12.3 Solutions
573
Fig. 12.47
ξ 1 + ξ 2 − i(R + R + r 1 + r 2 ) = 0
∴
i =
ξ 1 + ξ 2
2R + r 1 + r 2
=
1.5 + 3
2 × 10 + 5 + r 2
=
4.5
r 2 + 25
(1)
The P.D of the point B with respect to the negative terminal of the first cell is
V B = ξ 1 −
10
2
+ r 1
i = 1.5 − 10 i
(2)
The P.D of the point A with respect to the negative terminal of the first cell is
V A = ξ 1 + ξ 2 −
10
2
+ r 2 + 10 + r 1
i
= 1.5 + 3 − (5 + r 2 + 10 + 5)i = 4.5 − (20 + r 2 )
But V B = V A (∵ no current flows through the galvanometer)
∴
1.5 − 10i = 4.5 − (20 + r 2 )i
∴
i =
3
10 + r 2
(3)
From (1) and (2), r 2 = 20
12.48 (a) (i) R eq =
R 1 R 2
R 1 + R 2
+
R 3 R 4
R 3 + R 4
=
8 × 2
8 + 2
+
3.2 × 3.2
3.2 + 3.2
= 3.2 k
(ii) V p 1 = 320 ×
1.6
3.2
= 160 V
(iii) V p 2 = 320 ×
1.6
3.2
= 160 V
573
Fig. 12.47
ξ 1 + ξ 2 − i(R + R + r 1 + r 2 ) = 0
∴
i =
ξ 1 + ξ 2
2R + r 1 + r 2
=
1.5 + 3
2 × 10 + 5 + r 2
=
4.5
r 2 + 25
(1)
The P.D of the point B with respect to the negative terminal of the first cell is
V B = ξ 1 −
10
2
+ r 1
i = 1.5 − 10 i
(2)
The P.D of the point A with respect to the negative terminal of the first cell is
V A = ξ 1 + ξ 2 −
10
2
+ r 2 + 10 + r 1
i
= 1.5 + 3 − (5 + r 2 + 10 + 5)i = 4.5 − (20 + r 2 )
But V B = V A (∵ no current flows through the galvanometer)
∴
1.5 − 10i = 4.5 − (20 + r 2 )i
∴
i =
3
10 + r 2
(3)
From (1) and (2), r 2 = 20
12.48 (a) (i) R eq =
R 1 R 2
R 1 + R 2
+
R 3 R 4
R 3 + R 4
=
8 × 2
8 + 2
+
3.2 × 3.2
3.2 + 3.2
= 3.2 k
(ii) V p 1 = 320 ×
1.6
3.2
= 160 V
(iii) V p 2 = 320 ×
1.6
3.2
= 160 V