An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 m H inductor and 5 Ω resistor. The ratio of the currents at time t = ∞ and at t = 40 s is close to: (Take e 2 = 7.389 )

Step-by-step solution

i = i 0 1 - e - t L / R = 20 5 1 - e - t 0.01 / 5 = 4 1 - e - 500 t now at t = ∞ i ∞ = 4 at t = 40  s i 40 = 4 1 - e - 500 × 40 = 4 1 - 1 e 2 10000 = 4 1 - 1 7.29 10000 i ∞ i 40 ≈ 1 Slightly greater then one.