# 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

##### Super Moderator
Staff member

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.

### yefj

Points: 2

#### 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.

Last edited:

#### FvM

##### Super Moderator
Staff member
The original post showed a wrong formula $$\omega_0 = \sqrt{\frac{L}{C}}$$
apparently the post has been later edited.