Question

In a series $L-C$ circuit, if $L=10^{-3} \,H$ and $C=3 \times 10^{-7} \,F$ is connected to a $100\, V -50\, Hz$ a.c. source, the impedance of the circuit is

• A. $\frac{10^{5}}{3 \pi}-10 \pi$
• B. $0.1 \pi-3 \times 10^{-5} \pi$
• C. $\frac{10^{5}}{3 \pi}-\frac{\pi}{10}$
• D. None of these

Answer 1

Answer: (C)

$L=10^{-3} \,H$ and $C=3 \times 10^{-7}\, F$
$f=50\, Hz , V =100\, V$
$Z=\sqrt{\left(X_{L}-x_{c}\right)^{2}}$
$=\left(X_{L}-X_{C}\right)$
$=\omega L-\frac{1}{\omega C}$
Putting $\omega, L \,\& \,C$
$Z=\left(\frac{10^{5}}{3 \pi}-\frac{\pi}{10}\right)$