this is why the run cap is there
Ok the run cap acts as a limit on the current entering the start winding. This is why it there.
If you connect the start winding across the 240 volts with no cap the winding will burn up due to excess current.
Yes there is phase change due to the cap, but the current flowing in the start winding is limited by the cap.
Here is why inside the cap are to plates of aluminum foil separated by an insulating material. There is oil also to help dissipate heat from the cap charging and discharging. Not motor heat.
Ok here is what happens as the motor runs current flows through the start windings of the motor (here is the cap next to it in series so the same current flows through it) the current builds on the cap plates and charges it as charges its voltage increases and approaches line voltage it limits the current in the start winding. When the cap has the same voltage as line no current will flow and the windings donít burn.
Now donít forget current direction changes in alternating current voltages and so does voltage.
The voltage changes direction and so does the current. Well now the charge built on the cap flows through the start windings in the opposite direction till the new and opposite voltage builds on the plates and again limits current.
Here is why matching capacitance is important.
If you install too large a cap more current flows through start windings because the aluminum plates are larger and hold more charge. This can be enough excess current to burn the windings.
If the cap is too small not enough current will flow through the start winding and it will contribute reduced power to the motor.
The start cap is there allowing extra current for start up and then quickly removed from circuit before winding burn from current.
So if you think about it its is in parallel so it adds cap to winding for the short starting period and then its removed leaving only the capacitance of the run cap.