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Problem 7.4
Determine the phase angles by which v1  t  leads i1  t  and v1  t  leads i2 t  , where
v1  t   4sin 377t  25 V
i1 t   0.05cos 377t 10 A
i2 t   0.1sin 377t  75 A
Suggested Solution
v1  t   4sin  377t  25  V
 4 cos  377t  65  V
i1 t   0.05cos 377t 10 A
i2  t   0.1sin  377t  75  A
 0.1sin  377t  105  A
 0.1cos  377t  15  A
Then,
v1  t  leads i1  t  by  65   10  55
v1  t  leads i2  t  by  65  15  80
Problem 7.5
Calculate the current in the resistor if the voltage input is:
i(t)
(a) v1(t)=10 cos(377t+180°)
(b) v2(t)=12 sin(377t+45°)
+
v(t)
_
Give the answers in both the time and frequency domains.
2
Suggested Solution
v1 (t )
 5cos(377t  180) A  5180 A
R
v (t )
(b) i(t )  2  6sin(377t  45) A  6cos(377t  45) A  6 45 A
R
(a) i(t ) 
Problem 7.6
Calculate the current in the capacitor if the voltage input is:
i(t)
(c) v1(t)=16 cos(377t – 22°)
(d) v2(t)=8 sin(377t + 64°)
+
v(t)
_
Give the answers in both the time and frequency domains.
Suggested Solution
1
1
1


j C j (377)(1326 106 ) .5 j
(a)
v(t ) 16 22
i(t ) 

 8 68 A  8cos(377t  68) A
Zc
2 90
Zc 
(b) i(t ) 
v(t ) 8 64

 4 64 A  4cos(377t  64) A
Zc
2 90
C=1326F
Problem 7.7
Calculate the current in the inductor if the voltage input is:
(e) v1(t)=24 cos(377t + 12°)
(f) v2(t)=18 sin(377t – 48°)
i(t)
+
L=10.61 mH
v(t)
_
Give the answers in both the time and frequency domains.
Suggested Solution
Z L  j L  j (377)(10.61 103 )  4 j
(a)
i(t ) 
(b) i(t ) 
v(t ) 24 12

 6 78 A
ZL
4 90
v(t ) 18 42

 4.5 48 A
ZL
4 90
Problem 7.8
Find the frequency domain impedance, Z, for the network shown.
1
j2
-j1F
z
Suggested Solution
Z=1+j2-j1=1+j1
Problem 7.10
Find the frequency domain impedance, Z, for the network shown.
z
2
j2
-j4
Suggested Solution
1 1 1
1 1
 

 
Z 2 j2 j4 2
4
4(2  j )
Z

2  j (2  j )(2 
Z  1.6  j 0.8
1 1 1
j     2  j
2 4 4
84 j

 1.6  j 0.8
j)
4 1
Problem 7.13
Find Z(j) at a frequency of 60 Hz for the network shown.
2
z
4
10mH
500F
Suggested Solution
Z L  j L  j (377)(10  103 )  j 3.77
1
106

  j 5.3
j C j 377(5)
j 3.77(4  j 5.3)
j15.08  20
Z  2
 2
 5.1  j 4.96
j 3.77  4  j 5.3
4  j1.535
Zc 
Problem 7.21
Draw the frequency domain circuit and calculate v(t) for the circuit shown if
Is(t)=20 cos(377t+120°) A.
+
is(t)
V(t)
1
100 mH
10 mF
_
Suggested Solution
Z  j L  j 37.7
Zc 
1
1


j C j 3.77


1
V I
1
1
1
 

 R Z L Z C


2 120
2 120
2 120



 0.52 44.91V
j
1

j
3.74
3.84
75.03

 1
 j 3.77

37.7
v(t )  0.52 cos(377t  44.97)V