In steady state, a resistor is carrying a current $i$. The power lost to the surroundings is $b(T- T_0)$. Here $b$ is a constant, $T$ is the temperature of the resistance and $T_0$ is the surrounding temperature. If the coefficient of linear expansion is $\alpha$. The strain in the wire is

Question

$\begin {array} {1 1} (A)\;\alpha i^2 \large\frac{R}{\lambda} & \quad (B)\;\alpha i R \lambda \\ (C)\;\alpha^2i\large\frac{R}{\lambda} & \quad (D)\;\alpha i^2 \large\frac{R}{2\lambda} \end {array}$