Question

A copper wire has a resistance of 0.515 Ohms at 20 degrees C, and an iron wire has a resistance of 0.545 ohms at the same temperature.

At what temperature, in degrees celsius, are their resistances equal? The temperature coefficient of resistivity of copper is 3.9x10^-3 while that for iron is 5.0x10^-3.

Can somebody answer this question for me? thank you

Answer 1

There is an equation that gives relation of resistance with temperature.

R = Ro(1+@T)

Where Ro is temperature at 0 C. So, we first need to find this for both metals.

Cu
0.515 = Ro(1+3.9x10^-3x20)
Ro = 0.478 ohm

Fe
0.545 = Ro(1+5x10^-3x20)
Ro = 0.495 ohm

Now that we know the values of Ro for each, we just need to equate their resistance and find the corresponding T

Rcu = Rfe

Ro(1+@T) = Ro(1+@T)

0.478(1+3.9x10^-3xT) = 0.495 (1+5x10^-3 x T)

solving for T we get

T = -27.83 C

upvote if it helps