# 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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