Page 61 - Schaum's Outline of Theory and Problems of Electric Circuits

ANALYSIS METHODS
50

Fig. 4-20 [CHAP. 4
2 32 3 2 3
19 7 7 I 1 60
4
4 7 13 7 5 I 2 5 ¼ 4 60 5
7 7 19 I 3 60
2 3
19 7 7
6 7
Thus, R ¼ 4 713 7 5 ¼ 2880
7 7 19

Notice that in Problem 4.2, too, R ¼ 2880, although the elements in the determinant were different. All
valid sets of meshes or loops yield the same numerical value for R . The three numerator determinants are

60 7 7

N 1 ¼ 60 13 7 ¼ 4320 N 2 ¼ 8642 N 3 ¼ 4320

60 7 19
Consequently,
4320
N 1 N 2 N 3
I 1 ¼ ¼ ¼ 1:5A I 2 ¼ ¼ 3A I 3 ¼ ¼ 1:5A
R 2880 R R
The current supplied by the 60-V source is the sum of the three loop currents, I 1 þ I 2 þ I 3 ¼ 6A.
4.7 Write the mesh current matrix equation for the network of Fig. 4-21 by inspection, and solve for
the currents.

Fig. 4-21
2 32 3 2 3
7 5 0 I 1 25
4 5 19 4 5 I 2 5 ¼ 4 25 5
4
0 4 6 I 3 50

Solving,

25 5 0 7 5 0

I 1 ¼ 25 19 4 5 19 4 ¼ð 700Þ 536 ¼ 1:31 A

50 4 6 0 4 6