Question

How do you calculate the resonant frequency of an RLC circuit?

Answer 1

To calculate the resonant frequency of an RLC circuit, you need to consider the values of its components: the resistance (R), the inductance (L), and the capacitance (C). The resonant frequency is the frequency at which the impedance of the circuit is purely resistive, meaning there is no reactive component (inductive or capacitive). In other words, the impedance is at its minimum value at the resonant frequency.

The resonant frequency of an RLC circuit can be calculated using the formula:


res
=
1
2



f
res
    ​

=
2π
LC
    ​

1
    ​


Where:


res
f
res
    ​

 is the resonant frequency in Hertz (Hz).

L is the inductance of the inductor in Henrys (H).

C is the capacitance of the capacitor in Farads (F).

π is the mathematical constant pi, approximately equal to 3.14159.

To use the formula, make sure that the units of inductance and capacitance match (e.g., both in microhenrys and microfarads or both in henrys and farads).

Keep in mind that there are two types of resonant frequencies in an RLC circuit:

Series RLC circuit: In this configuration, the inductor (L), capacitor (C), and resistor (R) are connected in series. The resonant frequency is as calculated above.

Parallel RLC circuit: In this configuration, the inductor (L), capacitor (C), and resistor (R) are connected in parallel. The resonant frequency (

res
f
res
    ​

) for the parallel RLC circuit is calculated using a slightly different formula:


res
=
1
2



f
res
    ​

=
2π
LC
    ​

1
    ​


The behavior of the circuit at and around the resonant frequency can vary depending on the circuit's configuration (series or parallel) and the relative values of

R,

L, and

C. For example, in a series RLC circuit, the current amplitude will be at its maximum at the resonant frequency, while in a parallel RLC circuit, the voltage across the circuit will be at its maximum at the resonant frequency.