## Series resonance frequency formulas for LC, RC, RLC circuits

Resonance in electrical circuits occurs when the impedance (opposition to the flow of current) of the circuit reaches its minimum value, resulting in maximum current flow or voltage across the components. The resonant frequency is the frequency at which this condition occurs. The formulas for calculating the resonant frequency in LC (inductor-capacitor), RC (resistor-capacitor) and RLC (resistor-inductor-capacitor) circuits in resonance conditions are as follows. Series resonance formulas and resonant frequency calculators are useful tools in electrical and electronics for several reasons.

### Series resonance LC circuit

In LC circuit, inductor (L) and capacitor (C) are connected in series.
Resonance occurs when inductive reactance (XL) is equal to capacitive reactance (XC).
The resonant frequency formula for calculation in LC tank circuit is as follows.

f_{LC} = 1/(2*π(*L*C)^{0.5})

Where,

f_{LC} = Resonant frequency in Hertz (Hz)

L = Inductance of coil in Henrys (H)

C = Capacitance of the capacitor in Farads (F)

π = Mathematical constant approx. equal to 3.14159

### RC circuit (Series resonance)

In RC circuit, resistor (R) and capacitor (C) are connected in series.
Resonance occurs when impedance of the circuit is minimized.
The resonant frequency formula for calculation in RC tank circuit is as follows.

f_{RC} = 1/(2*π*R*C)

Where,

f_{RC} = Resonant frequency of RC series circuit in Hertz (Hz)

R = Resistance in Ohms

C = Capacitance in Farads (F)

π = Mathematical constant approx. equal to 3.14159

### Series resonance RLC circuit

In RLC circuit, resistor (R), inductor and capacitor (C) components
are connected in series.
In this circuit, resonance occurs when total impedance (Z) reaches its minimum value.
The resonant frequency formula for calculation in RLC circuit is as follows.

Resonant frequency f_{RLC} = 1/(2*π(*L*C)^{0.5})

In all these formulas, the resonant frequency is inversely proportional to the square root of the product of inductance (L) and capacitance (C) for LC and RLC circuits, while it is inversely proportional to the product of resistance (R) and capacitance (C) for RC circuits.

### LC and RLC Resonance Frequency calculator

Following calculator can be used to calculate resonant frequency of both LC and RLC series tank circuits as
there is same formula for both of these circuits.

➤Note : Enter values in INPUT boxes and Press CALCULATE button to check OUTPUT.

Example of RLC and LC Resonance Frequency calculation :

Inputs: Inductance (Henry) = 0.002, capacitance (Micro-farads) = 12

Output: Resonant frequency = 1027 Hz

### RC Resonant Frequency calculator

Following calculator can be used to calculate resonant frequency of RC series tank circuits.

Example of RC Resonance Frequency calculation :

Inputs: Resistance (Ohms) = 1000, capacitance (Micro-farads) = 10

Output: Resonant frequency = 15.92 Hz

**Conclusion** : The resonance frequency calculators and formulas help us to calculate the resonant frequency of
LC, RC, and RLC circuits which is useful in filter designs,
radio frequency tuning circuit designs and antenna design.

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