Question

A wire has a resistance of $3\Omega$ at ${40}^{\circ }$C and resistance of $5\Omega$ at ${100}^{\circ }$C. The temperature coefficient of resistance of the wire is

• A. ${0.0012}^{\circ }{C}^{-1}$
• B. ${0.0222}^{\circ }{C}^{-1}$
• C. ${0.0024}^{\circ }{C}^{-1}$
• D. ${0.0111}^{\circ }{C}^{-1}$

Answer 1

The correct option is D ${0.0111}^{\circ }{C}^{-1}$

According to formula for temperature dependence resistance $R_t=R_0(1+\alpha \Delta t)$
Here, $R_t$ is the resistance at given temperature = $5\Omega$
$R_0$ is the resistance at reference temperature = $3\Omega$
$\Delta t$ is change in temperature $i.e.$=$100-40={60}^{\circ }$C
and $\alpha$ is temperature coefficient
Now above equation will become,
$5=3(1+\alpha 60)$
$\alpha ={0.0111}^{\circ }{C}^{-1}$