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## Main Question or Discussion Point

the solution for current I, for series LCR circuit is

I = (E/Z)sin(wt+[tex]\phi[/tex])

Where Z = [tex]\sqrt{R^2 + (X_{L}-X_{C})^{2}}[/tex]

So for Resonance (i.e. maximum Current Amplitude) of LCR Circuit the necessary condition seems to be

[tex]X_{L}[/tex]=[tex]X_{C}[/tex]

Which gives [tex]\omega[/tex]=1/[tex]\sqrt{LC}[/tex]

But some text-books and wikipaedia have given that the damped resonace frequency is

where

How is this relation Derived ?

I = (E/Z)sin(wt+[tex]\phi[/tex])

Where Z = [tex]\sqrt{R^2 + (X_{L}-X_{C})^{2}}[/tex]

So for Resonance (i.e. maximum Current Amplitude) of LCR Circuit the necessary condition seems to be

[tex]X_{L}[/tex]=[tex]X_{C}[/tex]

Which gives [tex]\omega[/tex]=1/[tex]\sqrt{LC}[/tex]

But some text-books and wikipaedia have given that the damped resonace frequency is

where

How is this relation Derived ?

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