A capacitor C is first charged fully with potential difference of V₀ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L . In t ~s 25 % of the initial energy in the capacitor is transferred to the inductor. The value of t is _ _ _ _ s.

Step-by-step solution

In an LC circuit, energy oscillates sinusoidally. Initial energy in capacitor is E₀ = 1 2 CV₀^2 . When 25% is transferred to the inductor, 75% remains in the capacitor. Since energy in capacitor varies as E_C(t) = E₀ ^2( t) , we need ^2( t) = 0.75 . This gives ^2( t) = 0.25 , so ( t) = 0.5 , yielding t = 6 . With = 1 LC , we get t = LC 6 seconds.