Question

A $0.2\, k\Omega$ 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)

$291.5\, \Omega$

Answer 2

Here, $R = 0.2\,k\Omega = 200\,\Omega$ $C=15\,\mu F=15\times10^{-6}\,F$, $V_{rms}=220\,V, \upsilon=50\,Hz$ Capacitive reactance, $X_{C}=\frac{1}{2\pi\upsilon C}$ $=\frac{1}{2\times3.14\times50\times15\times10^{-6}}$ $=212\,\Omega$ The impedance of the $RC$ circuit is $Z=\sqrt{R^{2}+X^{2}_{C}}$ $=\sqrt{\left(200\right)^{2}+\left(212\right)^{2}}$ $=291.5\,\Omega$