Thank you for reporting, we will resolve it shortly
Q.
In the series $LCR$ circuit shown the impedance is
Alternating Current
Solution:
Here, $L = 1\,H$,
$C = 20\,\mu F = 20 \times 10^{-6}\, F$
$R=300\,\Omega, \upsilon=\frac{50}{\pi}Hz$
The inductive reactance is
$X_{L}=2\pi\upsilon L$
$=2\times\pi\times\frac{50}{\pi}\times1$
$=100\,\Omega$
The capacitive reactance is
$X_{C}=\frac{1}{2\pi\upsilon C}$
$=\frac{1}{2\times\pi\times\frac{50}{\pi}\times20\times10^{-6}}$
$=500\,\Omega$
The impedance of the series $LCR$ circuit is
$Z=\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}$
$=\sqrt{\left(300\right)^{2}+\left(500-100\right)^{2}}$
$=\sqrt{\left(300\right)^{2}+\left(400\right)^{2}}$
$=500\,\Omega$
