The second step
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With an ignition coil we need a voltage that are reasonable high and oscillating (AC).
We need typical 250 volt and a frequency that the ignition coil can transform to a higher voltage.
With too high voltage over the points it will destroy the points, and also it will be a spark over the points where a lot of the energy that are loaded in the ignition coil will be lost.
Too low voltage will not generate enough voltage to the spark plug.
We also need an oscillating voltage AC. This is created with the capacitor C and the coil L that created a LC circuit. When breaking the current that is going throw the coil we generated a high voltage that load up the capacitor. The voltage from one side of the capacitor will go via the coil and the battery to the other side of the capacitor. This going back and forth and will be repeated as long there is any voltage left in the circuit (energy). This creating an AC current (voltage) that the ignition coil is needed to transferee the voltage to the spark plug. This LC circuit is the same as a radio transmitter was using if it was of the old style. The difference is that the AC current dies out when the charge of the ignition coil is transferred to the spark plug. This will be repeated the next time the ignition coil is charged via the closed break points and the points is opened again.
A typical circuit of an ignition system:
A normal picture on an oscilloscope is looking like this.
Note the initial voltage of 234V.
On the left side you see the AC voltage on the input side of the ignition coil.
The AC voltage creating the high voltage out to the spark plug.
The effect of different capacitors
Normally the capacitor is of 0.2uF (micro farad) and it need the handle at least 400V AC.
This picture showing the differences with different capacitors.
The highest voltage is with a 0.1uF (left), the middle is with a 0.2uF and the lowest (right) with a 0.3uF capacitor.
This proof the formula U=L*d//dt, dt (lager capacitor)will generate a lower voltage as noted before Note also a slight difference of the AC frequency between the different capacitors.
The left has a higher frequency compare with the right one. A smaller capacitor will generate a higher frequency.