In the circuit shows in Fig, the coil has inductance and resistance. When `X` is joined to `Y`, the time constant is `tau` 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 produced 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 `2Ptau`
D. the data given is not sufficient to reach a conclusion

Answer

B

Explanation

Power, `P=(i_(0))^(2)R, i.e.,(i_(0))^(2)=(P)/(R) and I=(L)/(R)`
Total heat produced, `U=(1)/(2)Li_(0)^(2)=(1)/(2)(tauR)((P)/(R))=(1)/(2)P tau`