In the circuit shown switch $\mathrm{S}$ is connected to position $2$ for a long time and then joined to the position $1$. The total heat produced in resistance ${\mathrm{R}}_1$ is :

• Correct answer
  A

  $\frac{{\text{LE}}^2}{2{\text{R}}_2^2}$
• B

  $\frac{{\text{LE}}^2}{2{\text{R}}_1^2}$
• C

  $\frac{{\text{LE}}^2}{2{\text{R}}_1{\text{R}}_2}$
• D

  $\frac{{\text{LE}}^2{\left({\text{R}}_1+{\text{R}}_2\right)}^2}{2{\text{R}}_1^2{\text{R}}_2^2}$

Solution

When the key is at position (B) for a long time; the energy stored in the inductor is :

${\text{U}}_{\text{B}}=\frac{1}{2}{\text{Li}}_0^2=\frac{1}{2}·\text{L}·{\left(\frac{\text{E}}{{\text{R}}_2}\right)}^2=\frac{{\text{LE}}^2}{2{\text{R}}_2^2}$

          

This whole energy will be dissipated in the form of heat when the inductor is connected to ${\mathrm{R}}_1$ and no source is connected.

            

Hence, the correct answer is option: 'A'.