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

Options

A. `(LE^(2))/(2R_(2)^(2))`
B. `(LE^(2))/(2R_(1)^(2))`
C. `(LE^(2))/(2R_(1)R_(2))`
D. `(LE^(2)(R_(1)+R_(2))^(2))/(2R_(1)^(2)R_(2)^(2))`

Answer

A

Explanation

When the key is at position (2) for a long time the energy stored in the inductor is:
`U_(B)=1/2Li_(0)^(2)=1/2L(E/R_(2))^(2)=((LE^(2))/(2R_(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.