I'm toying with the idea of making a rail gun (just for fun I don't want to kill anyone) but I can't get my head around some of the formulae. Could someone please help me?
Discharge occurs in two separate phases, the initial discharge which is essentially the first part of a sinewave, then the freewheeling which is an exponential decay as the inductor's feild collapses causing power to be dissipated in D and R.
Firstly are my existing equations correct?
Phase 1:
[latex]f_0 = \frac {1}{2 \pi}{\sqrt{\frac{1}{LC}-\frac{R^2}{L^2}}[/latex]
[latex]v = V sin (\omega t) e^{\frac{-R}{2L}t}[/latex]
Does anyone know how to calculate i or even I?
I've worked out that if R = 0 then:
[latex]I = \sqrt{\frac{CV^2}{L}}[/latex]
However this isn't the case if I introduce R.
If I can calculate I then i should be easy.
[latex]i = I sin(\omega t)e^{\frac{-R}{2L}t}[/latex]
Phase 2:
I understand that this should be the same as the current in an inductor decaying through a resistor, but what about the voltage drop across D?
Please don't point be to a Wikipedia artical on LRC circuits, or differential calculus, because I've read them both and I don't fully understand either. I've touched on this stuff at college but the lecturer was poor and I didn't any point in learning it anyway so I scraped though with the lowest grad for that section and now I'd forgotton what little I knew.
However I don't what you to just give me the answer but how to come to the answer and no this isn't coursework.