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Find voltage v,(t) in the circuit shown. 0.005 F 10 n 0.1 H 100 cos 401 V v,(1) 40 cos (401 – 30°) V 0.2 H

Find voltage v,(t) in the circuit shown. 0.005 F 10 n 0.1 H 100 cos 401 V v,(1) 40 cos (401 – 30°) V 0.2 H

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
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### Circuit Voltage Problem **Objective:** Find the voltage \( v_x(t) \) in the circuit shown. **Circuit Description:** - The circuit consists of two voltage sources and several passive components (resistors, inductors, and a capacitor). - **Voltage Sources:** - The first source is \( 100 \cos 40t \) V. - The second source is \( 40 \cos (40t - 30^\circ) \) V. - **Resistors:** - One 10 Ω resistor in series with the first inductor. - One 5 Ω resistor in series with the second inductor. - **Inductors:** - A 0.1 H inductor in series with the 10 Ω resistor. - A 0.2 H inductor in series with the 5 Ω resistor. - **Capacitor:** - A 0.005 F capacitor connected between the nodes to measure \( v_x(t) \). **Diagram Explanation:** The circuit is arranged in a loop: - Starting from the top left, the first voltage source (\( 100 \cos 40t \) V) is connected to a 10 Ω resistor. - This resistor is in series with a 0.1 H inductor. - After the inductor, there is a connection point where \( v_x(t) \) is measured across the next segment of the circuit. - A 0.005 F capacitor is connected in parallel with the measurement location of \( v_x(t) \). - The circuit continues to the second voltage source (\( 40 \cos (40t - 30^\circ) \) V). On the lower path: - A 5 Ω resistor connects from the second voltage source. - A 0.2 H inductor follows this resistor. - The inductor then loops back to the initial voltage source (\( 100 \cos 40t \) V). **Goal:** Determine the expression for the voltage \( v_x(t) \) at the indicated point in the circuit.
Transcribed Image Text:### Circuit Voltage Problem **Objective:** Find the voltage \( v_x(t) \) in the circuit shown. **Circuit Description:** - The circuit consists of two voltage sources and several passive components (resistors, inductors, and a capacitor). - **Voltage Sources:** - The first source is \( 100 \cos 40t \) V. - The second source is \( 40 \cos (40t - 30^\circ) \) V. - **Resistors:** - One 10 Ω resistor in series with the first inductor. - One 5 Ω resistor in series with the second inductor. - **Inductors:** - A 0.1 H inductor in series with the 10 Ω resistor. - A 0.2 H inductor in series with the 5 Ω resistor. - **Capacitor:** - A 0.005 F capacitor connected between the nodes to measure \( v_x(t) \). **Diagram Explanation:** The circuit is arranged in a loop: - Starting from the top left, the first voltage source (\( 100 \cos 40t \) V) is connected to a 10 Ω resistor. - This resistor is in series with a 0.1 H inductor. - After the inductor, there is a connection point where \( v_x(t) \) is measured across the next segment of the circuit. - A 0.005 F capacitor is connected in parallel with the measurement location of \( v_x(t) \). - The circuit continues to the second voltage source (\( 40 \cos (40t - 30^\circ) \) V). On the lower path: - A 5 Ω resistor connects from the second voltage source. - A 0.2 H inductor follows this resistor. - The inductor then loops back to the initial voltage source (\( 100 \cos 40t \) V). **Goal:** Determine the expression for the voltage \( v_x(t) \) at the indicated point in the circuit.
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