12.3 Solutions
577
(ii) V p = V ×
R 3 R 4
R eq (R 3 + R 4 )
= 300 ×
20 × 60
30(20 + 60)
= 150 V
(iii) I T =
V
R eq
=
300
30 × 10 3 = 0.0 1 A
I 2 = I T
R 4
R 4 + R 3
= 0.01 ×
60
60 + 20
= 0.0075 A
I 4 = I T
R 3
R 4 + R 3
= 0.01 ×
20
60 + 20
= 0.0025 A
12.54 i 1 − i 2 − i 3 = 0
(junction theorem)
(1)
Traversing clockwise the top loop (Fig. 12.50)
Fig. 12.50
ξ 1 + i 1 R 1 − ξ 2 − ξ 4 + i 2 R 2 + ξ 3 = 0 (loop theorem)
∴
5 + 10i 1 − 10 − 20 + 20i 2 + 15 = 0
or
i 1 + 2i 2 − 1 = 0
( 2 )
Traversing clockwise the bottom loop
− ξ 3 − i 2 R 2 + ξ 4 − ξ 6 + i 3 R 4 + ξ 5 + i 3 R 3 = 0
(loop theorem)
∴
−15 − 20i 2 + 20 − 30 + 40i 3 + 25 + 30i 3 = 0
or
7i 3 − 2i 2 = 0
( 3 )
The required equations are (1), (2) and (3) in three unknown currents.