In an ac circuit shown in fig , the supply voltage has a constant rms value v but variable frequency f. At resonance, the circuit

Options

A. has current I given by `I=(V)/(R )`
B. has a resonance frequenv=cy 500 Hz
C. has a voltage across the capacitor which is `180^(@)` out of phase with that across the inductor
D. Has a current given by `I=(V)/(sqrt(R^(2)+((1)/(pi)+(1)/(pi))^(2))`

Answer

A, C

Explanation

`f_(res)=(1)/(2 pi sqrt(LC)) = (1)/(2 pi sqrt(1/(pi) xx(1)/(pi) xx 10^(-6)) = 500 Hz`
At resonace, Z=R,
so current `I=V/Z = V/R`
When L and C are in sereis, voltage across capacitor and inductor is `18^(@)` out of phase.