# Proof of natural frequency in RCL circuit

• alanchakhin
In summary, the natural frequency in an RCL circuit is the frequency at which the circuit resonates without any external input. It can be calculated using the equation f<sub>0</sub> = 1/(2&pi;&radic;(LC)) and is important because it determines the behavior of the circuit. At the natural frequency, the circuit will have maximum energy and will resonate, resulting in a larger output signal. The natural frequency can be changed by altering the values of the inductor and capacitor, as well as the presence of a resistor in the circuit.
alanchakhin
I am just wondering what is the proof of the equation
2*pi*f = 1/√(LC)

Welcome to PF;
The relation is derived from the differential equation describing the flow of charge in an ideal RCL circuit.

So what is the differential equation describing the flow of charge in an ideal RCL circuit?

I was going to suggest this one - but that works too. :)

The resonant frequency is when XL = Xc
That is when 2∏fL = 1/2∏fC
When this condition is satisfied V is in phase with I.

## 1. What is a natural frequency in an RCL circuit?

The natural frequency in an RCL (resistor-capacitor-inductor) circuit is the frequency at which the circuit resonates without any external input. This means that the circuit naturally oscillates at this frequency when powered by a constant source.

## 2. How is the natural frequency calculated in an RCL circuit?

The natural frequency in an RCL circuit can be calculated using the equation f0 = 1/(2π√(LC)), where f0 is the natural frequency, L is the inductance in henries, and C is the capacitance in farads.

## 3. What is the significance of the natural frequency in an RCL circuit?

The natural frequency in an RCL circuit is important because it determines the behavior of the circuit. At this frequency, the circuit will have maximum energy and will resonate, resulting in a larger output signal. It is also used in various applications such as filters, amplifiers, and oscillators.

## 4. How does the natural frequency affect the output of an RCL circuit?

The natural frequency directly affects the output of an RCL circuit. At the natural frequency, the output of the circuit will be at its maximum, resulting in a larger signal. If the input frequency is close to the natural frequency, the output will still be amplified, but not as much as at the natural frequency.

## 5. Can the natural frequency in an RCL circuit be changed?

Yes, the natural frequency in an RCL circuit can be changed by altering the values of the inductor and capacitor. Increasing the inductance or capacitance will decrease the natural frequency, while decreasing either will increase the natural frequency. Additionally, the presence of a resistor in the circuit can also affect the natural frequency.

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