Question

In the series $L-C-R$ circuit shown, the impedance is

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

Answer 1

The Correct Option is D

$X_{L} =2 \pi f L$
$=2 \pi\left(\frac{50}{\pi}\right) \times 1=100\, \Omega$
$X_{C} =\frac{1}{2 \pi f C}=\frac{1}{2 \pi\left(\frac{50}{\pi}\right) 20 \times 10^{-6}}=500\, \Omega$
Impedance, $Z =\sqrt{R^{2}+\left(X_{C}-X_{L}\right)^{2}}$
$Z =\sqrt{(300)^{2}-(400)^{2}}=500\, \Omega$