(ASSESSMENT PROBLEM
Objective 2—Know how to analyze a circuit in the 5 domain and be able to transform an 5 domain solution to the
time domain
13.3 The switch in the circuit shown has been in (b) i = 203—1250‘150) mA,
position a for a long time. At t = 0,
t
iL t 6exp ; 0 t tsw
1
1 25ms ; tsw 35ms
iL t 6exp 40t ; 0 t tsw
time expressed in sec
iL t 6exp 0.04t ; 0 t tsw
time expressed in msec
t tsw
tsw
iL t 6exp exp
; tsw t
1
2
1 25ms ; 2 16.67ms ; tsw 35ms
6
5
current, iL (A)
4
3
2
1
0
0
TABLE OF LAPLACE TRANSFORMS
fit} £{f(f)} = “5) fit} flan} 3 HS)
I k
l. I . ."‘ " : —-
5 18 9 5m k {s _ {U2 + k.
l S — a
2. — l9. "' . k —— -
F S; 9 cm I [S _ mg + F
n #11 I‘ I I , a! _ y k
3
c/ASSESSMENT PROBLEMS
Objective 1—Be able to transform a circuit into the 5 domain using Laplace transforms
13.1 A 500 Q resistor. a 16 ml-l inductor, and a 25 nF 13.2 The parallel circuit in Assessment Problem 13.1
capacitor are connected in parallel. is
lASSESSMENT PROBLEM
Objective 3—Knuw how to use circuit analysis techniques to solve a circuit in the frequency domain
9.13 Use the mesh-current method to find the pha- l a jg n
501" current I in the circuit shown.
Answer: I = 29 + 1'2 = 29.07 53.950 A.
c/ASSESSMENT PROBLEMS
Objective 1—Be able to transform a circuit into the 5 domain using Laplace transforms
13.1 A 500 Q resistor. a 16 ml-l inductor, and a 25 nF 13.2 The parallel circuit in Assessment Problem 13.1
capacitor are connected in parallel. is
I/ASSESSMENT PROBLEM
Objective 2—Know how to analyze a circuit in the 5 domain and be able to transform an 5 domain solution to the
time domain
13.5 The dc current and voltage sources are Answer: (a) V] = [5(s + 3)]/[s(s + 0.5)(3 + 2)],
ilpplied sin'iultt
JASSESSMENT PROBLEM
Objective 2—Know how to analyze a cirCuit in the 5 domain and be able to transform an s-domain solution to the
time domain
13.6 The initial charge on the capacitor in the circuit (b) fab = [20(5 + 2,4)]/[s(s + 3)(s + 6)].
shown is zero
I/ASSESSMENT PROBLEM
Objective 2—Know how to analyze a circuit in the 5 domain and be able to transform an 5 domain solution to the
time domain
13.4 The energy stored in the circuit shown is zero Answer; (a) I : 40/(52 + 1.25 + 1);
at the time when the sw
_
Name
Assessment quiz
1. What is the passive sign convention? Specifically, what are the positive values of current and
voltage for a device that generates energy and a device that consumes energy? Provide sketches.
2. Identify the following:
a) joule se
u/ASSESSMENT PROBLEM
Objective 2—Know how to analyze a circuit in the 5 domain and be able to transform an s-domain solution to the
time domain
13.7 a) Verify from EL]. 13.72 that :52 reaches a peak Answer: (a) dig/d, : 0 when t = %m3 (5);
value of 481.13
Partial Fraction Expansion
by equating coefficients
.5'2+l A B C
=—+—+
3(5 +1)2 5 S +1 (S +1)2
Step 1: Multiply both sides by denominator of LHS.
32 +1 =A(s+1)2 +Bs(s+1)+CS
Step 2: Expand all terms.
s2 +1 = A(s2 +23+1)+B(s2 +s)+Cs
Step 3: Group terms in
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