Question

Figure shows a series LCR circuit connected to a variable frequency 200V source. The source frequency which drives the circuit at resonance is

• A. 50 Hz
• B. (50 /$\pi$ )Hz
• C. 25 Hz
• D. (25 /$\pi$ ) Hz

Answer 1

Answer: (D)

(25 /$\pi$ ) Hz

For resonance frequency

$X_L=X_C$

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

$2\pi f=\frac{1}{\sqrt{LC}}$

$f=\frac{1}{2\pi }\times \frac{1}{\sqrt{LC}}$

$=\frac{1}{2\pi }\times \frac{1}{5\times 80\times {10}^{-6}}$

$=\frac{1}{2\pi }\times \frac{{10}^3}{20}$

$=\frac{25}{\pi }Hz$