Question

a series circuit with R=10 ohms,L=100mH and C=100microF is supplied with 200 V/50Hz. Find the impedance,current,power,power factor.

Answer 1

Impedance

$X_L=2\pi fL=2\pi \times 50 \times 100 \times 10^{-3}=20\pi$

$X_C=\frac{1}{2\pi fL}=\frac{1}{2\pi \times 50 \times 100 \times 10^{-3}}=\frac{1}{20\pi}$

$Z=\sqrt{10^2+(20\pi- \frac{1}{20\pi}})^2=63.6 \Omega$

Current

$I=\frac{V}{Z}= \frac{200}{63.6}=3.145 A$

Power

$P=IV=3.145 \times 200=628.93 W$

Power factor

$cos \phi =\frac{R}{Z}=\frac{10}{63.6}=0.157$