Question

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

The correct option is C $\frac{{10}^5}{3\pi }-\frac{\pi }{10}$

Impedance $Z=\sqrt{R^2+(X_L-X_C{)}^2}$

Where $X_L=\omega L$

$X_C=\frac{1}{\omega C}$

and $\omega =2\pi f$

$=2\pi \times 50=100\pi$

$\therefore X_L=100\pi \times {10}^{-3}=\frac{\pi }{10}$

$X_C=\frac{1}{100\pi \times 3\times {10}^{-7}}=\frac{{10}^5}{3\pi }$

$R=0$

$\therefore Z=\sqrt{(\frac{\pi }{10}-\frac{{10}^5}{3\pi }{)}^2}$

$=\frac{{10}^5}{3\pi }-\frac{\pi }{10}$ As, ($\frac{{10}^5}{3\pi }>\frac{\pi }{10}$)