is leading in nature.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eQuestion 5-\u003c/strong\u003e When voltage leads to the current the nature of the circuit is _____.\u003c/p\u003e\u003cp\u003eA. Lagging\u003c/p\u003e\u003cp\u003eB. Leading\u003c/p\u003e\u003cp\u003eC. Unity\u003c/p\u003e\u003cp\u003eD. None of these\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eCorrect answer:\u003c/strong\u003e (a)\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eExplanation: \u003c/strong\u003eWhen current lags voltage, the circuit is lagging in nature.\u003c/p\u003e"]}},"allCSSLinks":{"content":["https://cms-assets.bartleby.com/wp-includes/css/dist/block-library/style.min.css","https://cms-assets.bartleby.com/wp-includes/css/dist/block-library/theme.min.css","https://cms-assets.bartleby.com/wp-includes/css/dist/block-library/editor.min.css","https://cms-assets.bartleby.com/wp-content/plugins/getwid/assets/css/blocks.style.css"]},"conceptTitleSlug":"sinusoids-and-phasors","credentials":{},"userId":"","gated":false,"userAccess":{"learn":{"id":"learn","name":"bartleby 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