A condenser of capacity `C` is charged to a potential difference of `V_(1)`. The plates of the condenser are then connected to an ideal inductor of inductance `L`. The current through the inductor wehnn the potential difference across the condenser reduces to `V_(2)` is

Options

A. `((C(V_(1)-V_(2))^(2))/(L))^(1/2)`
B. `(C(V_(1)^(2)-V_(2)^(2)))/(L)`
C. `(C(V_(1)^(2)+V_(2)^(2)))/(L)`
D. `((C(V_(1)^(2)-V_(2)^(2)))/(L))^(1/2)`

Answer

D

Explanation

During discharging of a capacitor through inductor, charge at any time t is given by
`q=q_(0)cosomegat`
where, `omega=(1)/(sqrt(LC))`
`thereforecosomegat=(q)/(q_(0))=(CV_(2))/(CV_(1))=(V_(2))/(V_(1))`
`(becauseq=CV)` . . . (i)
Current through the inductor
`l=(dq)/(dt)=(d)/(dt)(q_(0)cosomegat)=-q_(0)omegasinomegat`
`|l|=CV_(1)(1)/(sqrt(LC))[1-cos^(2)omegat]^(1//2)`
`=V_(1)sqrt((C)/(L))[1-((V_(2))/(V_(1)))^(2)]^(1//2)`
`=[(C(V_(1)^(2)-V_(2)^(2)))/(L)]^(1//2)` [using eq. (i)]