Question

A $100 \, V$ , AC source of frequency $500 \, Hz$ is connected to an LCR circuit with $L=8.1 \, mH$ , $C \, = \, 12.5 \, \mu F, \, R \, = \, 10 \, \Omega$ all connected in series as shown in the figure. What is the quality factor of the circuit?

• A. $2.02$
• B. $2.54$
• C. $50.54$
• D. $200.54$

Answer 1

Answer: (B)

In the condition of resonance , quality factor
$Q=\frac{1}{R}\sqrt{\frac{L}{C}}$ $= \, \frac{1}{10} \, \sqrt{\frac{8.1 \times 10^{- 3}}{12.5 \times 10^{- 6}}}$
$=2.54$