Question

A voltage source, v = v₀ sin ωt, is connected across a series LCR circuit. The values of L and C, in the circuit, equal \(\frac{9R}{ω}\) and \(\frac{1}{10Rω}\), The phase angle (between the current and voltage in the circuit) and the quality factor, Q, of the circuit, are then equal, respectively, to

(1) \(\frac{\pi}{4}\) (Current lagging) and \(2\sqrt{10}\)

(2) \(\frac{\pi}{4}\) (Current lagging) and \(3\sqrt{10}\)

(3) \(\frac{\pi}{4}\) (Current lagging) and \(3\sqrt{10}\)

(4) \(\frac{\pi}{4}\) (Current lagging) and \(2\sqrt{10}\)

Answer 1

 (3) \(\frac{\pi}{4}\) (Current lagging) and \(3\sqrt{10}\)

The phase angle, θ, (current lagging), between the current flowing and the voltage applied, in a series LCR circuit (connected to a A.C. voltage source) is given by

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

Hence, for the given case,