Discussion Forum

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?

Answer:

Explanation:

since inductors are connected in parallel

$V_{L_{1}}=V_{L_{2}}$

$L_{1}\frac{dI_{1}}{dt}=L_{2}\frac{dI_{2}}{dt}$

$L_{1}I_{1}=L_{2}I_{2}$

$\frac{I_{1}}{I_{2}}=\frac{L_{2}}{L_{1}}$

Current through resistor  at any time t is given by

$I= \frac{V}{R}(1-e^{-\frac{RT}{L}}) where L=\frac{L_{1}L_{2}}{L_{1}+L_{2}}$

 after log time   $I= \frac{V}{R}$

                    I₁ +I₂ =I            .........(i)

                    L₁I₁  = L₂I₂       ........(ii)

From eq(i) and (ii) , we get

  $I_{1}=\frac{V}{R}\frac{L_{2}}{L_{1}+L_{2}}$,  $I_{2}=\frac{V}{R}\frac{L_{1}}{L_{1}+L_{2}}$

(d) value of current is zero at t=0

value of current V/R at t=∞

 hence option (d) is incorrect