# What is Resonant Circuit ?

The electric circuit consisting of inductor (L) and capacitor (C) components having equal inductive reactance and capacitive reactance is known as resonant circuit. If the L and C are connected in series, it is known as series resonant circuit. If the L and C are connected in parallel, it is known as parallel resonant circuit. Both of these resonant circuits are shown in the following diagram. At resonant frequency, reactance of inductor and capacitor cancel each other out which results in purely resistive impedance.

## Series Resonant Circuit

In this circuit, both L and C are connected in series with each other and load resistor (R) is connected in parallel to them.
The resonant frequency of this circuit is expressed as follows.

➨ f = 1/(2 * π * (L*C)^{0.5})

At resonant frequency, impedance of series circuit is at its minimum. This allows current to flow through the circuit at its maximum value. It is commonly used in radio frequency (RF) applications such as frequency filtering and tuning purposes.

## Parallel Resonant Circuit

In this circuit, both L and C are connected in parallel with each other and the load resistor is also connected in series to the combination. Usually, same formula above is used for parallel resonant frequency calculation.

At resonant frequency, impedance of the circuit is at its maximum. This allows high voltage across the load resistor. They are commonly used in audio applications such as to filter frequencies in audio signal processing.

## Other Types of Resonant Circuits

The other types of circuits are bandpass resonant circuit, bandstop resonant circuit and tuned transformer.

• Bandpass circuit : It is a combination of series and parallel resonant circuits. It passes narrow range of frequencies through the circuit.
It is used in communication systems and audio signal processing.

• Bandstop circuit : It is designed to attenuate or reject specific frequency band while allows other frequencies to pass through.

• Tuned transformer : It is a type of resonant circuit which uses a transformer with tuned primary and secondary windings.

## Equivalent Circuits of Resonant circuits

The figure-2 depicts equivalent circuits of resonant circuits shown in the figure-1.

## Difference between series and parallel resonance

Following table mentions difference between series and parallel resonance circuit with respect to various parameters.

Specifications |
Series resonance |
Parallel resonance |
---|---|---|

Configuration | Components are connected in series. | Components are connected in parallel. |

Impedance at resonance | Minimum | Maximum |

Current at resonance | Maximum | Minimum |

Effective impedance | R | L/CR |

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

Magnifying parameter | Voltage | Current |

Other name | Acceptor circuit | Rejector circuit |

Power factor value | Unity | Unity |

Bandwidth | Narrow | Wide |

Quality Factor (Q) | High | Low |

Applications | Used in tuning circuits, filters and amplifiers. | Used in impedance matching circuits, inductor/capacitor selection |

**Conclusion**: Resonance is a critical concept in various applications, including radio frequency (RF) circuits,
audio signal processing, filters, transformers, and antennas. By understanding and controlling resonance in electronic circuits,
engineers can design and optimize devices for specific frequency-related tasks and improve overall performance.
Refer basic difference between Series Resonance Vs Parallel Resonance>>.

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