572
12 Electric Circuits
Fig. 12.46
Applying junction theorem
i = i 1 + i 2 + i 3 + i 4
(4)
i 2 + i 3 = i 5 + i 6
(5)
V AB = V AD + V DB
∴
3i 4 = 8i 3 + 4i 5
(6)
Applying the loop theorem to CAFBC
ξ − ir − 3i 4 = 0
2
3
i + 3i 4 = 1.8
( 7 )
Solving (1), (2), (3), (4), (5), (6) and (7), i 4 = 0.4 A and i = 0.9 A. Applying
the loop theorem to the entire circuit
ξ − ir − i R = 0
( 8 )
where R is the equivalent resistance of the circuit
R =
ξ
i
=
1.8
0.9
−
2
3
=
4
3
Power dissipated in the entire circuit is
P = i
2
(R + r ) = (0.9)
2
4
3
+
2
3
= 1.62 W
12.47 Let A and B be the midpoints of the coils. As no current flows through the
galvanometer, P.D across AB is zero. Applying the loop theorem to the main
circuit, Fig. 12.47
12 Electric Circuits
Fig. 12.46
Applying junction theorem
i = i 1 + i 2 + i 3 + i 4
(4)
i 2 + i 3 = i 5 + i 6
(5)
V AB = V AD + V DB
∴
3i 4 = 8i 3 + 4i 5
(6)
Applying the loop theorem to CAFBC
ξ − ir − 3i 4 = 0
2
3
i + 3i 4 = 1.8
( 7 )
Solving (1), (2), (3), (4), (5), (6) and (7), i 4 = 0.4 A and i = 0.9 A. Applying
the loop theorem to the entire circuit
ξ − ir − i R = 0
( 8 )
where R is the equivalent resistance of the circuit
R =
ξ
i
=
1.8
0.9
−
2
3
=
4
3
Power dissipated in the entire circuit is
P = i
2
(R + r ) = (0.9)
2
4
3
+
2
3
= 1.62 W
12.47 Let A and B be the midpoints of the coils. As no current flows through the
galvanometer, P.D across AB is zero. Applying the loop theorem to the main
circuit, Fig. 12.47