HVAC question

Yeah, I know, there's a group by that name devoted to abuse. Nevertheless:
Wingnut (who should have known better) hooked up a new compressor-unit blower motor to a non-split capacitor instead of the stand-alone variety capacitor.
Fried the blower motor.
My quest is for the basic reason(s) on what went wrong, that is, why would connecting the capacitor leads to a non-split capacitor (that's where the previous motor was connected) vary from a stand-alone capacitor on a PSC blower motor.
Thanks for adding to my store of probably never-needed-again knowledge.
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My first guess is that the capacitor must be matched to the starting winding so that current amplitude in that winding is high enough to produce the torque needed to turn the motor and its load, but not high enough to burn out the winding. Also the phase angle between the current in the main winding and the current in the starting winding must ideally approach 90 degrees. That phase angle is determined by the inductance of the winding but more so by the capacitance of the capacitor. Did the microfarad rating differ between the two capacitors?
Second guess . . . bad capacitor.

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