Question

A source of constant voltage V is connected to a resistance R and two ideal inductors L₁ and L₂ 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?

(A) After a long time, the current through L₁ will be \(\frac{V}{R}\frac{L_2}{L_1 +L_ 2}\)

(B) After a long time, the current through L₂ will be \(\frac{V}{R}\frac{L_ 1}{L_ 1 + L_ 2}\)

(C) The ratio of the currents through L₁ and L₂ is fixed at all times (t > 0)

(D) At t = 0 , he current through the resistance R is \(\frac{V}{R}\)

Answer 1

(A) After a long time, the current through L₁ will be \(\frac{V}{R}\frac{L_2}{L_1 +L_ 2}\)

(B) After a long time, the current through L₂ will be \(\frac{V}{R}\frac{L_ 1}{L_ 1 + L_ 2}\)

(C) The ratio of the currents through L₁ and L₂ is fixed at all times (t > 0)

Let current through R, L₁ and L₂ is i, i₁ and i₂ respectively