# Statistics - Harmonic Resonance Frequency

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Harmonic Resonance Frequency represents a signal or wave whose frequency is an integral multiple of the frequency of a reference signal or wave.

## Formula

${ f = \frac{1}{2 \pi \sqrt{LC}} }$

Where −

• ${f}$ = Harmonic resonance frequency.

• ${L}$ = inductance of the load.

• ${C}$ = capacitanc of the load.

## Example

Calculate the harmonic resonance frequency 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 resonance frequency formula, let's compute the resonance frequency as:

${ f = \frac{1}{2 \pi \sqrt{LC}} \\[7pt] \implies f = \frac{1}{2 \pi \sqrt{6 \times 5}} \\[7pt] \, = \frac{1}{2 \times 3.14 \times \sqrt{30}} \\[7pt] \, = \frac{1}{ 6.28 \times 5.4772 } \\[7pt] \, = \frac{1}{ 34.3968 } \\[7pt] \, = 0.0291 }$

Thus harmonic resonance frequency is ${ 0.0291 }$.

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