Question

A wire has resistance of $3.1$ at $30C$ and resistance $4.5$ at ${100}^{o}C$. The temperature coefficient of resistance of the wire is

• A. ${0.0012}^o{C}^{-1}$
• B. ${0.0024}^o{C}^{-1}$
• C. ${0.0032}^o{C}^{-1}$
• D. ${0.0064}^o{C}^{-1}$

Answer 1

The correct option is D ${0.0064}^o{C}^{-1}$

Given : $R_T=3.1$ ohm @ $T={30}^{o}C$

Also, $R_{T^{\prime }}=4.5$ ohm @ $T^{\prime }={100}^{o}C$

Resistance of wire at any temperature $R_{T^{\prime }}=R_T[1+\alpha (T^{\prime }-T\left)\right]$

$\therefore$ $4.5=3.1[1+\alpha (100-30\left)\right]$

$⟹$ $\alpha =\frac{0.45}{70}={0.0064}^o{C}^{-1}$