A source of constant voltage V is connected to a resistance R and two ideal inductors L 1 and L 2 through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t = 0 , the switch is closed and current begins to flow. Which of the following options is/are correct?

Step-by-step solution

As L 1 and L 2 are in parallel so equivalent inductance, L = L 1 L 2 L 1 + L 2 Here, L 1 and L 2 are the inductance (shown in circuit) The current through the RL series circuit at anytime is given as I = V R 1 - e - Rt L At t = 0 , I = V R 1 - e 0 = 0 After a longtime i.e. at t = ∞ I = V R 1 - e - ∞ ⇒ I = V R Let currents through L 1 and L 2 are I 1 and I 2 respectively. As L 1 and L 2 are joined in parallel Voltage across L 1 = Voltage across L 2 ⇒ V L 1 = V L 2 ⇒ L 1 d I 1 d t = L 2 d I 2 d t ⇒ L 1 I 1 = L 2 I 2