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Problem 2 See the circuit below. The initial voltage across a capacitor is vc (0+)= 9 V. Find an expression for the voltage across the capacitor vc (t) and the current ic (t). Sketch the waveforms of vc (t) and ic (t) to scale versus time. 12 V + t-0 x。 R = 7 kΩ www C=0.6 µF ic (1) + vc(t) I

Problem 2 See the circuit below. The initial voltage across a capacitor is vc (0+)= 9 V. Find an expression for the voltage across the capacitor vc (t) and the current ic (t). Sketch the waveforms of vc (t) and ic (t) to scale versus time. 12 V + t-0 x。 R = 7 kΩ www C=0.6 µF ic (1) + vc(t) I

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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**Problem 2** See the circuit below. The initial voltage across a capacitor is \( v_C(0^+)=9 \, \text{V} \). Find an expression for the voltage across the capacitor \( v_C(t) \) and the current \( i_C(t) \). Sketch the waveforms of \( v_C(t) \) and \( i_C(t) \) to scale versus time. **Circuit Description:** - The circuit includes a voltage source of 12 V. - A switch is present, initially open at \( t = 0 \). - There is a resistor \( R = 7 \, \text{k}\Omega \) in series with the capacitor. - The capacitor has a capacitance \( C = 0.6 \, \mu\text{F} \). - The current through the capacitor is denoted as \( i_C(t) \). - The voltage across the capacitor is represented by \( v_C(t) \). **Task:** 1. Determine the expressions for \( v_C(t) \) and \( i_C(t) \). 2. Sketch the waveforms of \( v_C(t) \) and \( i_C(t) \) with respect to time, showing the behavior of the circuit as time progresses. The diagram is a simple RC circuit representing the relationship and dynamics of the resistor-capacitor connection when the switch is closed.
Transcribed Image Text:**Problem 2** See the circuit below. The initial voltage across a capacitor is \( v_C(0^+)=9 \, \text{V} \). Find an expression for the voltage across the capacitor \( v_C(t) \) and the current \( i_C(t) \). Sketch the waveforms of \( v_C(t) \) and \( i_C(t) \) to scale versus time. **Circuit Description:** - The circuit includes a voltage source of 12 V. - A switch is present, initially open at \( t = 0 \). - There is a resistor \( R = 7 \, \text{k}\Omega \) in series with the capacitor. - The capacitor has a capacitance \( C = 0.6 \, \mu\text{F} \). - The current through the capacitor is denoted as \( i_C(t) \). - The voltage across the capacitor is represented by \( v_C(t) \). **Task:** 1. Determine the expressions for \( v_C(t) \) and \( i_C(t) \). 2. Sketch the waveforms of \( v_C(t) \) and \( i_C(t) \) with respect to time, showing the behavior of the circuit as time progresses. The diagram is a simple RC circuit representing the relationship and dynamics of the resistor-capacitor connection when the switch is closed.
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