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496 ⏐⏐⏐ INDUCTORS
R
1.2 k�
L T
1.01 H
FIG. 12.42
Terminal equivalent of the network of
Fig. 12.41.
E
E
+
10 V
–
I
+
21 V
–
R 1
2 �
The inductor L1 is then in series with the equivalent parallel value, and
LT � L1 � L″ T � 0.56 H � 0.45 H
� 1.01 H
The reduced equivalent network appears in Fig. 12.42.
12.13 R-L AND R-L-C CIRCUITS
WITH dc INPUTS
We found in Section 12.7 that, for all practical purposes, an inductor
can be replaced by a short circuit in a dc circuit after a period of time
greater than five time constants has passed. If in the following circuits
we assume that all of the currents and voltages have reached their final
values, the current through each inductor can be found by replacing
each inductor with a short circuit. For the circuit of Fig. 12.43, for
example,
E 10 V
I1 �����5 A
R1 2 �
I 1
L = 2 H R 2 3 �
+
10 V
–
FIG. 12.43
Substituting the short-circuit equivalent for the inductor for t > 5t.
10 mH
R 1
5 �
E
R 1
2 �
For the circuit of Fig. 12.44,
E 21 V
I �����10.5 A
R2 � R3 2 �
R 2
I1 6 mH
3 �
R 3
6 �
E
+
21 V
–
R 1
5 �
FIG. 12.44
Establishing the equivalent network for t > 5t.
I
I
R 2
I 1
I 1
3 �
2 �
R 2
R 3
3 �
6 �