What is the Resonance in RLC Circuit? - Series and Parallel Resonance

By Aina Parasher|Updated : May 16th, 2022

Resonance in RLC Circuit: In the electrical circuits, the resonance happens because of the energy storing elements called inductor and capacitor. Resonance in RLC circuits has a lot of applications. The concept of resonance in this circuit, we will use in the communication system especially in the receivers whenever we want to tune the received signal to a particular frequency. 

In this article, get an overview of resonance in RLC circuits and how to calculate the resonant frequency. First will discuss what is resonance in the series and parallel circuit and then the condition to get resonance in the given network/ circuit. After that will discuss the power factor at resonance in the RLC circuit in the upcoming sections.

Table of Content

What is Resonance in RLC Circuit?

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. 

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.

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FAQs on Resonance in RLC Circuit

  • If we connect an AC source with variable frequency to the 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. 

  • At the resonant frequency, the voltage and current will be in phase. That means the phase angle difference between voltage and current is zero degrees. Hence, the power factor at resonance in the RLC circuit is equal to one for both series and parallel circuits.

  • In a series RLC circuit, at the resonant frequency, the voltage across the inductor and capacitor will become Q (Quality factor) times the supply voltage (AC). Hence, the series RLC circuit at resonance is called a voltage magnification circuit.

  • In a parallel RLC circuit, at the resonant frequency, the current flowing through the inductor and capacitor will become Q (Quality factor) times the supply current (AC). Hence, the parallel RLC circuit at resonance is called the current magnification circuit. 

  • In a series RLC circuit, at the resonant frequency, the value of impedance will be minimum. Hence, maximum current flows through the circuit. Due to this, the series RLC circuit at resonance is called an acceptor circuit.  

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