Question

An inductor of $0.5 \, mH$, a capacitor of $200\, \mu F$ and a resistor of $2 \, \Omega$ are connected in series with a $220\, V$ ac source. If the current is in phase with the emf, the frequency of ac source will be ______$\times 10^{2} Hz$.

Answer 1

If Current is in phase with emf then the frequency of source
$=\frac{1}{2 \pi \sqrt{ LC }}$ (Resonant frequency)
$\frac{1}{2 \pi \sqrt{\frac{1}{2} \times 10^{-3} \times 2 \times 10^{-4}}}$
$=\frac{1}{2 \pi} \times \sqrt{10} \times 1000=500\, Hz$