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)

$500\Omega$

Hence , $L=1H,C=20\mu F=20\times {10}^{-6}F$
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 cicuit is
$Z=\sqrt{R^2+(X_C-X_L{)}^2}=\sqrt{(300{)}^2+(500-100{)}^2}$

$Z=\sqrt{(300{)}^2+(400{)}^2}=500\Omega$