A fully charged capacitor C with initial charge q_0 is connected to a coil of self inductance L at t = 0 . The time at which the energy is stored equa - Physics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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A fully charged capacitor C with initial charge q_{0} is connected to a coil of self inductance L at t = 0 . The time at which the energy is stored equally between the electric and the magnetic field is:

Solution & Step-by-step Explanation

Total energy U = \frac{q _{0}^{2}}{2 C} .When energy is shared equally: U_{E} = \frac{1}{2} U = \frac{q _{0}^{2}}{4 C} .Also U_{E} = \frac{q ^{2}}{2 C} ⟹ \frac{q ^{2}}{2 C} = \frac{q _{0}^{2}}{4 C} ⟹ q = \frac{q _{0}}{2} .In LC oscillation, q = q_{0} cos (ω t), where ω = \frac{1}{L C} . \frac{q _{0}}{2} = q_{0} cos (ω t) ⟹ cos (ω t) = \frac{1}{2} ω t = \frac{π}{4} ⟹ \frac{1}{L C} t = \frac{π}{4} ⟹ t = \frac{π L C}{4}

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A fully charged capacitor C with initial charge q_{0} is connected to a coil of self inductance L at t = 0 . The time at which the energy is stored equally between the electric and the magnetic field is:

\frac{π L C}{4}

2 π L C

L C

π L C

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