Q. Two different conductors have same resistance at $0^{{^\circ}}C.$ It is found that the resistance of the first conductor at $t_{1}℃$ is equal to the resistance of the second conductor at $t_{2}℃.$ The ratio of the temperature coefficients of resistance of the conductors,$\frac{\alpha_{1}}{\alpha_{2}}$ is
A) $\frac{t_{1}}{t_{2}}$
B) $\frac{t_{2} - t_{1}}{t_{2}}$
C) $\frac{t_{2} - t_{1}}{t_{1}}$
D) $\frac{t_{2}}{t_{1}}$
Explanation
(d) Resistance of a conductor varies linearly with temperature as
$R_{t} = R_{0}(1 + \alpha t)$
For the first conductor
$T_{t_{1}} = R_{0}\left( 1 + \alpha_{1}t_{1} \right)$
$or\ \ \ \ \alpha_{1} = \frac{Rt_{1} - R_{0}}{t}\ \ \ \ \ldots.(i)$
Similarly, for second conductor
$\alpha_{2} = \frac{Rt_{2} - R_{0}}{t_{2}}\ \ \ldots\ldots..(ii)$
From Eq. (i) and Eq. (ii), we get
$\frac{\alpha_{1}}{\alpha_{2}} = \frac{t_{2}}{t_{1}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.