Consider a circuit that contains two switches as shown in Figure Q4. The switch on the right-hand side can be connected to nodes S₁ or S₂. The two switches operate as follows: If this right-hand switch is connected to node S₁, the switch labelled S3 is in the open position. >If the right-hand switch is connected to node S2, the switch labelled S3 is in the closed position. Both switches switch instantaneously and simultaneously. R = 20 ΚΩ C = 0.25 nF Ve S3 L= 1 mH R, = 20 ΚΩ Figure Q4 Vs=5 V a) After being connected to node S₂ for a very long time, the right-hand switch is connected to node S₁ at t= 0. Derive a differential equation for the current through the inductor iz(t) and find an expression for i(t) for all times > 0. Use numerical values for all known circuit elements ONLY in the final expression of iz(t) b) Following the events outlined in part a), the right-hand switch is connected to node S₂ at t=5 µs. Derive a differential equation for the current through the inductor iz(t) and find an expression for i(t) for all times 125 μs c) Following the events outlined in part a) and b), find the voltage across the capacitor vc() at t= 10 μs

Consider a circuit that contains two switches as shown in Figure Q4. The switch on the right-hand side can be connected to nodes S₁ or S₂. The two switches operate as follows: If this right-hand switch is connected to node S₁, the switch labelled S3 is in the open position. >If the right-hand switch is connected to node S2, the switch labelled S3 is in the closed position. Both switches switch instantaneously and simultaneously. R = 20 ΚΩ C = 0.25 nF Ve S3 L= 1 mH R, = 20 ΚΩ Figure Q4 Vs=5 V a) After being connected to node S₂ for a very long time, the right-hand switch is connected to node S₁ at t= 0. Derive a differential equation for the current through the inductor iz(t) and find an expression for i(t) for all times > 0. Use numerical values for all known circuit elements ONLY in the final expression of iz(t) b) Following the events outlined in part a), the right-hand switch is connected to node S₂ at t=5 µs. Derive a differential equation for the current through the inductor iz(t) and find an expression for i(t) for all times 125 μs c) Following the events outlined in part a) and b), find the voltage across the capacitor vc() at t= 10 μs

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

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Consider a circuit that contains two switches as shown in Figure Q4. The switch
on the right-hand side can be connected to nodes S₁ or S₂. The two switches
operate as follows:
➤ If this right-hand switch is connected to node S₁, the switch labelled S3 is
in the open position.
If the right-hand switch is connected to node S₂, the switch labelled S3 is
in the closed position.
Both switches switch instantaneously and simultaneously.
R = 20 ΚΩ
C = 0.25 nF
HE
+21
S3
L=1 mH
R, = 20 ΚΩ
S₁
1S₂
AS = SA
iL
Figure Q4
a) After being connected to node S₂ for a very long time, the right-hand switch
is connected to node S₁ at t = 0. Derive a differential equation for the
current through the inductor iz(t) and find an expression for iz(t) for all
times > 0. Use numerical values for all known circuit elements ONLY in
the final expression of iz(t)
b) Following the events outlined in part a), the right-hand switch is connected
to node S₂ at t = 5 µs. Derive a differential equation for the current through
the inductor iz(t) and find an expression for i(t) for all times 125 µs
c) Following the events outlined in part a) and b), find the voltage across the
capacitor vc(t) at t = 10 µs

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