Question

A copper wire has a resistance of 0.500Ω at 20.0ºC, and an iron wire has a resistance of 0.525Ω at the same temperature. At what temperature are their resistances equal?

a. 100.0ºC
b. 150.0ºC
c. 200.0ºC
d. 250.0ºC

Answer 1

The resistances of the copper wire and iron wire are equal at approximately 200.0ºC. The correct answer is c. 200.0ºC.

Step-by-step explanation:

To determine the temperature at which the resistances of a copper wire and an iron wire are equal, we can use the formula for electrical resistance:

R = R0 * (1 + α(T - T0))

R is the resistance at temperature T, R0 is the resistance at reference temperature T0, and α is the temperature coefficient of resistivity for the material.

Since the resistances are equal at the unknown temperature, we can set up an equation:

0.500Ω * (1 + α(T - 20.0ºC)) = 0.525Ω * (1 + α(T - 20.0ºC))

Simplifying the equation, we find:

0.500Ω = 0.525Ω

This allows us to solve for the temperature T, which is approximately 200.0ºC.