Page 295 - Schaum's Outline of Theory and Problems of Applied Physics

280 ELECTRIC CURRENT [CHAP. 24

SOLVED PROBLEM 24.8
What is the resistance of a copper wire 0.5 mm in diameter and 20 m long? The resistivity of copper is
1.7 × 10 −8 ·m.
−4
2
The wire’s cross-sectional area is πr , where r = 0.25 mm = 2.5 × 10 . Hence
L (1.7 × 10 −8 ·m)(20 m)
R = ρ = = 1.73
A (π)(2.5 × 10 −4 m) 2
SOLVED PROBLEM 24.9
A platinum wire 80 cm long is to have a resistance of 0.1 . What should its diameter be? The resistivity
of platinum is 1.1 × 10 −7 ·m.
2
Since R = ρL/A = ρL/πr ,

ρL (1.1 × 10 −7 ·m)(0.8m)
r = = = 5.3 × 10 −4 m = 0.53 mm
π R (π)(0.1 )
The wire’s diameter should therefore be 2r = 1.06 mm.

SOLVED PROBLEM 24.10
An electric motor draws a current of 20 A from a 240-V power source 15 m away. What is the minimum
cross-sectional area of the wire that can be used if the voltage at the motor is not to be lower than 230 V?
The permissible voltage drop is 10 V, and the resistance that would give rise to this drop when the current is
20Ais
V 10 V
R = = = 0.5
I 20 A
The total length of wire involved is twice the distance between the source and the motor, so L = (2)(15 m) = 30 m.
Since R = ρL/A,

ρL (1.7 × 10 −8 ·m)(30 m)
2
A = = = 1.02 × 10 −6 m = 1.02 mm 2
R 0.5
SOLVED PROBLEM 24.11
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A copper wire has a resistance of 10.0 at 20 C. (a) What will its resistance be at 80 C? (b)At0 C?
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The temperature coefficient of resistance of copper is 0.004/ C.
(a) Here R = 10.0 and T = 60 C. Hence the wire’s change in resistance is
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R = αR T = (0.004/ C)(10.0 )(60 C) = 2.4
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and the resistance at 80 C will be R + R = 12.4 .
(b) Here T = 20 C, and so
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R = αR T = (0.004/ C)(10.0 )(−20 C) =−0.8
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The resistance at 0 C will be R + R = 9.2 .
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SOLVED PROBLEM 24.12
A resistance thermometer makes use of the variation of the resistance of a conductor with temperature. If
the resistance of such a thermometer with a platinum element is 5 at 20 C and 9 when it is inserted
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in a furnace, find the temperature of the furnace. The value of α for platinum is 0.0036/ C.
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