Question

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

The correct option is C $R=R_0(1+T^2+T^3)$

$\alpha \left(T\right)=\frac{1}{R_0}\frac{dR}{dT}$

$\Rightarrow (3T^2+2T)=\frac{1}{R_0}\frac{dR}{dT}$

$\Rightarrow dR=R_0(3T^2+2T)dT$

$\Rightarrow \underset{R_0}{\overset{R}{\int }}dR=R_0\left[3\underset{0}{\overset{T}{\int }}{T}^{2}dT+2\underset{0}{\overset{T}{\int }}TdT\right]$

$\Rightarrow R=R_0[1+T^2+T^3]$

Hence, the correct answer is (C).