Give an expression for an ac driven series RLC circuit.

Explanation

For a series RLC circuit and for a sustained oscillation,
`L(d^(2)q)/(dt^(2))+R(dq)/(dt)+(q)/(C)=v_(m)sinomegat`
where, `q=q_(m)sin(omegat+theta)`
and `q_(m)=(v_(m))/([L^(2)(omega_(0)^(2)-omega^(2))^(2)+omega^(2)R^(2)]^(1//2))`
Note :
`i_(m)=omegaq_(m)`
It can also be shown that
`i_(m)=(v_(m))/(sqrt(R^(2)+(X_(C)-X_(L))^(2)))` where `Z=sqrt(R^(2)+(X_(C)-X_(L))^(2))`.