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Ksivusya [100]
2 years ago
3

A copper wire has a resistance of 0.500 Ω at 20.0ºC , and an iron wire has a resistance of 0.525 Ω at the same temperature. At w

hat temperature are their resistances equal?
Physics
1 answer:
Aleonysh [2.5K]2 years ago
7 0

Answer:

-17.04 ^0 C

Explanation:

The resistance of an object varies with temperature and is given by the formula:

R=R_0(1+\alpha (T - T_0)

Where R = resistance at temperature T

R_0 = resistance at reference temperature T_0

\alpha = Temperature coefficient of resistance

T = temperature in degree Celsius

T_0 = reference temperature.

For the copper wire:

R = 0.500(1 + 0.004041(20.0 - T_0)

For the iron wire:

R = 0.525(1 + 0.005671(20.0 - T_0)

When the resistance are equal for the two elements:

0.500(1 + 0.004041(20.0 - T_0) = 0.525(1 + 0.005671(20.0 - T_0)

0.500(1 + 0.08082 - 0.004041T_0) = 0.525(1 + 0.11342 - 0.005671T_0)

0.000956775‬‬T_0 = -0.0163‬

T_0 = -17.04

The temperature of equal resistance is -17.04 ^0 C

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