Question

A sinusoidal A.C. voltage source, of adjustable frequency, is connected across a series ‘LCR’ combination. The inductance (L) and the capacitance (C), present in the circuit, can be expresssed in terms of the quality factor (Q) the resonant frequency (ω₀) (of the circuit), and the resistance R, through the relations.

(1) \(L=(\frac{1}{ω_0QR})\) and C = \((\frac{QR}{ω_0})\)

(2) \(L=\frac{QR}{ω_0}\) and C = \(\frac{1}{ω_0QR}\)

(3) \(L=\frac{Q^2R^2}{ω_0}\) and \(C=\frac{1}{ω_0Q^2R^2}\)

(4) \(L=\frac{1}{ω_0Q^2R^2}\) and \(C = (\frac{Q^2R^2}{ω_0})\)

Answer 1

 (2) \(L=\frac{QR}{ω_0}\) and C = \(\frac{1}{ω_0QR}\)

The resonant frequency, ω₀ , and the quality factor, Q, are related, to L and C, as