resonance frequency formula meaning

[yefj]

Hello,There is a formula

ω0=√LCω0=LC​

which is used bellow.
Why why resonance frequency has such expression?
Thanks.

 

[FvM]

The resonance frequency formula is wrong, where did you get it? Please compare https://en.wikipedia.org/wiki/LC_circuit

 

[danadakk]

I think formula is correct -

Z = R + jwL -j/wC
= R + jwL/jwL( jwL - j/wC)
= R + jwL( jwL/jwL - j/jwLwC)
= R + jwL( 1 - 1/w²LC)

but w₀² = 1/LC resonance when Xl = Xc

So Z = R + jwL( 1 - w₀²/w²)

Resonance Z = R when w₀² = w²


Regards, Dana.

 

[c_mitra]

ω0=√LCω0=LC

Where did you find this?

The correct expression is w0=(LC)^(-1/2)

First convince yourself using a dimensional analysis.

Then of course you will get (w0)^2=1/(LC)

When the external frequency (w) is equal to the natural frequency (w0), the term in the parenthesis vanishes and Z =R (resistive)
When external freq w is much greater than w0, Z is apparently inductive and when w is much smaller than w0, Z is apparently capacitive.

 

[FvM]

The original post showed a wrong formula \( \omega_0 = \sqrt{\frac{L}{C}} \)
apparently the post has been later edited.

 

[danadakk]

https://www.edaboard.com/threads/in-a-series-lc-circuit-what-is-sqrt-l-c.307210/