In the circuit shows Fig the coil has inductance and resistance. When `X` is joined to `Y`, the time constant is `t` during the growth of current. When the steady state is reached, heat is produced in the coil at a rate `P`. `X` is now joined to `Z`. After joining `X` and `Z`:

Options

A. the total heat produed in the coil is `p tau`
B. The total heat produced in the coil is `(1)/(2) P tau`
C. The total heat produced in the coil is `2 P tau`
D. The data given are not sufficient to reach a conlusion

Answer

B

Explanation

In steady state: `P = I^(2)R`
Energy in inductor `= (1)/(2) LI^(2)`
After connecting `x` and `z`, the whole energy of inductor will go
into heat so heat produced : `H = (1)/(2) lI^(2) = (1)/(2) L (P)/(R ) = (1)/(2) P tau`