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  4. A 0.2 kΩ resistor and 15 μ F capacitor are connected in series to a 220 V, 50 Hz ac source. The impedance of the circuit is

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Q. 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

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Solution:

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
$Z=\sqrt{R^{2}+X^{2}_{C}}$
$=\sqrt{\left(200\right)^{2}+\left(212\right)^{2}}$
$=291.5\,\Omega$