Re: Timing of a single cap disharge

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-uswest-dot-net>" <jimlux-at-earthlink-dot-net>

Classic RLC circuit analysis.  There are several situations to consider.

First, if the resistance is very small, then a good model for the discharge
time will be the 1/4 cycle time of the resonant frequency (1/(2 * pi *
sqrt(LC)).  This also gives you the SHORTEST POSSIBLE rise time.  In your
case f= 850 Hz, so the minimum rise time to peak current is going to be
around 0.3 milliseconds.

As the resistance starts to get bigger, it starts to look more like a RC,
where the time constant is the familar RC. (0.2 milliseconds in your circuit).

You are in the horrible situation where you have an almost critically
damped circuit, in which case the calculation is much more complex.

here you go with the general case of a R, L, C, and a battery in series.

i(t) = exp(-R*t/(2*L))*(
	2*(Eb-E0)-R*I0)/(R*sqrt(D)) * sinh(R*t/(2*L)) * sqrt(D) +
         I0 * cosh(R*t/(2*L)*sqrt(D))

D = 1- (4*L/ (R^2*C)

I0 is initial current
E0 is the initial voltage across the cap

You can simplify a bit by assuming I0 =0 and Eb = 0
The D parameter is the critical one... If D = 0, then the circuit is
critically damped.  If D<0 then the circuit is oscillatory (and, if R not
zero, damped) (much like a TC). If D>0 then the circuit is overdamped.

I find that an excel spread sheet helps a bunch on this stuff...
	


Tesla list wrote:
> 
> Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>"
<Fucian-at-aol-dot-com>
> 
> Hi, all can anyone help me determine the time of a disharge?Say if i have a
> 450volt 7000uF cap and I have a 5uH coil and total resistance(SCR wiring and
> ESR of cap) is about.03 ohms.How do I determine the a single pulse time?How
> quickly will the current rise?
> 
> Matt