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This is solution to problems related Electrical Circuit Analysis course. It was given by Prof. Gurnam Kanth at Punjab Engineering College. Its main points are: Laplace, Transform, S-domain, Circuit, Superposition, Transform, Voltage, Source, Function, Signal
Typology: Exercises
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Chapter 16, Problem 1.
Determine i ( t ) in the circuit of Fig. 16.35 by means of the Laplace transform.
Figure 16.
For Prob. 16.1.
Chapter 16, Solution 1.
Consider the s-domain form of the circuit which is shown below.
(^2 ) (s 12 ) ( 32 )
s s 1
1 s 1 s
1 s I( s)
= t 2
e sin 3
i( t)
i( t) = 1. 155 e sin( 0. 866 t)A
-0.5t
1/s
1/s
s
I(s)
Chapter 16, Problem 2.
Find v (^) x in the circuit shown in Fig. 16.36 given v (^) s .= 4 u ( t )V.
Figure 16.
For Prob. 16.2.
we use superposition to help solve this problem?)
Figure 16.
For Prob. 16.3.
Chapter 16, Solution 3.
In the s-domain, the circuit becomes that shown below.
s
2 0.2s
We transform the current source to a voltage source and obtain the circuit shown below.
2 1 I 8 4 s
0.2s
s^ s^ A^ B I s s s s s
x A B
s s
t i t e u t
Chapter 16, Problem 5.
If i (^) s ( t ) = e
− 2 t u ( t ) A in the circuit shown in Fig. 16.39, find the value of i (^) 0 ( t ).
Figure 16.
For Prob. 16.5.
Chapter 16, Solution 5.
or
i (t) e 0. 3779 e e e 0. 3779 e e e u(t)A
s 0. 5 j 1. 3229
( 1. 5 j 1. 3229 )( j 2. 646 )
( 0. 5 j 1. 3229 )
s 0. 5 j 1. 3229
( 1. 5 j 1. 3229 )( j 2. 646 )
( 0. 5 j 1. 3229 )
s 2
(s 2 )(s 0. 5 j 1. 3229 )(s 0. 5 j 1. 3229 )
s
2
Vs I
(s 2 )(s 0. 5 j 1. 3229 )(s 0. 5 j 1. 3229 )
2 s
s s 2
2 s
s 2
s
s
s 2
2 t
2 t 90 t/ 2 j 1. 3229 t 90 t/ 2 j 1. 3229 t o
2 2
2
o
2
−
− − ° − − ° −
or i (^) o(t) = t u(t)A 2
sin 7
e
2 t ⎟
−
s s
s 2
I (^) o
Chapter 16, Problem 6.
Find v ( t ), t > 0 in the circuit of Fig. 16.40. Let v (^) s = 20 V.
Figure 16.
For Prob. 16.6.
Chapter 16, Solution 6.
For t<0, v(0) = v (^) s = 20 V
For t>0, the circuit in the s-domain is as shown below.
s
100 mF 0.1 F sC s
s I s s
s
t v t e u t
v 10 Ω 20
s
