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Harmonic Number
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] imppes H = frac{sqrt{ frac{1}{6 imes 5}} }{2 imes 3.14 imes 200} \[7pt] , = frac{0.18257}{1256} \[7pt] , = 0.0001 }$
Thus harmonic number is $ { 0.0001 }$.
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