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resonance frequency formula meaning

yefj

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Hello,There is a formula
ω0=√LCω0=LC​
which is used bellow.
Why why resonance frequency has such expression?
Thanks.

1619795269862.png
 

danadakk

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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

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c_mitra

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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.
 
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FvM

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

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