Tuned Circuit Resonance Formula

Here are some simple steps to derive the resonance formula for a parallel LC circuit of an AM radio.

Inductive Reactance XL

This is the formula for inductive reactance XL.

Capacitive Reactance XC

This is the formula for capacitive reactance XC.

At resonance XL = XC therefore we can derive the resonant frequency formula as follows.

Capacitive Reactance XC
Transposition Step
The resonance formula.

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Transpose Resonant Frequency Formula
Tuned Circuit Example 1
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Tuned Circuit Example 3