574
12 Electric Circuits
(iv) I T =
ξ
R eq
=
320
3.2 × 10 3 = 0.1 A
I 1 = I T ×
R 2
R 1 + R 2
= 0.1 ×
2
8 + 2
= 0.02 A
I 3 = I T ×
R 4
R 3 + R 4
= 0.1 ×
3.2
3.2 + 3.2
= 0.05 A
(v) W = I
2
T R eq = (0.1)
2
× 3.2 × 10
3
= 32 J
W 3 = I
2
3 R 3 = (0.05)
2
× 8 × 10
3
= 20 J
(b) P =
ξ 2
r
=
(24) 2
0.01
= 5.76 × 10
4 J
12.49 (i) i =
ξ
R + r
=
24
140 + 0.02
= 0.1714 A
(ii) V = ξ − ir = 24 − 0.1714 × 0.02 = 23.9966 V
(iii) P R = i
2 R = (0.1714)
2
× 140 = 4.113 W
P r = i
2 r = (0.1714)
2
× 0.02 = 5.87 × 10
−4 W
(iv) V = ξ = 24 V. Full voltage is available in the absence of load resistance.
12.50 (i) R eq =
R 1 R 2
R 1 + R 2
+ R 5 +
R 3 R 4
R 3 + R 4
=
80 × 80
80 + 80
+ 20 +
40 × 40
40 + 40
= 80 k
(ii) I T =
V
R eq
=
300
80 × 10 3 = 3.75 × 10
−3 A
I 1 = I T ×
R 2
R 2 + R 1
= 3.75 × 10
−3
×
80
80 + 80
= 1.875 × 10
−3 A
I 3 = I T ×
R 4
R 4 + R 1
= 3.75 × 10
−3
×
40
40 + 40
= 1.875 × 10
−3 A
(iii) V 1 =
V
R eq
×
R 1 R 2
(R 1 + R 2 )
=
300
80
×
80 × 80
(80 + 80)
= 150 V
V 2 =
V R 5
R eq
= 300 ×
20
80
= 75 V
V 3 =
V
R eq
×
R 3 R 4
(R 3 + R 4 )
=
300
80
×
40 × 40
(40 + 40)
= 75 V
(iv) P 5 = I
2
T R 5 = (3.75 × 10
−3
)
2
× 20 × 10
3
= 0.281 W
P = I
2
T R eq = (3.75 × 10
−3
)
2
× 80 × 10
3
= 1.125 W