Question

An LCR series circuit contains $L=8H$, C$=$0.5 $\mu$ F and R $=$ 100$\Omega$ .The resonant frequency of the circuit is

• A. $\frac{100}{\pi }Hz$
• B. $\frac{500}{\pi }Hz$
• C. $\frac{250}{\pi }Hz$
• D. $\frac{125}{\pi }Hz$

Answer 1

Answer: (C)

$\frac{250}{\pi }Hz$

For resonant frequency reactance should be zero.

So, $X_L-X_C=0$

$X_L=X_C$

$\omega L=\frac{1}{\omega C}$

$⟹\omega =\sqrt{\frac{1}{2C}}$

Or $2\pi f=\frac{1}{\sqrt{2C}}$

Thus resonant frequency $f=\frac{1}{2\pi }\times \frac{1}{\sqrt{2C}}$

$f=\frac{1}{2\pi }\times \frac{1}{\sqrt{8\times 0.5\times {10}^{-6}}}$

$f=\frac{1}{2\pi }\times \frac{{10}^3}{2}$

$f=\frac{250}{\pi }Hz$