Answer to Question #166557 in Electricity and Magnetism for JayJay

Question

A wire of a certain length is specified to be 200 Ω resistance at 18⁰C what error is caused  in using this wire as a standard on a day when the temperature is 32⁰C? The temperature coefficient of resistance of the specimen is 4 x 10^-3K^-1

Answer 1

The resistance of metals depends on the temperature as follows:

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

where $R_0 = 200\Omega$ is the reference resistance at the reference temperature $T_0 = 18\degree C$, and $\alpha = 4\times 10^{-3}K^{-1}$ is the temperature coefficient of resistance. Substituting $T = 32\degree C$, obtain:

$$R = 200\cdot (1 + 4\times 10^{-3}\cdot (32-18)) = 211.2\Omega$$

Answer. 211.2 Ω.