In a series RLC circuit, R = 4Ω, L = 4 mH and C = 20 μF. What is the value of Q-factor?

Question

Question

This question was previously asked in

SSC JE Electrical 16 Nov 2022 Shift 3 Official Paper

Answer 1

The correct answer is option 3):(3.535)

Concept:

Resonant frequency for a series RLC circuit is given by

: ω₀=\(1\over \sqrt{LC}\)

Bandwidth for a series RLC circuit is given by

B.W.= \(R\over L\)

Also, the quality factor is given by

\({\text{Q}} = \frac{{{\omega_o}}}{{{\text{B}}}} \)

Calculation:

Given that, R = 4 Ω, L = 4 mH, C = 25 μF

For the given RLC network, the resonant frequency will be:

ω0=\(1\over \sqrt{LC}\)

\(= \frac{1}{{\sqrt {4 \times {{10}^{ - 3}} \times 20 \times {{10}^{ - 6}}} }}\)

=3535 Hz

B.W.= \(R\over L\)

= \(4 \over 4 \times 10 ^{-3}\)

= 1000

\({\text{Q}} = \frac{{{\omega_o}}}{{{\text{B}}}} \)

= \(3535 \over 1000\)

= 3.535