# Re: A question about LCR circuits

```Subject:     Re: A question about LCR circuits
Date: Fri, 16 May 1997 07:47:22 +1200
From: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization: Wellington Polytechnic, NZ
To:  tesla-at-pupman-dot-com

John, (and anyone interested),

>   You show that   Q = sqrt(L/C)/R   Where did you find this equation?

I showed the derivation in this very place not two months ago.
Take Q = wl/R, Q = 1/wLC
Multiply them to give Q^2 = wl/R x 1/wLC
do the algebra, then take the square root.

>   As Z = sqrt(L/C)  this gives       Q = Z/R = cos A
>   Now I have often seen that   Q = X/R = Tan A   in the literature but
> not
>                 Q = Z/R = cos A
>   The Q factor cannot equal both cos A and tan A.

I think you may be confusing impedance and Q?

>   You indicate that the effective resistance (for Tesla coils?) is
> easily
> measured. Would you explain this test?

Measure the Q of a coil. The R that pops out of Q= whichever one of
the formulae you like to use is the ESR. For high Q air-cored coils it
is heavily dependent on the proximity to surroundings.

>   I agree with you that my last sentences regarding critical
> damping and Q
> below 0.5 were confusing and in partial error. If my description of what
> I
> thought I said was followed you would always arrive at Q = 0.5 which is
> what
> you pointed out at the beginning of this dissertation.
>
>   Tesla List appreciates that you are helping further the progress of
> Tesla
> coil understanding. Do not feel upset that it results in controversy
> because
> you are not alone. Many contributors to Tesla List including me run into
> the
> same difficulties.
>
>   John Couture

Fair enough.
Regards,
Malcolm

```