A capacitor C is fully charged to potential difference V₀, disconnected from the battery, and then connected across an inductor L. In time t, 25% of the initial energy of the capacitor is transferred to the inductor. The value of t is

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Accepted Answer

(3) (π√LC)/6. In the LC loop the charge is q=Q₀ cos ω t with ω=1/(√LC). Capacitor energy U_C=U₀ cos²ω t, inductor energy U_L=U₀ sin²ω t. 25% transferred to the inductor: sin²ω t=1/4⇒sin ω t=1/2⇒ω t=π/6. t=π/6 √LC=(π√LC)/6. (Scan note: printed options showed a duplicated π√LC/2; the fourth option is reconstructed. See DEFECTS.md.)

A capacitor C is fully charged to potential difference V₀, disconnected from the battery, and then connected across an inductor L. In time t, 25% of the initial energy of the capacitor is transferred to the inductor. The value of t is

Step-by-step solution

Why the other options are wrong