Question

An inductor of inductance $\left(L\right)$ and a resistor of resistance $\left(R\right)$ are initially connected with the battery in series to steady state and then the battery is removed. The total heat produced in the resistor $R$, when the current in the circuit decreases from maximum value $i_0$ to $0$ is -

• A. $L{i}_0^2$
• B. $\frac{1}{2}L{i}_0^2$
• C. $\frac{3}{2}L{i}_0^2$
• D. $\frac{1}{3}L{i}_0^2$

Answer 1

The correct option is B $\frac{1}{2}L{i}_0^2$

When the $RL$ circuit is connected to battery and at the steady state, maximum magnetic energy stored is $U=\frac{1}{2}L{i}_0^2$.

After the battery is removed and the current reduces from its maximum value to zero, all the stored energy in the inductor will be dissipated by the resistor.

So, the total heat produced will be $H=U=\frac{1}{2}L{i}_0^2$.

Hence, option $\left(B\right)$ is the correct answer.