1. For the following circuit, switch is closed at t=0. a. Write a differential equation in i(t). b. Find a and @o. c. Find the characteristic equation and the roots of the characteristic equation. d. Find the final value of current i(t) through the inductor. e. Find current i(t) through the inductor for t> 0 and sketch i(t). f. Find voltage v(t) for t > 0 and sketch v(t). PS Solution Switch S Vs 20V R1 ΣΚΩ www R2 2k2 v(t) V=4V I 50 nF i(t) 40mH lo=5mA
1. For the following circuit, switch is closed at t=0. a. Write a differential equation in i(t). b. Find a and @o. c. Find the characteristic equation and the roots of the characteristic equation. d. Find the final value of current i(t) through the inductor. e. Find current i(t) through the inductor for t> 0 and sketch i(t). f. Find voltage v(t) for t > 0 and sketch v(t). PS Solution Switch S Vs 20V R1 ΣΚΩ www R2 2k2 v(t) V=4V I 50 nF i(t) 40mH lo=5mA
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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need help with d e and f
Transcribed Image Text:1. For the following circuit, switch is closed at t=0.
a. Write a differential equation in i(t).
b. Find a and wo.
c. Find the characteristic equation and the roots of the characteristic equation.
d. Find the final value of current i(t) through the inductor.
e. Find current i(t) through the inductor for t> 0 and sketch i(t).
f. Find voltage v(t) for t≥ 0 and sketch v(t).
PS
Solution
Switch S
Vs
20V
R1
ΣΚΩ
www
R2
2k2
v(t)
V=4V I
50 nF
i(t)
40mH
lo=5mA
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Step 1: State the given data
VIEWStep 2: d) Finding the final value of the current through the inductor
VIEWStep 3: e) Finding the differential equation related to the circuit
VIEWStep 4: Finding the solution of the differential equation
VIEWStep 5: Finding the current through the inductor i(t) and it's sketch
VIEWStep 6: Finding the voltage across the capacitor and it's sketch
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