**Transcription of Educational Content****Title: Analyzing an RLC Circuit****Problem Statement:**Calculate \( v_o(t) \) in the circuit shown in Figure, when \( i_s(t) = 1 \cos(2500t - 45^\circ) \) A. Also, show that \( i_C(t) + i_R(t) = i_s(t) \) and draw a phasor diagram.**Circuit Description:**The given circuit is a parallel RLC circuit, consisting of the following components:1. **Current Source (\( i_s(t) \)):** - A sinusoidal current source, defined as \( i_s(t) = 1 \cos(2500t - 45^\circ) \) A, is the input to the circuit.2. **Capacitor (\( 20 \, \mu\text{F} \)):** - Connected parallel to the current source, the capacitor has a capacitance of \( 20 \, \mu\text{F} \). - The current through the capacitor is denoted as \( i_C(t) \).3. **Resistor (\( 10 \, \Omega \)):** - Connected in parallel with the capacitor, the resistor has a resistance of \( 10 \, \Omega \). - The voltage across the resistor is \( v_o(t) \), and the current through it is \( i_R(t) \).**Tasks:**1. Calculate \( v_o(t) \) across the resistor.2. Demonstrate that the sum of the currents through the capacitor and resistor \( (i_C(t) + i_R(t)) \) equals the source current \( i_s(t) \).3. Illustrate these relationships using a phasor diagram.This problem involves the application of AC circuit analysis, utilizing both time and frequency domain techniques to determine the voltage and current distributions in an RLC circuit. The phasor diagram will visualize the phase relationships between the various currents and voltages.

Note Current division method is used to find the current in each components of parallel network…

Answered: Calculate vo(t) in the circuit shown in…

Calculate vo(t) in the circuit shown in Figure, when is(t) =1 cos(2500t - 45°) A. Also, show that ic(t) + ir(t) = is(t) and draw a phasor diagram. is(t) 20 μF vic(t) ir(t) + 10 Ω Σ υ (1)

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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Question

**Transcription of Educational Content**

**Title: Analyzing an RLC Circuit**

**Problem Statement:**
Calculate \( v_o(t) \) in the circuit shown in Figure, when \( i_s(t) = 1 \cos(2500t - 45^\circ) \) A. Also, show that \( i_C(t) + i_R(t) = i_s(t) \) and draw a phasor diagram.

**Circuit Description:**

The given circuit is a parallel RLC circuit, consisting of the following components:

1. **Current Source (\( i_s(t) \)):**
- A sinusoidal current source, defined as \( i_s(t) = 1 \cos(2500t - 45^\circ) \) A, is the input to the circuit.

2. **Capacitor (\( 20 \, \mu\text{F} \)):**
- Connected parallel to the current source, the capacitor has a capacitance of \( 20 \, \mu\text{F} \).
- The current through the capacitor is denoted as \( i_C(t) \).

3. **Resistor (\( 10 \, \Omega \)):**
- Connected in parallel with the capacitor, the resistor has a resistance of \( 10 \, \Omega \).
- The voltage across the resistor is \( v_o(t) \), and the current through it is \( i_R(t) \).

**Tasks:**

1. Calculate \( v_o(t) \) across the resistor.
2. Demonstrate that the sum of the currents through the capacitor and resistor \( (i_C(t) + i_R(t)) \) equals the source current \( i_s(t) \).
3. Illustrate these relationships using a phasor diagram.

This problem involves the application of AC circuit analysis, utilizing both time and frequency domain techniques to determine the voltage and current distributions in an RLC circuit. The phasor diagram will visualize the phase relationships between the various currents and voltages.

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