Derivation of self inductance formula in an LC circuit

[PratyashAstro]

My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor :

L = 1/(4π^2 . f^2 . C)

Here,
f = different resonant frequencies,
C = capacitance of the capacitor in the LC circuit.How can this be derived from the general formula of self inductance of a coil?

 

[berkeman]

My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor :

L = 1/(4π^2 . f^2 . C)

Here,
f = different resonant frequencies,
C = capacitance of the capacitor in the LC circuit.How can this be derived from the general formula of self inductance of a coil?

Welcome to the PF.

What reading have you been doing about this subject? Can you post some links to websites that discuss LC resonance?

 

[cnh1995]

My observation is to verify self inductance formula by measuring the resonant frequencies of different coils in an LC circuit.For this, I am asked to use this formula by my mentor :

L = 1/(4π^2 . f^2 . C)

Here,
f = different resonant frequencies,
C = capacitance of the capacitor in the LC circuit.How can this be derived from the general formula of self inductance of a coil?

What are you going to compare the experimental value (formula by your mentor)with? Is the inductance already known to you?