Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively L_A=10 H and L_B=10 mH . The total resistance of each circuit is 40 . The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is

Step-by-step solution

To determine the ratio of energy consumed in circuits A and B while building up the current to a steady value, the energy stored in the inductor at steady state is compared. The energy stored is given by U = 1 2 L I^2 , where L is the self-inductance and I is the steady-state current. The steady-state current is identical for both circuits due to the same emf of 10 V and total resistance of 40 , resulting in I₀ = 10 40 = 0.25 A. Circuit A has L_A = 10 H, so the energy is U_A = 1 2 10 (0.25)^2 = 0.3125 J. Circuit B