Statistics Harmonic Number – lesscss

By | March 14, 2019

Statistics – Harmonic Number

Harmonic Number is the sum of the reciprocals of the first n
natural numbers. It represents the phenomenon when the inductive
reactance and the capacitive reactance of the power system
becomes equal.

Formula

${ H = frac{W_r}{W} \[7pt] , where W_r = sqrt{
frac{1}{LC}} } \[7pt] , and W = 2 pi f $

Where −

  • ${f}$ = Harmonic resonance frequency.

  • ${L}$ = inductance of the load.

  • ${C}$ = capacitanc of the load.

Example

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

Solution:

Here capacitance, C is 5F. Inductance, L is 6H. Frequency, f is
200Hz. Using harmonic number formula, let’s compute the number
as:

${ H = frac{sqrt{ frac{1}{LC}}}{2 pi f} \[7pt] implies H
= frac{sqrt{ frac{1}{6 times 5}} }{2 times 3.14 times
200} \[7pt] , = frac{0.18257}{1256} \[7pt] , = 0.0001 }$

Thus harmonic number is $ { 0.0001 }$.

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