Question

A condenser of 10 $\mu$F and an inductor of 1H are connected in series with an A.C. source of frequency 50Hz. The impedance of the combination will be (take ${\pi }^2$ $=$10 ):

• A. zero
• B. Infinity
• C. 44.7$\Omega$
• D. 5.67$\Omega$

Answer 1

The correct option is A zero

Impedance = $X_L-X_C=\omega L-\frac{1}{\omega C}$

$=2\pi fL-\frac{1}{2\pi fC}$

$=2\pi \times 50\times 1-\frac{1}{2\pi \times 50\times 10\times {10}^{-6}}$

$=\pi (100-\frac{{10}^6}{2{\pi }^2\times 50\times 10})$

$=\pi (100-\frac{{10}^6}{2\times 10\times 50\times 10})$

$(\because {\pi }^2=10)$

$=0$

So, impedance $=0$