Question

Define temperature coefficient of resistance. Deduce an expression for it.​

Answer 1

Answer:

Temperature coefficient is defined as the the change in resistance per degree change in temperature.

The change in resistance is directly proportional to the initial resistance and change and temperature,

$\\\tt (R_{2} - R_{1}) \propto R_{1} \\ \\\tt (R_{2} - R_{1}) \propto (T_{2} - T_{1})$

Now,

$\\\\\tt (R_{2} - R_{1}) \propto R_{1} (T_{2} - T_{1}) \\\\\tt R_{2} - R_{1}=\alpha R_{1} (T_{2} - T_{1}) \\ \\\tt R_{2}= R_{1} +\alpha R_{1} (T_{2} - T_{1}) \\\\\tt R_{2}= R_{1} [1+\alpha (T_{2} - T_{1}) ]$

Hence the expression gained.