Question

In the ideal inductor circuit shown, $\text{X}$ is joined to $\text{Y}$ for a long time, and then $\text{X}$ is joined to $\text{Z}$. 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 the switch $\text{X}$ is connected to the $\text{Y}$, the current flowing in the circuit is,

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


$\therefore$ Energy stored in the inductor is,

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

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

When the switch $\text{X}$ is connected to $\text{Z}$ the current and the energy stored in the inductor will decay through resistance $R_2$.

Therefore, the total energy stored in the inductor will be converted into the heat energy produced in $R_2$.

Hence, $\left(\text{A}\right)$ is the correct answer.

Note: The total heat produced in the circuit is independent of the resistance $R_2$.