Question

A silver wire has a resistance of $2.1\Omega$ at ${27.5}^{o}C$, and a resistance of $2.7\Omega$ at ${100}^{o}C$. Determine the temperature coefficient of resistivity of silver.

Answer 1

$\text{Step 1: Using Relation for variation of resistance with Temperature}$

Resistance R varies with Temperature as follows:

$R=R_0[1+\alpha (T-T_0\left)\right]$

Where, $R_0$ is initial Resistance at Temperature $T_0$

$R$ is initial Resistance at Temperature $T$

$\alpha$ is the temperature coefficient of resistance.

$\text{Step 2: Putting values}$

Given, $T_0={27.5}^{o}C,R_0=2.1\Omega ,T={100}^{o}C,R=2.7\Omega$

So, Equation $\left(1\right)\Rightarrow$ $2.7\Omega =2.1\Omega [1+\alpha (100-27.5{)}^{o}C]$

$\Rightarrow \alpha =\frac{R-R_0}{R_0(T-T_0)}=\frac{2.7-2.1}{2.1(100-27.5)}=3.9\times {10}^{-3}{}^o{C}^{-1}$