Question

Resistance of a resistor at temperature $t^{\circ} C$ is $R_{t}=R_{0}\left(1+\alpha t+\beta t^{2}\right)$ Here $R_{0}$ 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. $\frac{(\alpha+2 \beta t)}{2(1+\alpha t+\beta t)}$

Answer 1

Answer: (C)

Temperature coefficient of resistance $=\frac{1}{R_{t}} \frac{dR}{d t}$
$=\frac{1}{R_{0}\left(1+\alpha t+\beta t^{2}\right) d t} R_{0}\left(1+\alpha t+\beta t^{2}\right) $
$=\frac{\alpha+2 \beta t}{1+\alpha t+\beta t^{2}}$