Page 57 - Schaum's Outline of Theory and Problems of Electric Circuits

ANALYSIS METHODS
46

Fig. 4-13 [CHAP. 4

0
V ab ¼ V ¼ 20 30 ð3Þ¼ 10 V
9

30
0
or V ab ¼ V ¼ 6 10 ¼ 10 V
9
0
The resistance R can be obtained by shorting out the voltage sources [Fig. 4.13(c)] and finding the equivalent
resistance of this network at terminals ab:
ð3Þð6Þ
0
R ¼ 3 þ ¼ 5
9
When a short circuit is applied to the terminals, current I s:c: results from the two sources. Assuming that it
runs through the short from a to b, we have, by superposition,
2 3 2 3

0
4
4
5
I s:c: ¼ I ¼ 6 6 20 7 3 6 10 7
5 ¼ 2A
6 þ 3 ð3Þð6Þ 3 þ 3 ð3Þð3Þ
3 þ 6 þ
9 6
0
0
Figure 4-14 shows the two equivalent circuits. In the present case, V , R , and I 0 were obtained
independently. Since they are related by Ohm’s law, any two may be used to obtain the third.

Fig. 4-14

The usefulness of The ´ venin and Norton equivalent circuits is clear when an active network is to be
examined under a number of load conditions, each represented by a resistor. This is suggested in