1. The switch in the circuit shown in the Figure has been closed for a long time before it is opened at t = 0. SW R3 R₁ ww 10 ΚΩ ww 15 ΚΩ i(t) + V₂ с R₂ 36 ΚΩ 18 V R₁ 30 ΚΩ v(t) T9μF a. Find the initial voltage Vo across the capacitor at t = 0. b. After switch is opened, find the resistance seen from the capacitor. C. Find the time constant t. d. Find voltage v(t) across the capacitor for t 20 and Sketch or plot v(t) for t > 0. Solution:

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1. The switch in the circuit shown in the Figure has been closed for a long time before it is opened at t = 0.
SW
R₁
R3
M
M
10 ΚΩ
15 ΚΩ
+
i(t)
V₂
R₂
R4
18 V
v(t)
с
9 μF
· 36 ΚΩ
30 ΚΩ
a. Find the initial voltage Vo across the capacitor at t = 0.
b. After switch is opened, find the resistance seen from the capacitor.
c.
Find the time constant T.
d.
Find voltage v(t) across the capacitor for t 20 and Sketch or plot v(t) for t > 0.
Solution:
-5.8824r
u(t) V
Answer: d.
v(t) = 8e 0.17
= 8e
Transcribed Image Text:1. The switch in the circuit shown in the Figure has been closed for a long time before it is opened at t = 0. SW R₁ R3 M M 10 ΚΩ 15 ΚΩ + i(t) V₂ R₂ R4 18 V v(t) с 9 μF · 36 ΚΩ 30 ΚΩ a. Find the initial voltage Vo across the capacitor at t = 0. b. After switch is opened, find the resistance seen from the capacitor. c. Find the time constant T. d. Find voltage v(t) across the capacitor for t 20 and Sketch or plot v(t) for t > 0. Solution: -5.8824r u(t) V Answer: d. v(t) = 8e 0.17 = 8e
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