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672 ⏐⏐⏐ SERIES AND PARALLEL ac CIRCUITS
100
75
50
25
0
I L (mA)
as appearing in Figs. 15.83 and 15.84.
f � 1 kHz Applying Eq. (15.37):
XL � 2pfL � 2p(1 kHz)(4 mH) � 25.12 �
and �R� 2 ��� X� 2 L� � �(2�2�0� ��) 2 � �� (�2�5�.1�2� ��) 2 � � 221.43 �
RI (220 �)(100 mA)
and IL ��� ��� �99.35 mA
2 2 �R� ��� X� L� 221.43 �
with
v L � tan �1
X L < R (I L ≅ I s )
FIG. 15.83
The magnitude of the current I L versus frequency for the parallel R-L network
of Fig. 15.79.
X L
� R
Network inductive
��tan �1
I L ( f )
25.12 �
� 220 �
and I L � 99.35 mA ��6.51°
a c
X L > R (I L => 0 mA)
Network resistive
1 5 10 20 30 40 f (kHz)
��tan �1 0.114 � �6.51°
The result is a current IL that is still very close to the source current I
in both magnitude and phase.
Continuing:
f � 5 kHz: IL � 86.84 mA ��29.72°
f � 10 kHz: IL � 65.88 mA ��48.79°
f � 15 kHz: IL � 50.43 mA ��59.72°
f � 20 kHz:
f � 30 kHz:
IL � 40.11 mA ��66.35°
IL � 28.02 mA ��73.73°
f � 40 kHz: IL � 21.38 mA ��77.65°
The plot of the magnitude of I L versus frequency is provided in Fig.
15.83 and reveals that the current through the coil dropped from its
maximum of 100 mA to almost 20 mA at 40 kHz. As the reactance of
the coil increased with frequency, more of the source current chose the