Question

In the circuit shown, the coil has inductance and resistance. When X is joined to Y, the time constant is τ during 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.

(a) The total heat produced in the coil is Pτ.

(b) The total heat produced in the coil is 1/2 Pτ. 

(c) The total heat produced in the coil is 2Pτ.

(d) The data given is not sufficient to reach a conclusion.

Answer 1

Correct Answer is: (b) The total heat produced in the coil is 1/2 Pτ. 

Let L and R be the inductance and the resistance of the coil respectively. Let ℰ = emf of the cell.

τ = L/R.

Steady-state current = i₀ = ℰ/R.

P = i₀ 2R = ℰ²/R² . R = ℰ²/R.

Energy stored in the coil

= total heat produced in the coil.