Question

A source of alternating emf of $220V$ and $50Hz$ is connected in series with a resistance of $200\Omega$, an inductance of $100mH$ and a capacitance of $30mF$. Does the current lead or lag the voltage and by what angle?

Answer 1

$\gamma =50Hz,R=200\Omega ,L=100mH=0.1H$ and $C=30mF$
Inductive reactance $X_L=2\pi fL=2\pi \times 50\times 0.1=31.42\Omega$
Capacitive reactance $X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 50\times 30\times {10}^{-6}}$
$X_C=106.10\Omega$
Since capacitance reactance, current leads emf.
It ${}^{\prime }{\varphi }^{\prime }$ is the phase difference
$\tan \varphi =\frac{X_C-X_L}{R}=\frac{106.10-31.42}{200}$
$\varphi ={\tan }^{-1}\left(0.3734\right)$
$\varphi ={20}^{\circ }{29}^1$.