Question

A 0.2 $\Omega$ resistor and 15 $\mu$F capacitor are connected in series to a 220 V, 50 Hz ac source. The impedance of the circuit is

• A. $250\Omega$
• B. $268\Omega$
• C. $29.15\Omega$
• D. $291.5\Omega$

Answer 1

Answer: (D)

$291.5\Omega$

Here, $R=0.2k\Omega =200\Omega$
$C=15\mu F=15\times {10}^{-6}F$

$\nu =50Hz$

Capacitive reactance,
$X_C=\frac{1}{2\pi \nu C}=\frac{1}{2\times 3.14\times 50\times 15\times {10}^{-6}}=212\Omega$

The impedance of the RC circuit is
$Z=\sqrt{R^2+X_C^2}=\sqrt{(200{)}^2+(212{)}^2}=291.5\Omega$