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Find the voltage across the capacitor, vc(t). Note that the two sources have non-identical frequencies. [hint: treat the two sources independently and use superposition to get your final answer. For w #wo, a voltage source looks like a short and a current source looks like an open]. 6 cos(3t)V 60 www 1/12 F +1₁ Ve 2 H 12 sin(2t)A

Find the voltage across the capacitor, vc(t). Note that the two sources have non-identical frequencies. [hint: treat the two sources independently and use superposition to get your final answer. For w #wo, a voltage source looks like a short and a current source looks like an open]. 6 cos(3t)V 60 www 1/12 F +1₁ Ve 2 H 12 sin(2t)A

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Problem Statement**: Find the voltage across the capacitor, \( v_c(t) \). Note that the two sources have non-identical frequencies. **Hint**: Treat the two sources independently and use superposition to get your final answer. For \(\omega \neq \omega_0\), a voltage source looks like a short and a current source looks like an open. **Circuit Diagram**: The circuit consists of the following components and sources connected in a loop: 1. **Voltage Source**: \( 6 \cos(3t) \, V \). 2. **Resistor**: \( 6 \, \Omega \). 3. **Capacitor**: \( \frac{1}{12} \, F \). 4. **Inductor**: \( 2 \, H \). 5. **Current Source**: \( 12 \sin(2t) \, A \). **Connections**: - The voltage source, resistor, and capacitor are connected in series. - The inductor and current source are also connected, with the positive terminal of the current source connected to the common node of the capacitor-inductor junction. - The circuit is grounded, with a reference node between the capacitor and the current source. **Overall Approach**: - Utilize the principle of superposition, considering the effects of each source independently. - For each source acting alone, replace the other with its internal impedance characteristics: - Voltage source (\(\omega \neq \omega_0\)) as a short circuit. - Current source (\(\omega \neq \omega_0\)) as an open circuit. - Calculate the resulting voltage across the capacitor due to each source and sum them for \( v_c(t) \).
Transcribed Image Text:**Problem Statement**: Find the voltage across the capacitor, \( v_c(t) \). Note that the two sources have non-identical frequencies. **Hint**: Treat the two sources independently and use superposition to get your final answer. For \(\omega \neq \omega_0\), a voltage source looks like a short and a current source looks like an open. **Circuit Diagram**: The circuit consists of the following components and sources connected in a loop: 1. **Voltage Source**: \( 6 \cos(3t) \, V \). 2. **Resistor**: \( 6 \, \Omega \). 3. **Capacitor**: \( \frac{1}{12} \, F \). 4. **Inductor**: \( 2 \, H \). 5. **Current Source**: \( 12 \sin(2t) \, A \). **Connections**: - The voltage source, resistor, and capacitor are connected in series. - The inductor and current source are also connected, with the positive terminal of the current source connected to the common node of the capacitor-inductor junction. - The circuit is grounded, with a reference node between the capacitor and the current source. **Overall Approach**: - Utilize the principle of superposition, considering the effects of each source independently. - For each source acting alone, replace the other with its internal impedance characteristics: - Voltage source (\(\omega \neq \omega_0\)) as a short circuit. - Current source (\(\omega \neq \omega_0\)) as an open circuit. - Calculate the resulting voltage across the capacitor due to each source and sum them for \( v_c(t) \).
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