How do you calculate the resonant frequency of a series RLC circuit?

The resonant frequency (f₀) of a series RLC circuit is the frequency at which the inductive reactance (XL) and capacitive reactance (XC) are equal in magnitude and opposite in sign. At this frequency, the total impedance of the circuit is purely resistive, and the current flow is at its maximum.

Here's how you can calculate the resonant frequency:

Calculate the inductive reactance (XL):

XL = 2πfL

where:

XL is the inductive reactance in ohms (Ω)

f is the frequency in Hertz (Hz)

L is the inductance in henries (H)

Calculate the capacitive reactance (XC):

XC = 1 / (2πfC)

where:

XC is the capacitive reactance in ohms (Ω)

f is the frequency in Hertz (Hz)

C is the capacitance in farads (F)

Set XL equal to XC and solve for the resonant frequency (f₀):

2πf₀L = 1 / (2πf₀C)

Solve for f₀:

f₀ = 1 / (2π√(LC))

Now you have the formula for the resonant frequency (f₀) of the series RLC circuit. To use this formula, simply plug in the values of inductance (L) and capacitance (C) into the equation, and you will obtain the resonant frequency in Hertz (Hz). Keep in mind that the units of L and C must be in henries (H) and farads (F), respectively, to get the result in Hertz.

res

=

1

2

f

res

=

2π

LC

1

Where:

res

f

res

= Resonant frequency in Hertz (Hz)

L = Inductance of the coil in Henries (H)

C = Capacitance of the capacitor in Farads (F)

π (pi) = A mathematical constant approximately equal to 3.14159

To find the resonant frequency, you need to know the values of the inductance (

L) and capacitance (

C) components of the series RLC circuit. Once you have these values, you can plug them into the formula and calculate the resonant frequency in Hertz.

It's worth noting that the resonant frequency is the frequency at which the impedance of the circuit is purely resistive, meaning that the reactive components (inductive and capacitive reactance) cancel each other out. At the resonant frequency, the series RLC circuit exhibits maximum current amplitude and minimum impedance.