**Problem 8: Phasor Representation at 200 Hz**Consider the phasor representation shown below for a circuit at 200 Hz for the following two subproblems.**Circuit Diagram:**- The circuit consists of a source voltage \( V_s = 6 \angle 0^\circ \, V \).- There are two resistors, each with a resistance of \( 2 \, \Omega \).- A capacitor with an impedance of \( -j4 \, \Omega \) is connected in parallel with the second resistor.- An inductor with an impedance of \( j2 \, \Omega \) follows in line with the second resistor.- The output voltage across the inductor and the second resistor is labeled as \( V_0 \).**Tasks:**(a) **Find the phasor voltage \( V_0 \) in the circuit shown, and the corresponding voltage waveform \( v_0(t) \) that \( V_0 \) represents.**(b) **Suppose that the source \( V_s \) in the circuit is replaced with a new voltage source \( v_S(t) = 6 \cos(800\pi t) \). Find the new phasor \( V_0 \) and waveform \( v_0(t) \).****Explanation:**To solve this problem, analyze the circuit using phasor techniques, applying Kirchhoff's voltage law (KVL) and impedance analysis to find the output voltage \( V_0 \). Once \( V_0 \) is identified, the phasors are converted back into time-domain expressions using cosines or sines, suitable for AC analysis. For part (b), recalculate with the modified frequency of the source.

Answered: Image /qna-images/answer/7fc41d66-2d77-4c5a-b08e-eb420942f484.jpg

(a) Find the phasor voltage Vo in the circuit shown, and the corresponding voltage waveform o(t) that Vo represents. (b) Suppose that the source Vs in the circuit is replaced with a new voltage source vs(t) = 6 cos(800xt), find the new phasor Vo and waveform to(t).

(a) Find the phasor voltage Vo in the circuit shown, and the corresponding voltage waveform o(t) that Vo represents. (b) Suppose that the source Vs in the circuit is replaced with a new voltage source vs(t) = 6 cos(800xt), find the new phasor Vo and waveform to(t).

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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Question

**Problem 8: Phasor Representation at 200 Hz**

Consider the phasor representation shown below for a circuit at 200 Hz for the following two subproblems.

**Circuit Diagram:**

- The circuit consists of a source voltage \( V_s = 6 \angle 0^\circ \, V \).
- There are two resistors, each with a resistance of \( 2 \, \Omega \).
- A capacitor with an impedance of \( -j4 \, \Omega \) is connected in parallel with the second resistor.
- An inductor with an impedance of \( j2 \, \Omega \) follows in line with the second resistor.
- The output voltage across the inductor and the second resistor is labeled as \( V_0 \).

**Tasks:**

(a) **Find the phasor voltage \( V_0 \) in the circuit shown, and the corresponding voltage waveform \( v_0(t) \) that \( V_0 \) represents.**

(b) **Suppose that the source \( V_s \) in the circuit is replaced with a new voltage source \( v_S(t) = 6 \cos(800\pi t) \). Find the new phasor \( V_0 \) and waveform \( v_0(t) \).**

**Explanation:**

To solve this problem, analyze the circuit using phasor techniques, applying Kirchhoff's voltage law (KVL) and impedance analysis to find the output voltage \( V_0 \). Once \( V_0 \) is identified, the phasors are converted back into time-domain expressions using cosines or sines, suitable for AC analysis. For part (b), recalculate with the modified frequency of the source.

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