(C(V1−V2)2L)12
C(V21−V22)L
C(V21+V22)L
(C(V21−V22)L)12
In case of oscillatory discharge of a capacitor through an inductor, charge at instant t is given by
q=q0cosωt
where ω=1√LC
∴cosωt=q/q0=CV2/CV1=V2/V1 (∵q = CV) .. (i)
Also, q=q0cosωt
dq/dt=-q0ωsinωt
i=-q0ωsinωt
The current through the inductor is given by i = dq/dt.
From (i), cosωt = V2/V1
sinωt = √(1-cos²ωt) = √(1-(V2/V1)²) = √((V1²-V2²)/V1²)
Therefore, i = -q0ω √((V1²-V2²)/V1²)
= -CV1ω √((V1²-V2²)/V1²)
i = -Cω√(V1²-V2²) = -C(1/√LC)√(V1²-V2²)
i = -√(C/L)√(V1²-V2²) = -√(C(V1²-V2²)/L)
i = -√(C(V1²-V2²)/L) [Minus sign indicates direction]
|i| = √(C(V1²-V2²)/L) = √(C(V1²-V2²)/L)