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594 ⏐⏐⏐ THE BASIC ELEMENTS AND PHASORS
Or, since I eff �
(W) (14.16)
then P � � (W) (14.17)
V 2
� � I effR
R
Inductor
In a purely inductive circuit, since v leads i by 90°, |vv � vi| � v �
|�90°| � 90°. Therefore,
VmIm VmIm P �� cos 90° � �(0) � 0 W
2
2
The average power or power dissipated by the ideal inductor (no
associated resistance) is zero watts.
Capacitor
In a purely capacitive circuit, since i leads v by 90°, |vv � vi| � v �
|�90°| � 90°. Therefore,
VmIm VmIm P �� cos(90°) � �(0) � 0 W
2
2
The average power or power dissipated by the ideal capacitor (no
associated resistance) is zero watts.
EXAMPLE 14.10 Find the average power dissipated in a network
whose input current and voltage are the following:
i � 5 sin(qt � 40°)
v � 10 sin(qt � 40°)
Solution: Since v and i are in phase, the circuit appears to be purely
resistive at the input terminals. Therefore,
VmIm (10 V)(5 A)
P ����� �25 W
2 2
10 V
or R �����2 �
Im 5A
V 2 eff
[(0.707)(10 V)]
and P � � �25 W
2
� ��
R
2
or P � I 2 eff R � [(0.707)(5 A)] 2 (2) � 25 W
I m
P � � Vm � � VeffI eff
2
V eff
� R
2 eff
V m
For the following example, the circuit consists of a combination of
resistances and reactances producing phase angles between the input
current and voltage different from 0° or 90°.
�