Fourier and Laplace
455
P.4.33 Use the LT to fi nd the current i(t) and voltage drop v(t) of the circuit diagram shown
in Figure 4.98 for the following voltage sources:
a. v s (t) = 5δ(t)
b. v s (t) = 5u(t)
c. v s (t) = 5t u(t)
P.4.34 Use the LT to fi nd the current i(t) and voltage v(t) of the circuit shown in Figure 4.99
for the following voltage sources:
a. v s (t) = 5δ(t)
b. v s (t) = 5u(t)
c. v s (t) = 5t u(t)
P.4.35 For the circuit shown in Figure 4.100, determine expressions and the corresponding
plots of i 1 (t) versus t and i 2 (t) versus t. Evaluate i 1 (∞) and i 2 (∞) by hand computations
and by using the fi nal value theorem.
P.4.36 Construct a function of s as the ratio of two polynomials such that the following
conditions are satisfi ed:
f
sFs
s
( ) lim [
( )]
0
ϩ
ϭ
ϭ
→
⋅
ϱ
5
and
f
sFs
s
( ) lim [
( )]
ϱ ϭ
ϭ
→
⋅
0
15
Obtain an expression of the ILT of F(s) and verify, using MATLAB, that f(0
+
) =
lim t→0 [f(t)] = 5 and f(∞) = lim t→∞ [f(t)] = 15.
L = 1 H
IL(0) = 1.3 A
v (t ) = exp(−2t)
sw closes at t = 0
R = 1 Ω
I (s)
FIGURE 4.97
Circuit diagram of P.4.32.
R = 1 k Ω
i (t )
L = 0.1 H
v s (t )
v (t )
+
−
−
FIGURE 4.98
Circuit diagram of P.4.33.
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