In the circuit shown in figure, the fins currents I₁, I₂ and I₃ are altered by varying the frequency f of the oscillator. The output voltage of the oscillator remains sinusoidal and has a fixed amplitude.

Which curves in figure indicates correctly the variation of the current I₁, I₂ and I₃ with frequency?

Reactance of inductor L is given by ${\mathrm{X}}_{\mathrm{L}}=2\mathrm{\pi fL}$

$\therefore$    R.m.s. current through the inductor L is

${\mathrm{I}}_2=\frac{\mathrm{V}}{2\mathrm{\pi fL}}\propto \frac{1}{\mathrm{f}}$

where V is the r.m.s. of the supply voltage.

Reactance of the capacitor C is given by ${\mathrm{X}}_{\mathrm{c}}=\frac{1}{2\mathrm{\pi fC}}$

$\therefore$  R.m.s. current through the capacitor is

${\mathrm{I}}_3=\frac{\mathrm{V}}{{\mathrm{X}}_{\mathrm{c}}}=2\mathrm{\pi fCV}\propto \mathrm{f}$

The total current I₁ is given by ${\mathrm{I}}_1,={\mathrm{I}}_2+{\mathrm{I}}_3$

$=\frac{\mathrm{V}}{2\mathrm{\pi fL}}-2\mathrm{\pi fCV}$

Thus, I₂ is best represented by curve R.

I₃ is best represented by curve P.

I₁ is best represented by curve Q.