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In the parallel RLC circuit, find v(t) for t> 0. Assuming v(0)= 7 V, i(0)= 0, L = 1H, and C= 15 mF Consider R = 1.5 n +

In the parallel RLC circuit, find v(t) for t> 0. Assuming v(0)= 7 V, i(0)= 0, L = 1H, and C= 15 mF Consider R = 1.5 n +

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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Hello, I started learning about Electrical circuits but got this exercise and I'm confused on how to solve it

In the parallel RLC circuit shown, you are tasked with finding the voltage across the circuit, \( v(t) \), for \( t > 0 \). The circuit parameters are given as follows: the initial voltage across the circuit, \( v(0) \), is 7 volts, and the initial current, \( i(0) \), is 0. The inductance \( L \) is 1 henry, and the capacitance \( C \) is 15 millifarads. The resistance \( R \) is specified to be 1.5 ohms. ### Circuit Diagram Explanation: 1. **Resistor (R):** The circuit includes a resistor on the left branch, denoted by the symbol \( R \), where the current flows downward through it. 2. **Inductor (L):** The center branch consists of an inductor \( L \) with current flowing downward, labeled as \( i_0 \). 3. **Capacitor (C):** On the right branch, there is a capacitor \( C \), with the voltage across it labeled \( V_0 \). 4. **Voltage and Current Directions:** Red arrows indicate the direction of the current flow and polarity of voltage across the components. The voltage across the inductor, \( v \), is labeled in parallel with the capacitor. The objective is to determine \(( v(t) )\), taking into account the initial conditions and component values provided.
Transcribed Image Text:In the parallel RLC circuit shown, you are tasked with finding the voltage across the circuit, \( v(t) \), for \( t > 0 \). The circuit parameters are given as follows: the initial voltage across the circuit, \( v(0) \), is 7 volts, and the initial current, \( i(0) \), is 0. The inductance \( L \) is 1 henry, and the capacitance \( C \) is 15 millifarads. The resistance \( R \) is specified to be 1.5 ohms. ### Circuit Diagram Explanation: 1. **Resistor (R):** The circuit includes a resistor on the left branch, denoted by the symbol \( R \), where the current flows downward through it. 2. **Inductor (L):** The center branch consists of an inductor \( L \) with current flowing downward, labeled as \( i_0 \). 3. **Capacitor (C):** On the right branch, there is a capacitor \( C \), with the voltage across it labeled \( V_0 \). 4. **Voltage and Current Directions:** Red arrows indicate the direction of the current flow and polarity of voltage across the components. The voltage across the inductor, \( v \), is labeled in parallel with the capacitor. The objective is to determine \(( v(t) )\), taking into account the initial conditions and component values provided.
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