Question

In the circuit shown in figure, $X$ is joined to $Y$ for a long time and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

• A. $\frac{L{E}^2}{2R_1^2}$
• B. $\frac{L{E}^2}{2R_2^2}$
• C. $\frac{L{E}^2}{2R_1{R}_2}$
• D. $\frac{L{E}^2{R}_2}{2R_1^3}$

Answer 1

The correct option is A $\frac{L{E}^2}{2R_1^2}$

When X is joined to Y, energy will be stored in the inductor.
Current through the inductor, $I_o=\frac{E}{R_1}$
When X is joined to Z, energy stored in the inductor$\left(U_L\right)$ will be dissipated by $R_2$ in the form of heat$\left(H_{R_2}\right)$ i.e
$\begin{array}{}{U}_L=H_{R_2}& \text{(1)}\end{array}$
Energy stored in the inductor, $U=\frac{1}{2}L{I}_o^2$
Since $I_o=\frac{E}{R_1}$
Therefore, $U=\frac{1}{2}L{I}_o^2=\frac{1}{2}L\times \frac{E^2}{R_1^2}$
$U_L=H_{R_2}=\frac{L{E}^2}{2R_1^2}$