Question

A circuit containing a 20 $\Omega$ resistor and 0.1$\mu F$ capacitor in series is connected to 230 V AC supply of angular frequency 100 rad $s^{-1}$. The impedance of the circuit is

• A. ${10}^5\Omega$
• B. ${10}^4\Omega$
• C. ${10}^6\Omega$
• D. ${10}^{10}\Omega$

Answer 1

The correct option is A ${10}^5\Omega$

Hence, $R=20\Omega ,C=0.1\mu F=0.1\times {10}^{-6}F={10}^{-7}F$

Impedance ,$Z=\sqrt{R^2+\frac{1}{{\omega }^2{C}^2}}$

$\sqrt{{20}^2+\frac{1}{(100{)}^2\times ({10}^{-7}{)}^2}}=\sqrt{400+{10}^{10}}={10}^5\Omega$