Calculate the quality factor Q for an RLC circuit having R = 10 Ω, C = 30μF, and L = 27mH.

CONCEPT:

RLC CIRCUIT:

•  An RLC circuit is an electrical circuit consisting of an inductor (L), Capacitor (C), Resistor (R) it can be connected either parallel or series.
• When the LCR circuit is set to resonate (XL = XC), the resonant frequency is expressed as 

\(\Rightarrow f = \frac{1}{{2\pi }}\sqrt {\frac{1}{{LC}}}\)

• Quality factor is

 \(\Rightarrow Q=\frac{{{\omega }_{0}}L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}\)

Where, XL & XC = Impedance of inductor and capacitor, L, R & C = Inductance, resistance, and capacitance, f = frequency and, ω0 = angular resonance frequency

CALCULATION:

Given that: R = 10 Ω, C = 30 μF = 30 × 10^-6 F, and L = 27mH = 27 × 10-3 H

From the above discussion,

\(\Rightarrow Q=\frac{{{\omega }_{0}}L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}\)

\(\Rightarrow Q = \frac{1}{10}\sqrt{\frac{27×10^{-3}}{30×× 10^{-6}}}\)

\(\Rightarrow Q= \frac{3×10}{10} = 3\)

• Hence option (1) is correct.