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. `{:(I_(1),I_(2),I_(3)),(q,q,q):}`
B. `{:(I_(1),I_(2),I_(3)),(r,q,q):}`
C. `{:(I_(1),I_(2),I_(3)),(q,p,r):}`
D. `{:(I_(1),I_(2),I_(3)),(q,r,p):}`

Answer

D

Explanation

Resistance of inductor `O` is given by `X_(L)=2pifL`
`:.` r.m.s current through the inductor `L` is `I_(2)`
`=V/(2pifL) prop1/f`
where `V` is the r.m.s. of the supply voltage.
Reactance of the capacitor `C` is given by `X_(c)=1/(2pifc)`
`:.` r.m.s. current through the capacitor is
`I_(3)=V/(X_(c))=2pifCV prop f`.
The total current `I_(1)` is given by `I_(1),=I_(2)+I_(2)`
`=(V/(2pifL)-2pifCV)`.
Thus, `I_(2)` is given by represented by curve `R`.
`I_(3)` is best represented by curve `P`.
`I_(1)` is best represented buy curve `Q`.