Question

A copper wire has a resistance of 0.525 at 20.0°C, and an iron wire has a resistance of 0.545 at the same temperature. At what temperature are their resistances equal?

Answer 1

Resistance , R(T) = Ro(1 + alpha*T)
0.525 = Ro(1 + 0.00386*20) and 0.545 = Ro(1 + 0.00651*20)
so, Ro = 0.48737 and Ro = 0.482215
so, For same resitnace
0.48737(1 + 0.00386T) = 0.482215(1+0.00651*T)
4.03363 degree C

Answer 2

SOLUTION :

Temperature coefficient of resistance  “ alpha” of

Copper  =  0.004 per ºC

Iron       = 0.005 per ºC

Resistance increases with increase in temperature and it is given by the following formula :

R = Ro ( 1 + alpha * temperature difference)

Let their resistances be equal at temperature T ºC,

So,

Resistance of copper at TºC = Resistance of iron at TºC

=> 0.525(1 + 0.004(T - 20)) = 0.545(1 + 0.005(T - 20))

=> 0.525 + 0.0021 T - 10.50 = 0.545 + 0.002725 T - 10.90

=> (0.002725 - 0.0021) T = (0.525 - 0.545) - 10.50 + 10.90

=> 0.000625 T = 0.38

=> T = 0.38/0.000625

=> T = 608 ºC (ANSWER).