Question

The temperature coefficient of resistance of conductor varies as $\alpha \left(T\right)=3T^2+2T$. If $R_0$ is resistance at $T=0$ and $R$ is resistance at $T$, then

• A. $R=R_0(6T+2)$
• B. $R=2R_0(3+2T)$
• C. $R=R_0(1+T^2+T^3)$
• D. $R=R_0(1-T+T^2+T^3)$

Answer 1

Answer: (C)

$R=R_0(1+T^2+T^3)$

We know that the temperature coefficient of resistor is $\alpha =\frac{1}{R_0}\frac{dR}{dT}$
$dR=R_0\alpha dT=R_0(3T^2+2T)dT$
Integrating, ${\int }_{R_0}^{R}dR=R_0{\int }_0^T(3T^2+2T)dT$
$R-R_0=R_0(T^3+T^2)$
$\therefore R=R_0(1+T^2+T^3)$