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JEE Main 2010
Exam
JEE Main
Year
2010
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2010 · Physics · Electromagnetic Induction

In the circuit shown below, the key K is closed at t=0 . The...

In the circuit shown below, the key K\mathrm{K} is closed at t=0\mathrm{t}=0. The current through the battery is In the circuit shown below, the key K is closed at t=0 . The current through the battery is

Options

  1. AVR1R2R12+R22\frac{\mathrm{VR}_1 \mathrm{R}_2}{\sqrt{\mathrm{R}_1^2+\mathrm{R}_2^2}} at t=0\mathrm{t}=0 and VR2\frac{\mathrm{V}}{\mathrm{R}_2} at t=∞\mathrm{t}=\infty
  2. BVR2\frac{V}{R_2} at t=0t=0 and V(R1+R2)R1R2\frac{V\left(R_1+R_2\right)}{R_1 R_2} at t=∞t=\infty
  3. CVR2\frac{V}{R_2} at t=0t=0 and VR1R2R12+R22\frac{V R_1 R_2}{\sqrt{R_1^2+R_2^2}} at t=∞t=\infty
  4. DV(R1+R2)R1R2\frac{V\left(R_1+R_2\right)}{R_1 R_2} at t=0t=0 and VR2\frac{V}{R_2} at t=∞t=\infty

Correct answer

B. VR2\frac{V}{R_2} at t=0t=0 and V(R1+R2)R1R2\frac{V\left(R_1+R_2\right)}{R_1 R_2} at t=∞t=\infty

Step-by-step solution

At t=0\mathrm{t}=0, inductor behaves like an infinite resistance So at t=0,i=VR2t=0, i=\frac{V}{R_2} and at t=∞t=\infty, inductor behaves like a conducting wire i=VReq =V(R1+R2)R1R2\mathrm{i}=\frac{\mathrm{V}}{\mathrm{R}_{\text{eq }}}=\frac{\mathrm{V}\left(\mathrm{R}_1+\mathrm{R}_2\right)}{\mathrm{R}_1 \mathrm{R}_2}
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