Question

In the circuit shown switch $S$ is connected to position $2$ for a long time and then joined to the position $1$ . The total heat produced in resistance $R_1$ is :

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

Answer 1

Answer: (A)

When the key is at position (B) for a long time; the energy stored in the inductor is :
${\left(\text{U}\right)}_{\text{B}}=\frac{1}{2}{\text{Li}}_0^2=\frac{1}{2}\cdot \text{L}\cdot {\left(\frac{\text{E}}{{\left(\text{R}\right)}_2}\right)}^2=\frac{{\left(\text{LE}\right)}^2}{2{\text{R}}_2^2}$

This whole energy will be dissipated in the form of heat when the inductor is connected to $R_1$ and no source is connected.