Question

In the circuit shown in figure, the rms current $I_1,I_2\&I_3$ , are altered by varying frequency $f$ of the oscillator. The output voltage of the oscillator remains sinusoidal and has a fixed amplitude. Which curves in figure correctly indicate the variation with frequency of currents $I_1,I_2\&I_3$?

• A. $I_1\to Q;I_2\to Q;I_3\to Q$
• B. $I_1\to R;I_2\to Q;I_3\to Q$
• C. $I_1\to Q;I_2\to P;I_3\to R$
• D. $I_1\to Q;I_2\to R;I_3\to P$

Answer 1

The correct option is D $I_1\to Q;I_2\to R;I_3\to P$

Reactance of the inductor is given by $X_L=2\pi fL$ . Therefore, rms current through inductor L is
$I_2=\frac{V}{2\mathrm{\pi fL}}\propto \frac{1}{f}$ (represented by curve R) where $V$ is the rms of supply voltage.
Reactance of the capacitor is given by
$X_C=\frac{1}{2\pi fC}$. Therefore, rms current through the capacitor is
$I_3=\frac{V}{X_C}=2\mathrm{\pi fCV}\propto f$(represented by curve P).
The total current $I_1$is given by
$I_1=I_2+I_3=\left(\frac{V}{2\mathrm{\pi fL}}-2\mathrm{\pi fCV}\right)$ which will a decreasing curve upto an extent and then will become zero and then will increase as $f$ increases as represented by curve Q.