Question

In the circuit shown, initially the switch is in position 1 for a long . Then the switch is shifted to position 2 for a long time. Find the total heat produced in $R_2$.

Answer 1

When switch $S$ is at position $1$ for a long time then inductor store energy.

$U=\frac{1}{2}L{i}^2$

$i=\frac{E}{R_1}$

$U=\frac{1}{2}L\left(\frac{E^2}{R_1^2}\right)$

When switch $S$ is shifted to position $2$ then the stored energy in inductor is dissipate in resistor $R_2$

Total heat produced in $R_2=U=\frac{1}{2}\frac{L{E}^2}{R_1^2}$