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and (R 1 � R 2)I 1 � R 2I
R 1I 1 � R 2I 1 � R 2I
R 1I 1 � R 2I � R 2I 1
Substituting values:
R 1 �
R1 �� R2(I � I
�
1)
I
6 42 �
� 7 ���� 21�
���2 �
21
An alternative approach is
I2 � I � I1 (Kirchhoff’s current law)
� 27 mA � 21 mA � 6 mA
V2 � I2R2 � (6 mA)(7 �) � 42 mV
V1 � I1R1 � V2 � 42 mV
42 mV
and R1 �����2 �
I1 21 mA
V 1
From the examples just described, note the following:
Current seeks the path of least resistance.
That is,
1. More current passes through the smaller of two parallel resistors.
2. The current entering any number of parallel resistors divides into
these resistors as the inverse ratio of their ohmic values. This relationship
is depicted in Fig. 6.39.
I 1
I
4 � 4 �
I
I 1 = I
2
I 1
7 �(27 mA � 21 mA)
���
21 mA
2I 1
1
I
I 1
1 � 2 �
I
I 1 = I
3
6.7 VOLTAGE SOURCES IN PARALLEL
3I 1
I
2 � 6 �
I
I 1 = I
4
FIG. 6.39
Current division through parallel branches.
Voltage sources are placed in parallel as shown in Fig. 6.40 only if they
have the same voltage rating. The primary reason for placing two or
more batteries in parallel of the same terminal voltage would be to
VOLTAGE SOURCES IN PARALLEL ⏐⏐⏐ 187
I 1
6I 1
I
2I 1
1 � 3 �
I
I 1 = I
9
I 1
6 �