# Resonant Frequency Formula

## Resonant Frequency Formula

Resonance is a concept in oscillatory motion. Resonant Frequency Formula is the natural frequency of an object or system at which it reaches its maximum vibration level. In electrical systems, the Resonant Frequency Formula is defined as the frequency at which the transfer function reaches its maximum value. Therefore, for a given input, we can get the maximum output. It has been proven that resonance is obtained when the capacitive and inductive impedance values are equal. This article uses an example to explain the formula for Resonant Frequency Formula. Students can visit the Extramarks website for more information.

### Resonant Frequency Formula

The Resonant Frequency Formula is defined as the frequency of the circuit at which the capacitive and inductive impedance values are equal. It is defined as the frequency at which an object or system reaches its highest level of vibration. A resonant circuit consists of a capacitor and an inductance connected in parallel. It is mainly used to generate specific frequencies or look up specific frequencies in complex circuits. A Resonant Frequency Formula exists only if the circuit is purely resistive.

### method

The Resonant Frequency Formula is the reciprocal of the product of twice pi and the square root of the product of inductance and capacitance. Represented by the symbol f. Its standard unit of measurement is hertz or per second (Hz or s-1) and its dimensional formula is given by [M0L0T-1].

The Resonant Frequency Formula is the natural frequency of vibration of the object and is usually denoted by f (f0) with a zero subscript. This type of resonance occurs when an object is in equilibrium with an applied force and, under ideal conditions, can oscillate for long periods of time. The resonant frequency of a single continuous wave is given by the formula v = λf. The letter ‘v’ represents the wave velocity, and ‘λ’ represents the wavelength interval. This formula states that the wave velocity is equal to the wavelength spacing multiplied by the Resonant Frequency Formula. Manipulating this equation, the resonant frequency is equal to the wave velocity divided by the wavelength spacing.

### Concept Of Resonance Frequency

The Resonant Frequency Formula is the frequency at which the circuit resonates. A resonant circuit is also called an LC circuit or an oscillating circuit. This circuit contains an inductor and a capacitor connected in parallel with each other. A resonant circuit is used to generate a specific frequency or to select a specific frequency from a complex circuit.

### The Formula For Resonant Frequency:

Resonance frequency formula:

So the Resonant Frequency Formula is:

f0=12πLC√

where f0 is the resonant frequency represented by , the inductance is L and the capacitance is C.

### Derivation:

Consider the following series connection: R, L, and C.This series circuit is energised by the AC power supply.

First, let’s calculate the impedance Z of the circuit.

Z=R+jωL-jωC

Z=R+j(ωL–1ωC)

At resonance, the circuit is purely resistive. This means that the imaginary part of impedance Z is zero at resonance or at resonance frequency. This should always be kept in mind when calculating the resonant frequency of a particular circuit. this means,

ωL-1ωC=0

ωL=1ωC

yes,

ω2=1LC

Similarly

ω=12πf

i.e. f = 12πω

After substituting the values:

f0=12π(√LC)

The resonant frequency is therefore f_0 of the resonant circuit.

f0=12πLC√

### Solved Examples

Q.1: Given an electrical circuit, determine the resonant frequency of this circuit. The inductance is 25mH and the capacitance is 5μF?

The parameters specified in the question are:

L=50mH=50×10-3H

C=5μF=5×10−6F

The formula for resonant frequency is:

f0=12πLC√

Substituting the values ​​in the above expression, we get

f0=12π50×10−3×5×10−6√

f0=12π×5×10−4

f0 = 318.47Hz

Therefore, the resonant frequency is 318.47 Hz.