Question

In an ac circuit shown below in figure, the supply voltage has a constant rms value $V$ but variable frequency $f$. At resonance, the circuit

• A. has current $I$ given by $I=\frac{V}{R}$
• B. has a resonance frequency $500\, Hz$
• C. has a voltage across the capacitor which is $180^{\circ}$ out of phase with that across the inductor
• D. has a current given by $I=\frac{V}{\sqrt{R^{2}+\left(\frac{1}{\pi}+\frac{1}{\pi}\right)^{2}}}$.

Answer 1

Answer: (A), (C)

$f_{\text {res }}=\frac{1}{2 \pi \sqrt{L C}}$
$=\frac{1}{2 \pi \sqrt{\frac{1}{\pi} \times \frac{1}{\pi} \times 10^{-6}}}=500 \,Hz$
At resonance, $Z=R$,
So current $I=\frac{V}{Z}=\frac{V}{R}$
When $L$ and $C$ are in series, voltage across capacitor and inductor is $180^{\circ}$ out of phase.