RE: Piezo HV Power Supply

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

Original poster: "Jan Florian Wagner by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jwagner-at-cc.hut.fi>


> >>Your formula for energy is wrong in that it should be:
> >>joule = farad * volt^2
> Pete K.
> >Your formula for energy is incorrect.  The energy in a cap is:
> >Joules = farads times volts squared divided by two.
> Well, let's take a look at this.
> >From NIST http://physics.nist.gov/cuu/Units/units.html
<snip>
> Farad * Volt^2 = m-2*kg-1*s4*A2*m2*kg*s-3*A-1*m2*kg*s-3*A-1
> Farad * Volt^2 = s-2*m2*kg
> Farad * Volt^2 = joule

You should be aware that those are just the relations between _units_.
They are by no means the actual formulas! Numbers are without quantity,
thus 1/2 does not show up in the definition of the unit.

For example, energy is Joules = [E] = [ [(m^2)/s^3]*kg ] = [ N*m ] in
units, whereas the formulas for energy vary according to case. 

For a capacitor, 
 E = integral ( dQ/C ) = 0.5 * Q^2 / C
 and beacause charge of a capacitor is Q = C*U , we get
 E = 0.5 * C * U^2
 (which is, because Q=I*t, the work done over time to move charge into
 the capacitor)

For an inductor, it is, via similar integration
 E = 0.5 * L * I^2

That integration part is where the 1/2 factor comes from. 

Numbers are without quantity, thus they are not part of the unit for E
(Joule=Farad*Volt^2) i.e. for energy.

There's a heap more of energy definitions for static and dynamic field
theory at:
 http://www-ibt.etec.uni-karlsruhe.de/postscript/encf_3.pdf

cheers,
 - Jan

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