Under the condition of resonance in rlc series circuit, the power factor of the circuit is

We know that Resistor (R), Inductor (L), and Capacitor (C) are the passive elements. We can connect these passive elements in a number of ways. For the time being, let us consider the basic connections. These are series connections and parallel connections.

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Series Resonance
Parallel Resonance
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If we connect an AC source with variable frequency to the combination of RLC network/ circuit, then at one frequency the energy stored in both inductor and capacitor will be equal or the net energy stored in the circuit will be zero. This frequency is known as resonant frequency, and we can say that the circuit is at resonance. Since we are having two basic connections accordingly we will be having two types of Resonances. Now, let’s discuss the following two types of resonances one by one.

Series Resonance
Parallel Resonance

Series Resonance

In the series RLC circuit, we will connect the AC voltage source, Resistor (R), Inductor (L), and Capacitor (C) all are in series. This circuit diagram is shown in the figure below. In series, the current is the same, but the supply voltage (AC) gets divided among the passive elements.

Since, R, L, and C are connected in series, the equivalent impedance will be Z=R+j(ωL-1/ωC).
The impedance, Z will be real, and it is equal to R when the imaginary part of impedance becomes zero at ω=0.
At ω=ω0, the reactance of both the inductor and capacitor are the same.

ω0L=1/ω0C

=>ω02=1/LC

=>ω0=1/√LC

=>f0=1/2π√LC

f0 is the series resonant frequency and it is equal to 1/2π√LC.
At ω=ω0, V=IZ=IR. That is voltage and current are in phase at a resonant frequency. i.e., ∅=0.
At the series resonant frequency, the power factor cos ∅ will be equal to 1. Hence, it is called a unity power factor.

Parallel Resonance

In a parallel RLC circuit, we will connect the AC current source, Resistor (R), Inductor (L), and Capacitor (C) all in parallel. This circuit diagram is shown in the figure below. In parallel, voltage is the same, but the supply current (AC) gets divided among the passive elements.

Since R, L and C are connected in parallel, the equivalent admittance will be Y=1/R+j(ωC-1/ωL).
The admittance, Y will be real, and it is equal to 1R when the imaginary part of admittance becomes zero at ω=ω0.
At ω=ω0, the susceptance of both the inductor and capacitor are the same.

ω0C=1/ω0L

=>ω02=1/LC

=>ω0=1/√LC

=>f0=1/2π√LC

f0 is the parallel resonant frequency and it is equal to 1/2π√LC.
At ω=ω0, I=VY=V/R. That is current and voltage are in phase at a resonant frequency. i.e., ∅=0.
At the parallel resonant frequency, the power factor cos ∅ will be equal to 1. Hence, it is called a unity power factor.

Therefore, the power factor at resonance in RLC circuit is equal to 1 for both series and parallel circuits. In this article, we discussed resonance in RLC circuits for both series and parallel connections.

16. In a R-L-C circuit

A. Power is consumed in resistance only and is equal to I SquareR

B. Exchange of power does not take place between resistance and supply mains

C. Exchange of power take place between capacitor and supply mains

D. All of the above

17. Under the condition of resonance in R-L-C series circuit, the power factor of the circuit is

A. 0.5 lagging

B. 0.5 leading

C. Unity

D. Zero

C. Unity

18. A series R-L-C circuit will have unity power factor if operated at a frequency of

A. 1/LC

B.1/w2 LC

C. 1/w2 LC

D. 1/ 2 Π √ LC

19. In a series R-L-C circuit at resonance, the magnitude of voltage developed across the capacitor

A. Is always zero

B. Can never be greater than the input voltage

C. Can be greater than the input voltage however it is 90o out of phase with the input voltage

D. Can be greater than the input voltage and is in phase with the input voltage

C. Can be greater than the input voltage however it is 90o out of phase with the input voltage

20. In a series R-L-C circuit, voltage across inductance will be maximum

A. At resonant frequency

B. Just after resonant frequency

C. Just before resonant frequency

D. Just before and after resonant frequency

B. Just after resonant frequency

Option 1 : Purely resistive circuit

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In a series RLC circuit, the impedance is given by

At resonance, the magnitude of inductive reactance is equal to the magnitude of capacitive reactance.

The magnitude of XL = XC

At this condition, Z = R.

Hence at resonance, the impedance is purely resistive and it is minimum.

Current in the circuit, I = V/Z

As impedance is minimum the current is maximum.

As impedance is purely resistive, the power factor is unity.

Important Points:

In a purely inductive circuit, the current lags the voltage by 90° and the power factor is zero lagging
In a purely capacitive circuit, the current leads the voltage by 90° and the power factor is zero leading

The plot of the frequency response of the series circuit is as shown in the figure: