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RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT ⏐⏐⏐ 583
V m
25 V
b. Eq. (14.2): Im ����� 2.5 A
R 10 �
(v and i are in phase), resulting in
i � 2.5 sin(377t � 60°)
The curves are sketched in Fig. 14.14.
V m = 25 V
I m = 2.5 A
– p 2
60°
0
i R
p 2
v R
FIG. 14.14
Example 14.1(b).
3
p 2 p
In phase
EXAMPLE 14.2 The current through a 5-� resistor is given. Find the
sinusoidal expression for the voltage across the resistor for i �
40 sin(377t � 30°).
Solution: Eq. (14.3): Vm � ImR � (40 A)(5 �) � 200 V
(v and i are in phase), resulting in
v � 200 sin(377t � 30°)
EXAMPLE 14.3 The current through a 0.1-H coil is provided. Find
the sinusoidal expression for the voltage across the coil. Sketch the v
and i curves.
a. i � 10 sin 377t
b. i � 7 sin(377t � 70°)
Solutions:
a. Eq. (14.4): XL � qL � (377 rad/s)(0.1 H) � 37.7 �
Eq. (14.5): Vm � ImXL � (10 A)(37.7 �) � 377 V
and we know that for a coil v leads i by 90°. Therefore,
v � 377 sin(377t � 90°)
The curves are sketched in Fig. 14.15.
vL v leads i by 90°.
– p 2
V m = 377 V
2p
90°
Im = 10 A
iL 0 p
2
p 3
2
2p
p
FIG. 14.15
Example 14.3(a).
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