Question

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

• A. ${0.008}^o{C}^{-1}$
• 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 ${0.0064}^o{C}^{-1}$

$R_2=R_1[1+\alpha (T_2-T_1\left)\right]$

Given,

$R_2=4.5\Omega$

$R_1=3.1\Omega$

$T_1={30}^{\circ }C$

$T_2={100}^{\circ }C$

$T_2-T_1=(100-30{)}^{\circ }C$

$={70}^{\circ }$

$\Rightarrow 4.5=3.1[1+\alpha (70\left)\right]$

$\Rightarrow 70\alpha =\frac{4.5}{3.1}-1$

$\alpha =\frac{4.5-3.1}{3.1\times 70}$

$\alpha =6.45\times {10}^{-3}$

$\alpha ={0.0064}^{\circ }{C}^{-1}$