Q. Resistance of a resistor at temperature $t{^\circ}\ C$ is $R_{t} = R_{0}\left( 1 + \alpha t + \beta t^{2} \right)$. Here $R_{o}$is the resistance at $0{^\circ}C$. The temperature coefficient of resistance at temperature $t{^\circ}C$ is
A) $\frac{\left( 1 + \alpha t + \beta t^{2} \right)}{\alpha + 2\beta t}$
B) $(\alpha + 2\beta t)$
C) $\frac{\alpha + 2\beta t}{\left( 1 + \alpha t + \beta t^{2} \right)}$
D) $\frac{(\alpha + 2\beta t)}{2\left( 1 + \alpha t + \beta t^{2} \right)}$
Explanation
(c) Temperature coefficient of resistance$= \frac{1}{R_{t}}\frac{dR}{dt}$
$= \frac{1}{R_{o}\left( 1 + \alpha t + \beta t^{2} \right)}\frac{d}{dt}R_{o}(1 + \alpha t + \beta t^{2})$
$= \frac{\alpha + 2\beta t}{1 + \alpha t + \beta t^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.