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- Statistics - Discussion
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 }$.