Question

In a series LCR circuit, removing L or C gives a phase difference of π/3. Find the power factor.

Options

• 0.5

• 1.0

• -1.0

• zero

Answer 1

1.0

Explanation:

LCR circuit will be:

When L is removed, \[\tan\phi=\frac{|X_{\mathrm{C}}|}{R}\]

⇒ \[\tan\frac{\pi}{3}=\frac{X_{C}}{R}\]

When C is removed, \[\tan\phi=\frac{|X_{L}|}{R}\]

⇒ \[\tan\frac{\pi}{3}=\frac{X_L}{R}\]

Since, X_L = X_C, the circuit is in resonance, Z = R

Power factor = cos Φ = \[\frac {R}{Z}\] = 1