Question

Adjoining figure shows a series $RCL$ circuit connected to an ac source which generates an alternating emf of frequency $50Hz$. The reading of the voltmeters $V_1$ and $V_2$ are $80V$ and $60V$ respectively.
Find:
The capacitance $C$ of the capacitor

Answer 1

Let the voltage across the capacitor be $V_C$
$V_C=I\times X_C$
$60=0.8\times X_C$

$X_C=\frac{60\times 10}{80}=75\Omega$

$X_C=\frac{1}{2\pi fC}$
$C=\frac{1}{2\pi f\times X_C}$
$=\frac{1}{2\pi \times 50\times 75}$
$=4.25\times {10}^{-5}F$