Question

In the circuit shown in figure, 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.

Which curves in figure indicates correctly the variation of the current $I_1,I_2$ and $I_3$ with frequency?

	$I_1$	$I_2$	$I_3$
a	Q	Q	Q
b	R	Q	Q
c	Q	P	R
d	Q	R	P

• A. a
• B. b
• C. c
• D. d

Answer 1

Answer: (D)

Reactance of inductor $L$ is given by $X_L=2\pi fL$
$\therefore$ R.m.s. current through the inductor $L$ is
$I_2=\frac{V}{2\pi fL}\propto \frac{1}{f}$
where $V$ is the r.m.s. of the supply voltage.
Reactance of the capacitor $C$ is given by $X_c=\frac{1}{2\pi fC}$
$\therefore$ R.m.s. current through the capacitor is
$I_3=\frac{V}{X_c}=2\pi fCV\propto f$
The total current $I_1$ is given by $I_1,=I_2+I_3$
$=\frac{V}{2\pi fL}-2\pi fCV$
Thus, $I_2$ is best represented by curve $R$.
$I_3$ is best represented by curve $P$.
$I_1$ is best represented by curve $Q$.