The smaller cylindrical object on the starter motor is a solenoid
(high power electromagnet plus a high amperage switch).
It has two functions:
- engages the drive pinion on the starter driveshaft and meshes
the pinion with the ring gear on the flywheel
- when the mesh is complete it closing the high amp contacts,
letting the current flow through the starter motor.
The ignition switch is not capable to handle the starter motor's
current, therefore the ignition switch enables the strater solenoid only.
The starter motor initial current is around 320 Ampers, the running
amps around 70-85 Ampers (while cranking). The solenoid draws
another 10-16 Ampers during cranking. These currents would require
a really huge capacitor (at least 5 Farad - not microFarad).
And huge capacitors also have enormous initial currents too.