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JEE Main 2026 (21 Jan, Shift 2) · LC Oscillations

LC Oscillations question from JEE Main 2026 (21 Jan, Shift 2)

Q6JEE Main 2026 · 21 JAN · SHIFT 2Medium

LC Oscillations

A capacitor C is first charged fully with potential difference of V0V_0 and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In tt s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of tt is ________ s.

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Answer: (d)

  1. Starting from full charge: q=Q0cos⁡ωtq = Q_0\cos\omega t, so UL=U0sin⁡2ωtU_L = U_0\sin^2\omega t with ω=1LC\omega = \frac{1}{\sqrt{LC}}.
  2. UL=0.25 U0⇒sin⁡ωt=12⇒ωt=π6U_L = 0.25\,U_0 \Rightarrow \sin\omega t = \frac{1}{2} \Rightarrow \omega t = \frac{\pi}{6}
  3. t=π6LCt = \frac{\pi}{6}\sqrt{LC}
  4. So the answer is (d) πLC6\frac{\pi\sqrt{LC}}{6}.
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