Question

A $0.2k\Omega$ resistor and $15\mu F$ capacitor are connected in series to a $220V$, $50Hz$ 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)

Here, $R=0.2k\Omega =200\Omega$
$C=15\mu F=15\times 10^{-6}F$,
$V_{rms}=220V,\upsilon =50Hz$
Capacitive reactance,
$X_C=\frac{1}{2\pi \upsilon C}$
$=\frac{1}{2\times 3.14\times 50\times 15\times 10^{-6}}$
$=212\Omega$
The impedance of the $RC$ circuit is
$Z=\sqrt{R^2+X_C^2}$
$=\sqrt{{\left(200\right)}^2+{\left(212\right)}^2}$
$=291.5\Omega$