# Learn How to Calculate Harmonic Number and Resonance Frequency – Tutorial

## How to Calculate Harmonic Number and Resonance Frequency – Definition, Formula and Example

#### Definition:

##### Harmonic Number:

It is the sum of the reciprocals of the first n natural numbers. This is a phenomenon which occurs when the inductive reactance and the capacitive reactance of the power system become equal.

##### Harmonic Resonance Frequency:

It is a signal or wave whose frequency is an integral multiple of the frequency of some reference signal or wave.

##### Example :

Calculate the harmonic number and harmonic resonance frequency for the power system with the capcitance 5F, Inductance 6H and frequency 200Hz.

##### Given,

Capacitance = 5F
Inductance = 6H
Frequency = 200Hz

##### To Find,

Harmonic number and resonance frequency

##### Solution:

###### Step 1:

Substitute the values in harmonic number formula

Harmonic number | w_{r} / w |

w | 2 x 3.14 x 200 |

w | = 1256 |

w_{r} | = 1 / √( 6 x 5 ) |

w_{r} | = 0.18257 |

Harmonic number | = 0.18257 / 1256 |

| = 0.0001 |

###### Step 2:

Substitute the values in harmonic resonance frequency formula
f = 1 / 2π x √(LC)
f = 1 / (2 x 3.14) x (√6 x 5)
f = 1 / (6.28 x 5.4772)
f = 1 / 34.3968
f = 0.0291 Hz

Learn how to calculate Harmonic number and resonance frequency in this tutorial, given with the definition, formula and example.