Proof of natural frequency in RCL circuit

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Discussion Overview

The discussion revolves around the proof of the equation for natural frequency in an RCL circuit, specifically the relationship 2*pi*f = 1/√(LC). Participants explore the underlying differential equation and conditions for resonance in the circuit.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the proof of the equation relating natural frequency to inductance and capacitance.
  • Another participant states that the relation is derived from the differential equation governing charge flow in an ideal RCL circuit.
  • A subsequent participant asks for clarification on what the differential equation is.
  • Some participants share links to resources that may provide the needed information regarding the differential equation.
  • One participant mentions that resonance occurs when the inductive reactance equals the capacitive reactance, leading to a specific condition involving frequency.

Areas of Agreement / Disagreement

The discussion includes multiple viewpoints regarding the proof and derivation of the equation, with no consensus reached on the specific form of the differential equation or its implications.

Contextual Notes

Participants reference external resources for clarification, indicating potential limitations in their current understanding or access to information about the differential equation.

alanchakhin
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I am just wondering what is the proof of the equation
2*pi*f = 1/√(LC)
 
Physics news on Phys.org
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.
 

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