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 $X_{L}=2 \pi f L$
$\therefore $ R.m.s. current through the inductor $L$ is
$I_{2}=\frac{V}{2 \pi f L} \propto \frac{1}{f}$
where $V$ is the r.m.s. of the supply voltage.
Reactance of the capacitor $C$ is given by $X_{c}=\frac{1}{2 \pi f C}$
$\therefore $ R.m.s. current through the capacitor is
$I_{3}=\frac{V}{X_{c}}=2 \pi f C V \propto f$
The total current $I_{1}$ is given by $I_{1},=I_{2}+I_{3}$
$=\frac{V}{2 \pi f L}-2 \pi f C V$
Thus, $I_{2}$ is best represented by curve $R$.
$I_{3}$ is best represented by curve $P$.
$I_{1}$ is best represented by curve $Q$.