Question

A coil of inductance $L=2.0\mu H$ and resistance $R=1.0\Omega$ is connected to a source of constant emf $ϵ=3.0V$.
Resistance $R_0=2.0\Omega$ is connected in parallel with the coil.The amount of heat generated in the coil after the switch $S_w$ is disconected is (in microjoule)? (The internal resistance of the source is negligible.)

Answer 1

In steady state, the current in the inductor is $i=\frac{\epsilon }{R}=\frac{3}{1}=3A$.
So, the energy stored in the inductor is $\frac{1}{2}L{i}^2=\frac{1}{2}2\mu 3^2=9\mu J$
After the switch is closed, this energy gets dissipated in $R$ and $R_0$ in the ratio of $\frac{R}{R_0}=\frac{1}{2}$.
So out of $9J$, $3J$ is lost in $R$ and $6J$ is lost in $R_0$.