12.3 Solutions
563
Fig. 12.39
12.27 Let ξ be the emf of each cell, i the current flowing in the circuit, r 1 and r 2
be the internal resistance of the first and the second cells, respectively. The
potential drop across the first cell will be
V 1 = ξ − ir 1 = 0
(by problem)
(1)
i =
2ξ
r 1 + r 2 + R
(2)
Combining (1) and (2)
ξ = ir 1 =
2ξr 1
r 1 + r 2 + R
∴
R = r 1 − r 2
12.28 Total power P = P 1 + P 2 + P 3 =
10 3 W h
2 h
= 500 W
P 1 : P 2 : P 3 = 5 : 3 : 2
∴ P 1 = 250 W,
P 2 = 150 W,
P 3 = 100 W
R 1 =
V 2
P 1
=
(200) 2
250
= 160 , R 2 =
V 2
P 2
=
(200) 2
150
= 267 ,
R 3 =
V 2
P 3
=
(200) 2
100
= 400
In series total resistance R = R 1 + R 2 + R 3 = 160 + 267 + 400 = 827 .
Required power for the series arrangement
P
=
V 2
R =
(248) 2
827
= 74.4 W
563
Fig. 12.39
12.27 Let ξ be the emf of each cell, i the current flowing in the circuit, r 1 and r 2
be the internal resistance of the first and the second cells, respectively. The
potential drop across the first cell will be
V 1 = ξ − ir 1 = 0
(by problem)
(1)
i =
2ξ
r 1 + r 2 + R
(2)
Combining (1) and (2)
ξ = ir 1 =
2ξr 1
r 1 + r 2 + R
∴
R = r 1 − r 2
12.28 Total power P = P 1 + P 2 + P 3 =
10 3 W h
2 h
= 500 W
P 1 : P 2 : P 3 = 5 : 3 : 2
∴ P 1 = 250 W,
P 2 = 150 W,
P 3 = 100 W
R 1 =
V 2
P 1
=
(200) 2
250
= 160 , R 2 =
V 2
P 2
=
(200) 2
150
= 267 ,
R 3 =
V 2
P 3
=
(200) 2
100
= 400
In series total resistance R = R 1 + R 2 + R 3 = 160 + 267 + 400 = 827 .
Required power for the series arrangement
P
=
V 2
R =
(248) 2
827
= 74.4 W