Proof of natural frequency in RCL circuit

AI Thread Summary
The equation 2*pi*f = 1/√(LC) describes the resonant frequency of an ideal RCL circuit, derived from the differential equation governing charge flow. The resonant frequency occurs when the inductive reactance (XL) equals the capacitive reactance (Xc). This condition is expressed as 2∏fL = 1/2∏fC, which leads to the voltage being in phase with the current. Resources were shared to further explain the differential equation related to this topic. Understanding these relationships is crucial for analyzing RCL circuits effectively.
alanchakhin
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I am just wondering what is the proof of the equation
2*pi*f = 1/√(LC)
 
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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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