Re: A question about LCR circuits

To: tesla-at-poodle.pupman-dot-com
Subject: Re: A question about LCR circuits
From: Tesla List <tesla-at-stic-dot-net>
Date: Sun, 18 May 1997 23:36:59 -0500
Approved: tesla-at-stic-dot-net
Subject:       Re: A question about LCR circuits
       Date:   Mon, 19 May 1997 09:26:54 +1200
       From:   "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization:  Wellington Polytechnic, NZ
         To:   tesla-at-pupman-dot-com


John,
        The formula _does_ contain R.

>   From:  "John H. Couture" <couturejh-at-worldnet.att-dot-net>
>     To:  Tesla List <tesla-at-pupman-dot-com>
> 
> 
> At 05:26 AM 5/16/97 +0000, you wrote:
> >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
> >
> 
>   Malcolm -
> 
>   Regarding your reply to my post
> 
> ----------------------------------------------------
> 
> >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.
> >
> >----------------------------------------------
>  
>  I do not agree that your derivation and your equation Q = 1/wLC  are
> correct because an equation for the Q factor must contain a resistance
> (R).
> The Q equations of which I am aware are -
> 
>        Q = wL/R = 1/wCRs = Rp/wL = wCRp  
> 
> where Rs = series resistance and Rp = parallel resistance

OK, here goes (again):

Q = wL/Rs = 1/wCRs

Q^2 = wL/Rs x 1/wCRs

Q^2 = L/Rs x 1/CRs

Q^2 = L/C x 1/Rs^2

=> Q = SQRT(L/C)/Rs

This formula is indeed correct and appears in a number of texts.
 
Malcolm

> ------------------------------------------------
>  
> >>   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.
> >
> ----------------------------------------------------
> 
>   Thank you for the method to measure the effective resistance. Note
> that at
> the design stage for a Tesla coil that both the eff R and the Q factor
> are
> unknown. This presents a problem for anyone developing a TC computer
> program. The JHCTES TC program gets around this problem by using a graph
> shown in the TC Notebook. This graph is based on empirical data and
> seems to
> be working. However, it needs to be verified by other coilers willing
> and
> capable of doing the work or replacing it with a better method to find
> the Q
> and R for a classical TC.
> 
>  John Couture
> 
>