A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is 3π. If instead C is removed from the circuit, the phase difference is again 3π between current and voltage. The power factor of the circuit is (1) 0.5 (2) 1.0 (3) -1.0 (4) zero

Answer:(2) 1.0

An LCR circuit is also known as a resonant circuit or tuned circuit. It consists of an inductor-L, capacitor-C, and resistor-R which are connected in either in series or parallel. For an LCR series circuit with an ac source of angular frequency ω, power factor of circuit will be unity if capacitive reactance equals inductive reactance. The LCR circuit is used for the detection of the frequencies of radio waves in which the broad spectrum of the radio waves are on the narrow range.

For RC circuit

\(\begin{array}{l}tanphi = frac{X_{C}}{R}\end{array} \)

\(\begin{array}{l}tanfrac{pi }{3} = frac{X_{C}}{R}\end{array} \)

XC = √3R

For RL circuit

\(\begin{array}{l}tanphi = frac{X_{L}}{R}\end{array} \)

\(\begin{array}{l}tanfrac{pi }{3} = frac{X_{L}}{R}\end{array} \)

XL = √3R

Power factor for LCR circuit

\(\begin{array}{l}tanphi = frac{X_{C}-X_{L}}{R}\end{array} \)

tanΦ = (√3R – √3R)/R

tanΦ = 0

Φ = tan-10

Φ = 0

Power factor is given by

cosΦ = cos0 = 1

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