# What is resonance ?

When alternating voltage is applied to a resonant circuit which contains capacitor and coil, response of the circuit is maximum when applied voltage frequency is equal to natural frequency of the circuit. The form of electrical response depends on whether the capacitor(C) and inductor coil (L) are connected in series or parallel.

If the components are connected in series as shown in figure-1, the condition is referred as series resonance and circuit is known as series resonant circuit. If the components are connected in parallel as shown in figure-2, the condition is referred as parallel resonance and circuit is known as parallel resonant circuit.

In other words:

In AC circuits, a condition in which inductive reactance becomes exactly equal to capacitive reactance is referred as
resonance.

XL = XC

➨ 2*πf*L = [ 1/{ (2*π)* (f*C)^{0.5} } ]

➨ Z = { R^{2} + ( XL - XC )^{2} }^{0.5}

## What is resonance frequency

In a circuit consisting of L and C components, the frequency at which resonance occurs is called resonance frequency.

➨Fr = 1 / { (2*π)*(L*C)^{0.5} }

Where,

Fr = resonant frequency or resonance frequency

L = Inductance in henrys

C = Capacitance in Farads

At this resonant frequency, the reactance of the inductor and capacitor cancel each other out, resulting in a purely resistive impedance.

## Series resonance circuit

A series L-C circuit in which magnitudes of capacitive and inductive reactances are exactly equal is known as series resonant circuit as mentioned above. It is also known as acceptor circuit.

At this resonant frequency, the impedance of the circuit is at its minimum, and the current flowing through the circuit is at its maximum.

Characteristics of series resonance circuit:

• Minimum impedance

• Maximum circuit current

• cos(φ) = 1 , hence current and voltage becomes in phase.

• Circuit current becomes proportional to circuit resistance i.e. I ~ 1/R

Uses of series resonance circuit:

• As frequency selection circuit in radio and TV tuner circuits.

• As band pass filter circuit.

## Circuit Q or Q factor

Ratio of inductive reactance to the resistance is called **circuit-Q**.
It is known as magnification factor.

➨ Q = XL/R

Where,

Q = circuit-Q, unitless

XL = inductive reactance, Ohm

R = circuit resistance, Ohm

Selectivity is proportional to Q.

## Bandwidth of Resonance Curve

F2-F1 = R/(2*π*L)

Where,

F2 = Upper frequency of bandwidth (Hertz)

F1 =Lower frequency of bandwidth (Hertz)

R = circuit resistance, Ohm

L = Inductance , Henrys

## Parallel resonance circuit

A parallel L-C circuit in which magnitudes of capacitive and inductive reactances are exactly equal is known as parallel resonant circuit as mentioned above. It is also known as rejector circuit.

At the resonant frequency, the impedance of the circuit is at its maximum, resulting in a high voltage across the load resistor.

Characteristics of parallel resonance circuit:

• Maximum impedance

• Minimum circuit current

• cos(φ) = 1, hence voltage and current becomes in phase

• Circuit current depends on circuit impedance, Z = L/C or I ~ -(1/R)

Uses of parallel resonance circuit:

• As a Band Stop Filter

• As a tank circuit in Oscillators

• As a plate load in IF and RF amplifiers

• As I.F. trap in aerial circuit of radio as well as TV receivers.

## Difference between series and parallel resonance

Let us compare both series vs parallel resonant circuits and other parameters and derives difference between series and parallel resonance types in table format.

Parameters |
Series resonance circuit |
Parallel resonance circuit |
---|---|---|

Impedance at resonance | Minimum | Maximum |

Current at resonance | Maximum | Minimum |

Voltage at resonance | Minimum | Maximum |

Effective impedance | R | L/CR |

Resonant frequency |
1/(2*π*(LC)^{0.5}) |
(1/2*π)*{(1/LC)- R^{2}/L^{2}}^{0.5} |

It magnifies | Voltage | Current |

Bandwidth | Narrow | Wide |

Quality Factor | High | Low |

It is known as | Acceptor circuit | Rejector circuit |

**Conclusion**: The choice between series and parallel resonance depends on the specific application and design requirements.
Both of these resonant circuits involve the exchange of energy between the inductor (L) and capacitor (C).
This results in a significant response at the resonant frequency.
Series resonance is commonly used in RF (Radio Frequency) applications, filters and tuning circuits.
Parallel resonance is used in audio applications, notch filters and impedance matching.

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