AIIMS2019Physics-Electromagnetic Induction

AIIMS 2019 Physics LCR Circuits MCQ Question

Type: MCQ-numerical-Medium-Class 12

In a LCR oscillatory circuit find the energy stored in inductor at resonance. If voltage of source is 10 V and resistance is 10 Ω and inductance=1 H.

A

0.5 J

B

2 J

C

4 J

D

10 J

Correct Answer

Option A

Detailed Explanation

At resonance in an LCR circuit, the impedance is minimized, and the current is maximized. The energy stored in the inductor (U) can be calculated using the formula U=12LI2U = \frac{1}{2} L I^2, where L=1HL = 1 \, \text{H} and II is the maximum current. The maximum current II can be found using Ohm's law, I=VR=10V10Ω=1AI = \frac{V}{R} = \frac{10 \, \text{V}}{10 \, \Omega} = 1 \, \text{A}. Substituting these values gives U=12×1H×(1A)2=0.5JU = \frac{1}{2} \times 1 \, \text{H} \times (1 \, \text{A})^2 = 0.5 \, \text{J}. Other options are incorrect as they do not align with the calculated energy stored in the inductor at resonance.

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