In the circuit shown if fig, the rms currents `(I_1), (I_2)` and` (I_3)` are altered by varying the frequency f of the oscillator. The output voltage of the oscillator remains sinusoidal and has a fixed amplitude.
When curves in figure correctly indicate the variation with frequency of the currents `(I_1), (I_2),and (I_3)`.

Options

A. (A)`(I_1)=Q`, `(I_2)=Q`, `(I_3)=Q`
B. (B)`(I_1)=R`, `(I_2)=Q`, `(I_3)=Q`
C. (C) `(I_1)=Q`, `(I_2)=P`, `(I_3)=R`
D. (D)`(I_1)=Q`, `(I_2)=R`, `(I_3)=P`

Answer

D

Explanation

Rectancae of the inductor O is given by `X_(L)=2 pi f L`.
Therefore, rms current through inductor L is `(I_2)`
`=(V)/(2 pi f L) prop (1)/(f)` where V is the rms of the supply voltage .
Reactance of the capacitor C is given by `(X_C)=(1)/(2 pi f C)`
therefore, rms current through the capacitor is
`(I_3)=(V)/(X_C) = 2 pi f CV prop f`
The total current `(I_1)` is given by `(I_1)=(I_2)+(I_3)`
`((V)/( 2 pi f L)- 2 pi f CV)`
thus, `(I_2)` is best represented by curve R.
`(I_3)` is best represented by curve P.
`(I_1)` is best represented by curve Q.