This document shows the mathematical steps to derive the formula for the resonant frequency of an LC circuit. It starts with the equations for inductive and capacitive reactance and sets them equal since at resonance they cancel each other out. It then performs algebraic manipulations to isolate the frequency term and derives the final formula that the resonant frequency is equal to 1 over 2π times the square root of the inductance times the capacitance.

4. XL = XC
2 π fR L =
1
2 π fR C

5. 2 π fR L x 2 π fR C = 1

6. (2 π fR)² x L C = 1

7. (2 π fR x L C = 1
) 2
12 1 2
2 π fR x √ L C = 1

8. 2 π fR =
1
√ (L C)

9. fR =
1
2 π √ (L C)