Question

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

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

Answer 1

Answer: (B)

$\frac{10(10-{\pi }^2)}{\pi }\Omega$

$X_L=L\omega =L2\pi f=100\pi \Omega$
$X_C=\frac{1}{C\omega }=\frac{1}{C2\pi f}=1000/\pi \Omega$
impedance =$|X_L-X_C|=100\frac{10-{\pi }^2}{\pi }\Omega$