Basic Circuit Theory
Chpter10 Problems
1 The physical construction of three pairs of coupled coils is shown in Fig. 10-16 . Show two
different possible locations for the two dots on each pair of coils.
2 For the circuit illustrated in Fig. 10-17 (a) find and ; (b) repeat if a 6? resistor is
connected between the terminals at the right.
?
A
I
?
B
V
1
42
3
1
4
2
3
1
4
2
3
(a) (b) (c)
Fig. 10-16 For prob.1.
-
+
-
+
?10
100
H4
s/rad5=ω
V°0/
H3
H5
AI
?
BV
?
-
+
x
i
1
i
2
i
v
1=k
H5
7.0=k
H20 H8H18
Fig. 10-17 For prob.2. Fig. 10-18 For prob.3.
3 Let i
1
= 5 sin 40t A and i = 2 sin 40t A in Fig. 10-18. Find i (t) and v(t). Is the direction of
average power flow to the right or to the left in the center of the circuit?
2 x
4 If the circuit shown in Fig. 10-19 is series resonant at
r
ω = 1k rad/s find C and Q.
+
-
C
?10
H4
sV
?
H1
?10
5.0=k
?20 ?2
mH25
in
Z
L
Z
k
mH100
Fig. 10-20 For prob.5. Fig. 10-19 For prob.4.
5 In Fig. 10-20, let Z be a 4
L
μ F capacitor having an – j25? and calculate Z
in
when k = (a) 0;
(b) 0.5; (c) 1.
6 Find the average power delivered to each resistor in the circuit shown in Fig. 10-21.
- -
- +
+ +
1
?
V 2
?
V
V°0/
x
120
a:1
?12 ?36
y
1:5
+
-
?2
?5
?3
30 V°0/
2:1
Fig. 10-21 For prob.6.
Fig. 10-22 For prob.7.
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Basic Circuit Theory
Chpter10 Problems
7 (a) In the circuit of Fig. 10-22 find the turns ratio α and the average power delivered to each
resistor. (b) If there is no voltage between points x and y, determine and .
?
1
V
?
2
V
8 It is desired to connect a resistor between points a and b in Fig. 10-23. (a) What is the maximum
power that can be delivered to this resistor and what should the value of resistance be? (b)
Repeat for the where the dot is at the lower terminal of the secondary winding.
+
-
?50 H3
ω
2
100
V°0/
s/rad100=
?k2
H5H2
+
-
a
?90 ?10
?3V°0/50
?1
b
1:10
Fig. 10-24 For prob.9and 10.
Fig. 10-23 For prob.8.
9 In the circuit shown in Fig. 10-24, find the average power absorbed by (a) the source; (b) each of
the two resistors; (c) each of the two inductances; (d) the mutual inductance.
10 (a) Find the Thevenin equivalent network faced by the 2 k?resistor in the circuit of Fig. 10-24.
(b) What is the maximum average power that can be drawn from the network by an optimum
value of Z (instead of 2 k )?
L
?
Reference Answers to Selected Problems
1: (a) 1—3 or 2—4; (b) 2—3 or 1—4, (c) 2—3 or 1—4.
2: (a) 3.714 A, 37.14 V;(b)4.296 A, 15.96 V.
2
o
8.21∠
o
9.58?∠
o
1.17?∠
3: 2.11 sin 40t A, -286 cos 40t.
4: 1.333Fμ F, 46.2.
5: 20+j1000 , 20+j722.2 , 20-j111? ? ?.
6: P =119.7W, P
2
=19.9W, P =49.9W,
3 5
7: (a) α =1, p
12
108W, P =324W; (b) V
1
=V =108 V.
36 2
o
180∠
8: (a) 64.2 , 5.62W; (b) 85.8 , 56.4W. ? ?
9: (a) –10.4W; (b) P =5.63, P =4.77W; (c) 0 each; (d) 0.
50 2000
10: (a) =145.5 V, Z =105.9+j76.5
?
V
OC
o
6.166?∠
th
?; (b) 25W.
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