Question

The resistance of resistor at temperature $t^{o}C$ can be expressed as $R_t=R_0(1+2\gamma t+\varphi t^2)$, where $R_0$ is the resistance at $0^{o}C$ and $\gamma$,$\varphi$ are constants. The temperature coefficient of the resistance at $t^{o}C$ is

• A. $\frac{2\left(\gamma +\varphi t\right)}{\left(}$
• B. $\frac{1}{\left(}$
• C. $2\left(\gamma +\varphi t\right)$
• D. $2\gamma t+\varphi t^2$

Answer 1

The correct option is A $\frac{2\left(\gamma +\varphi t\right)}{\left(}$

Resistance of a resistor at temperature $t^{o}C$ is
$R_t=R_0(1+2\gamma t+\varphi t^2)$

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

$=\frac{R_0}{R_0(1+2\gamma t+\varphi t^2)}\frac{d}{dt}(1+2\gamma t+\varphi t^2)$

$=\frac{2(\gamma +\varphi t)}{1+2\gamma t+\varphi t^2}$