Re: Reactive impedance question

On Wed, 5 Oct 2005 16:12:25 -0500, "Tim Williams" <tmoranwms@xxxxxxxxxxx> wrote:

>"The Phantom" <phantom@xxxxxxx> wrote in message
>news:u8r7k110llvljemldmvr60qfstgt224mig@xxxxxxxxxx
>> (4*f^2*L^2*Pi^2+R^2-8*C*f^2*L*Pi^2*R^2+16*C^2*f^4*L^2*Pi^4*R^2)
>> SQRT(-------------------------------------------------------------)
>> ( 1+4*C^2*f^2*Pi^2*R^2 )
>
>I've been looking at this today. Some algebra finds:
> sqrt[1 - 2(C/L) + (2piFC)^2]
>Z = 2piFRL ------------------------------
> sqrt[1 + (2piFRC)^2]

This would be correct if you hadn't taken the operator in front of the first R^2 in the
numerator to be a * instead of a +.

>
>I may be wrong on something in that long expression, but at any rate, in
>your original equation, Z goes to zero as R goes to zero, no matter what the
>frequency is (R^2 is a common term in the numerator radical).

Look more closely; the 4 terms in the numerator are:

4*f^2*L^2*Pi^2

+R^2

-8*C*f^2*L*Pi^2*R^2

+16*C^2*f^4*L^2*Pi^4*R^2

>I know
>matter-of-factly this circuit will show an R-limited peak in current (i.e.,
>Z local minima) at resonance, whereas the above equation ultimately has F to
>the first power (showing no resonance).
>
>And you're certain that the above equation is the real derivation of the
>imaginary equation, which is also correct?

It is correct.

>This is rather curious...
>
>Tim

.

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