A circuit containing two capacitor `C_(1)` and `C_(2)` shown in figure is in steady state with switch `K_(1)` closed and `K_(2)` open. At the instant `t=0,K_(1)` is opened and `K_(2)` is closed. The correct statements are.

Options

A. Angular frequency of oscillation of LC circuit is `5xx10^(4)(rad)/(sec)`
B. charge on capacitor `C_(1)` at `t=0` is `40muC`
C. Maximum current in iductor is `1A`
D. Charge on capacitor `C_(1)` is `10sqrt(3)muC` when energy in the inductor becomes one third of the energy in capacitor.

Answer

A, C, D

Explanation

`omega=(1)/(sqrt(LC))=5xx10^(4)(rad)/(sec)`
`q=C_(eq)V=1xx10^(-6)xx20=20muC`
`I_(max)=omegaq_(max)=5xx10^(-4)xx20xx10^(-6)=1A`
`U_(C)+U_(L)=U_("total")`
`U_(C)+(U_(C))/(3)U_("total")`
`U_(C)=(3)/(4)U_("Total")`
`(q^(2))/(2C)=(3)/(4)((q_(max))^(2))/(2C)`
`q=(sqrt(3))/(2)xx20muC=10sqrt(3)muC`