576
12 Electric Circuits
(ii) i 1 = i 2 + i 3
(junction theorem)
(1)
Traversing the top loop counterclockwise
− ξ 1 − i 2 R 2 + ξ 3 + ξ 2 − i 1 R 1 = 0 (loop theorem)
∴
−11 − 200 i 2 + 33 + 22 − 100 i 1 = 0
or
100 i 1 + 200i 2 − 44 = 0
( 2 )
Traversing the bottom loop counterclockwise
− ξ 4 − i 3 R 3 + ξ 5 − ξ 3 + i 2 R 2 = 0
∴
−44 − 300 i 3 + 55 − 33 + 200 i 2 = 0
or
200 i 2 − 300 i 3 − 22 = 0
( 3 )
Equations (1), (2) and (3) are the required equations in the three
unknown currents i 1 , i 2 and i 3 .
Fig. 12.49
12.53 (i) The equivalent resistance of the circuit is
R eq = R 1 + R 2 +
R 3 R 4
R 3 + R 4
= 5 + 10 +
20 × 60
20 + 60
= 30 k
V 1 = V ×
R 1
R eq
= 300 ×
5
30
= 50 V
V 2 = V ×
R 2
R eq
= 300 ×
10
30
= 100 V