Answered: 3 ka t-0s o to- 12 µF v(t)2 kn 12 mA…

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

Determine the response for v(t) after the switch is opened. Assume the switch
has been in the position shown for a long time. Use step-by-step analysis. Plot the
solution and indicate the time for full response.

t=0s
3 ka
oto
12 µF
v(t) 2 ka
2 mA
1 ka
4 µF

Expert Solution

Step 1

Calculate the equivalent capacitance.

$\begin{array}{rcl} C & = & C_{1} ∥ C_{2} \\ = & (12 μ F) ∥ (4 μ F) \\ = & \frac{(12 μ F) (4 μ F)}{(12 μ F) + (4 μ F)} \\ = & 3 μ F \end{array}$

Step 2

Draw the circuit for t < 0.

Step 3

Calculate the voltage across the capacitor.

$\begin{array}{rcl} V_{c} (0) & = & (2 m A) (2 k Ω) \\ = & 4 V \end{array}$

Step 4

Draw the circuit for t > 0 in the s-domain.

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