tech99 said:
It is the rate of change of current in the primary, which creates such a high voltage. V = -L dI/dt. The capacitor speeds up the rate of change.
Indeed it's di/dt that causes high voltage in both the LV and HV windings.
Current can't drop to zero immediately for that would make infinite voltage(were the coil a perfect inductor)
and without a capacitor the voltage rises so fast that it establishes an arc across the points before they've moved far enough to make a decent air gap.
That's why
@Asymptotic's anecdote is so relevant.
Adding a capacitor let's flow of current continue, into the capacitor instead of through the points,
giving the points time to separate far enough they'll withstand a couple hundred volts.
Last car condenser i measured was 0.2 microfarads (my kids' 65 Buick)
and coil current was set to ~2 amps by the ballast resistor.
Now,
pumping 2 amps into 0.2 μF raises voltage by 10 volts per microsecond (##~i = c\frac{dv}{dt}~## )
giving the points a fraction of a milisecond to establish a small air gap before voltage across them rises high enough to strike an arc.
Dielectric strength of air is maybe 75 volts per mil (3 megavots per meter
https://hypertextbook.com/facts/2000/AliceHong.shtml )
and perhaps 30 to 40 megavolts per meter at very small gaps, see Paschen's Law
so using the lesser dielectric strength
a point gap of 0.018" should hold off at least 1350 volts
which with a 30::1 step up could hand 40kv to the sparkplug.
A plug with gap of 0.030 should require less than that to fire.
New CD systems charge a capacitor to high voltage (400 volts in Evinrude outboard motors I've worked on)
and connect that across the primary of a stepup transformer 'coilpack' .
They'll make higher voltage than these old systems we're discussing
and that's why new engines keep running when the spark plug electrode wears away and plug gap exceeds a hundred mils.
my observations - corrections welcome.
old jim