Question

Resistance of a resistor at temperature $t^{0}C$ is $R_t=R_0(1+\alpha t+\beta t^2)$. Here $R_0$ is the resistance at $0^{0}C$. The temperature coefficient of resistance at temperature $t^{0}C$ is

• A. $\frac{(1+\alpha t+\beta t^2)}{\alpha +2\beta t}$
• B. $\alpha +2\beta t$
• C. $\frac{\alpha +2\beta t}{(1+\alpha t+\beta t^2)}$
• D. $\frac{\alpha +2\beta t}{2(1+\alpha t+\beta t^2)}$

Answer 1

The correct option is C $\frac{\alpha +2\beta t}{(1+\alpha t+\beta t^2)}$

Resistance of a resistor at temperature $t^{0}C$ is

$R_t=R_0(1+\alpha t+\beta t^2)$.

The temperature coefficient of resistance is given by:

Temperature coefficient of resistance$=\frac{1}{R_t}\frac{dR}{dt}$.

Temperature coefficient of resistance $=\frac{R_0}{R_0(1+\alpha t+\beta t^2)}\frac{d}{dt}(1+\alpha t+\beta t^2)$
Temperature coefficient of resistance$=\frac{\alpha +2\beta t}{(1+\alpha t+\beta t^2)}$.