Question

The inductance, capacitance and resistance in a given series LCR circuit, have values of (n) henry, (1/n³) farad and (n²) ohm. The quality factor, Q, and the resonant frequency (v₀) , of this circuit, equal, respectively,

(1) \(Q=\frac{1}{2};v_0=\frac{n}{4\pi}\) 

(2) \(Q=1;v_0=(\frac{n}{2\pi})\)

(3) \(Q=\frac{4\pi^2}{n^2};v_0=\frac{2\pi}{n}\)

(4) \(Q=\frac{8\pi^2}{n^2}; v_0=\frac{4\pi}{n}\)

Answer 1

 (2) \(Q=1;v_0=(\frac{n}{2\pi})\)

The quality factor, Q, of a series LCR circuit, equals

Also the resonant frequency, v₀ , is given by

[Note: We can check the consistency of these results by noting that \(Q=\frac{ω_0L}{R}\) 

∴ In the case, \(Q=\frac{(2\pi\frac{n}{2\pi}n)}{n^2}\) = 1 as obtained above].