Question

If the resistance of a conductor is $5\Omega$ at ${50}^{\circ }C$ and $7\Omega$ at ${100}^{\circ }C$, then the mean temperature coefficient of resistance is

• A. $0.01{\left({}^{\circ }C\right)}^{-1}$
• B. $0.04{\left({}^{\circ }C\right)}^{-1}$
• C. $0.06{\left({}^{\circ }C\right)}^{-1}$
• D. $0.08{\left({}^{\circ }C\right)}^{-1}$

Answer 1

The correct option is A $0.01{\left({}^{\circ }C\right)}^{-1}$

Assuming temperature varies linearly,
$R=R_0(1+\alpha \Delta \theta )$

$5=R_0(1+\alpha 50)$

$7=R_0(1+\alpha 100)$

From the equations,

$5+500\alpha =7+350\alpha$

$(500-350)\alpha =2$

$\alpha =\frac{2}{150}=0.013$

$\approx$$0.01{\left({}^{\circ }C\right)}^{-1}$