# Formula Resonant Frequency of a (R)LC Resonant Circuit Inductance Capacitance

## Resonant frequency

`$$ f_{\text r} $$`Unit

`$$ \mathrm{Hz} $$`

Resonant frequency of an LC resonant circuit, that is a coil-capacitor circuit. This circuit usually also contains a resistor \(R\) to avoid a

*resonance catastrophe*, because the resonance frequency occurs exactly when the inductive resistance \( X_{\text L } = \omega \, L \) and the capacitive resistance \( X_{\text C} = -\frac{1}{\omega \, C} \) cancel each other out.The resonant frequency indicates the number of oscillations of the voltage or current per second. In this case, both oscillate in phase as if no capacitances and inductances were connected in the circuit. The formula applies to both an LC series and an LC parallel resonant circuit.

## Inductance

`$$ L $$`Unit

`$$ \mathrm{H} $$`

The inductance of the coil connected to the RLC circuit. The larger the inductance, the lower the resonant frequency.

## Capacitance

`$$ C $$`Unit

`$$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$`

Capacitance of the capacitor connected to the RLC circuit. The larger the capacitance, the lower the resonant frequency.