Question

In the series $LCR$ circuit shown the impedance is

• A. $200\Omega$
• B. $100\Omega$
• C. $300\Omega$
• D. $500\Omega$

Answer 1

Answer: (D)

Here, $L=1H$,
$C=20\mu F=20\times 10^{-6}F$
$R=300\Omega ,\upsilon =\frac{50}{\pi }Hz$
The inductive reactance is
$X_L=2\pi \upsilon L$
$=2\times \pi \times \frac{50}{\pi }\times 1$
$=100\Omega$
The capacitive reactance is
$X_C=\frac{1}{2\pi \upsilon C}$
$=\frac{1}{2\times \pi \times \frac{50}{\pi }\times 20\times 10^{-6}}$
$=500\Omega$
The impedance of the series $LCR$ circuit is
$Z=\sqrt{R^2+{\left(X_C-X_L\right)}^2}$
$=\sqrt{{\left(300\right)}^2+{\left(500-100\right)}^2}$
$=\sqrt{{\left(300\right)}^2+{\left(400\right)}^2}$
$=500\Omega$