# 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 ${ 0.0001 }$.