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568 ⏐⏐⏐ SINUSOIDAL ALTERNATING WAVEFORMS
0.01
0
25
p
6
v (V)
0
v (V)
11
18 p
(a)
f = 60 Hz
f = 25 Hz
qt
FIG. 13.87
Problem 31.
qt
SECTION 13.5 Phase Relations
27. Sketch sin(377t � 60°) with the abscissa
a. angle in degrees.
b. angle in radians.
c. time in seconds.
28. Sketch the following waveforms:
a. 50 sin(qt � 0°) b. �20 sin(qt � 2°)
c. 5 sin(qt � 60°) d. 4 cos qt
e. 2 cos(qt � 10°) f. �5 cos(qt � 20°)
29. Find the phase relationship between the waveforms of
each set:
a. v � 4 sin(qt � 50°)
i � 6 sin(qt � 40°)
b. v � 25 sin(qt � 80°)
i � 5 � 10 �3 sin(qt � 10°)
c. v � 0.2 sin(qt � 60°)
i � 0.1 sin(qt � 20°)
d. v � 200 sin(qt � 210°)
i � 25 sin(qt � 60°)
*30. Repeat Problem 29 for the following sets:
a. v � 2 cos(qt � 30°) b. v ��1 sin(qt � 20°)
i � 5 sin(qt � 60°) i � 10 sin(qt � 70°)
c. v ��4 cos(qt � 90°)
i ��2 sin(qt � 10°)
31. Write the analytical expression for the waveforms of Fig.
13.87 with the phase angle in degrees.
2
3 p
i (A)
0
–3 × 10 –3
(b)
f = 1000 Hz
32. Repeat Problem 31 for the waveforms of Fig. 13.88.
3
p
4
0
i (A)
2 × 10 –3
(a) (b)
FIG. 13.88
Problem 32.
f = 10 kHz
qt
�t