Question

A capacitor of $10\mu F$ and an inductor of $1H$ are joined in series. An $AC$ of $50\text{Hz}$ is applied to this combination. What is the impedance of the combination?

• A. $\frac{5({\pi }^2-5)}{\pi }\Omega$
• B. $\frac{100(10-{\pi }^2)}{\pi }\Omega$
• C. $\frac{10({\pi }^2-5)}{\pi }\Omega$
• D. $\frac{10(10-{\pi }^2)}{\pi }\Omega$

Answer 1

The correct option is B $\frac{100(10-{\pi }^2)}{\pi }\Omega$

From given,

$Z=|X_L-X_c|$
$X_L=\omega L=2\pi \times f\times L=2\pi \times 50\times 1$
$X_L=100\pi \Omega$
and
$X_C=\frac{1}{\omega C}=\frac{1}{2\pi \times 50\times 10\times {10}^{-6}}=\frac{1000}{\pi }\Omega$
Now
$X_C=\frac{1000}{\pi }\Omega$
$Z=|X_L-X_C|$
$Z=|100\pi -\frac{1000}{\pi }|\Omega$
=$\frac{100(10-{\pi }^2)}{\pi }\Omega$