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

Question

A 100 V , AC source of frequency 500 Hz is connected to an LCR circuit with L=8.1 mH , C = 12.5 μ F, R = 10 Ω all connected in series as shown in the figure. What is the quality factor of the circuit? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-ucyw0ylkmnuf8vlm.jpg" /> (A) 2.02 (B) 2.54 (C) 50.54 (D) 200.54

Tardigrade Admin · Accepted Answer

In the condition of resonance , quality factor Q=(1/R)√(L/C) = (1/10) √(8.1 × 10- 3/12.5 × 10- 6) =2.54

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

$2.02$

$2.54$

$50.54$

$200.54$

In the condition of resonance , quality factor
$Q = \frac{1}{R} \frac{L}{C}$ $= \frac{1}{10} \frac{8.1 \times 1 0 ^{- 3}}{12.5 \times 1 0 ^{- 6}}$
$= 2.54$

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

2.02

2.54

50.54

200.54