could the sync (the delay, when you depress the shutter button, between the firing of the flash and the actual opening of the shutter - for example about 20 ms for M3 bulbs, allowing the burning bulb to reach peak power before the picture is taken) be affected when using just the battery without a capacitor?
I am puzzled by your results, as the switching characteristics of the shutter should not be affected by shutter speed setting.
(To my understanding. Maybe though in your case the switching time is proportional to the shutter speed.)
However, the internal resistance of a batterie is greater than that of a capacitator. In case the sync switch for whatever reason closes only for a very short time, the battery in that time might not deliver enough energy to heat up that wire in the bulb.
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