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JEE Advanced 2022 Paper 1 · Physics · Electromagnetic Induction and Alternating Current · medium

A coil of inductance 2 H and resistance 10 Ω is connected at t=0 across an ideal battery of emf 20 V.

One or more options correct

A coil of inductance 2 H2\ \mathrm{H} and resistance 10 Ω10\ \Omega is connected at t=0t=0 across an ideal battery of emf 20 V20\ \mathrm{V}. Choose the correct option(s).
  1. A. The current at t=0.2 st=0.2\ \mathrm{s} is about 1.26 A1.26\ \mathrm{A}.
  2. B. The initial rate of rise of current is 10 A s−110\ \mathrm{A\,s^{-1}}.
  3. C. The steady-state energy stored in the inductor is 8 J8\ \mathrm{J}.
  4. D. The induced emf equals the voltage across the resistor at t=0.2 st=0.2\ \mathrm{s}.
Show answer and solution

Answer: A, B

Time constant τ=L/R=0.2 s\tau=L/R=0.2\ \mathrm{s}. (A) I=2(1−e−1)=1.26 AI=2(1-e^{-1})=1.26\ \mathrm{A}, true. (B) At t=0t=0, dI/dt=ε/L=10 A s−1dI/dt=\varepsilon/L=10\ \mathrm{A\,s^{-1}}, true. (C) I∞=2 AI_\infty=2\ \mathrm{A}, so U=12⋅2⋅4=4 JU=\tfrac12\cdot2\cdot4=4\ \mathrm{J}, not 8 J8\ \mathrm{J}; false. (D) The two voltages are equal when εe−t/τ=ε(1−e−t/τ)\varepsilon e^{-t/\tau}=\varepsilon(1-e^{-t/\tau}), i.e. t=τln⁡2=0.139 st=\tau\ln2=0.139\ \mathrm{s}; at 0.2 s0.2\ \mathrm{s} the resistor voltage is larger; false.
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