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Determine the capacitor voltage v(t) for t > 0 t = 0 6Ω 12V Μ 200 mF Η + v(t) – 3 Ω 2Ω

Determine the capacitor voltage v(t) for t > 0 t = 0 6Ω 12V Μ 200 mF Η + v(t) – 3 Ω 2Ω

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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DETERMINE V(t) ( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).

### Electrical Engineering: Capacitor Voltage Analysis **Problem Statement:** Determine the capacitor voltage \( v(t) \) for \( t > 0 \). **Circuit Description:** The provided circuit diagram consists of the following components: 1. **Voltage Source:** - A \( 12 \text{V} \) DC voltage source. 2. **Resistors:** - A \( 6 \Omega \) resistor connected in series with the voltage source. - A \( 3 \Omega \) resistor and a \( 2 \Omega \) resistor connected in parallel. 3. **Capacitor:** - A capacitor with a capacitance of \( 200 \text{ mF} \) is placed in the circuit with the parallel resistors. **Switch:** - There is a switch in the circuit that closes at \( t = 0 \). This action dictates the analysis of the circuit for \( t > 0 \). **Circuit Analysis:** To determine the capacitor voltage \( v(t) \) for \( t > 0 \), follow these steps: 1. **Initial Conditions:** - Determine the initial voltage across the capacitor just before \( t = 0 \). 2. **Applying Kirchhoff's Laws:** - Apply Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL) to set up differential equations governing the circuit. 3. **Solve the Differential Equation:** - Solve the differential equation using appropriate methods (e.g., Laplace Transform) to find \( v(t) \). 4. **Determine Time Constants:** - Calculate the time constant \( \tau \) of the circuit, which involves the equivalent resistance seen by the capacitor and the capacitance \( C \). The time constant \( \tau \) is given by \( \tau = R_{eq} \times C \). This circuit requires a detailed transient analysis to determine how the capacitor voltage \( v(t) \) evolves over time after the switch is closed at \( t = 0 \). **Note:** The detailed steps for solving the differential equation and finding the exact expression for \( v(t) \) are typically covered in advanced circuit analysis courses.
Transcribed Image Text:### Electrical Engineering: Capacitor Voltage Analysis **Problem Statement:** Determine the capacitor voltage \( v(t) \) for \( t > 0 \). **Circuit Description:** The provided circuit diagram consists of the following components: 1. **Voltage Source:** - A \( 12 \text{V} \) DC voltage source. 2. **Resistors:** - A \( 6 \Omega \) resistor connected in series with the voltage source. - A \( 3 \Omega \) resistor and a \( 2 \Omega \) resistor connected in parallel. 3. **Capacitor:** - A capacitor with a capacitance of \( 200 \text{ mF} \) is placed in the circuit with the parallel resistors. **Switch:** - There is a switch in the circuit that closes at \( t = 0 \). This action dictates the analysis of the circuit for \( t > 0 \). **Circuit Analysis:** To determine the capacitor voltage \( v(t) \) for \( t > 0 \), follow these steps: 1. **Initial Conditions:** - Determine the initial voltage across the capacitor just before \( t = 0 \). 2. **Applying Kirchhoff's Laws:** - Apply Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL) to set up differential equations governing the circuit. 3. **Solve the Differential Equation:** - Solve the differential equation using appropriate methods (e.g., Laplace Transform) to find \( v(t) \). 4. **Determine Time Constants:** - Calculate the time constant \( \tau \) of the circuit, which involves the equivalent resistance seen by the capacitor and the capacitance \( C \). The time constant \( \tau \) is given by \( \tau = R_{eq} \times C \). This circuit requires a detailed transient analysis to determine how the capacitor voltage \( v(t) \) evolves over time after the switch is closed at \( t = 0 \). **Note:** The detailed steps for solving the differential equation and finding the exact expression for \( v(t) \) are typically covered in advanced circuit analysis courses.
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