Question

The resistance of a conductor at ${15}^{\circ }C$ is $16\Omega$ and at ${100}^{\circ }C$ is $20\Omega$. What will be the temperature coefficient of resistance of the conductor?

• A. ${0.010}^{\circ }{C}^{-1}$
• B. ${0.033}^{\circ }{C}^{-1}$
• C. ${0.003}^{\circ }{C}^{-1}$
• D. ${0.042}^{\circ }{C}^{-1}$

Answer 1

The correct option is C ${0.003}^{\circ }{C}^{-1}$

As we know that
$R=R_0(1+\alpha (\theta -{\theta }_0\left)\right)$, where, $\alpha$ is the temperature coefficient of resistance of the conductor.
Therefore, we have
$16=R_0[1+\alpha (15-{\theta }_0)]$
$20=R_0[1+\alpha (100-{\theta }_0)]$
Assuming
${\theta }_0=0^{\circ }C$, as a general convention.
Thus, we have
$\frac{16}{20}=\frac{1+\alpha \times 15}{1+\alpha \times 100}\Rightarrow 4(1+100\alpha )=5(1+15\alpha )\Rightarrow 325\alpha =1$
$\Rightarrow \alpha ={0.003}^{\circ }{C}^{-1}$