Is it technicaly necesary to put resistor parallel to ac capaci2r when conected to motor compresor or ac motr? I ned answer on the effects to the motor being connected to it (and running).
Some motors need a motor starting capacitor in series with one winding to create a phase difference in the magnetic fields and start the motor turning. In some motors that AC capacitor is switched out automatically after the motor gets up to speed. If you mean that capacitor then the answer is definitely NO.
The resistor is there to discharge the capacitor after disconnecting the power. It usually has a large resistance (470kΩ or 1MΩ are common values) and its effect is negligible in comparison to the reactance of the capacitor. It's necessary if there is a plug and socket connection anywhere in the circuit, because there would be a current path through the windings of the motor to the pins of the plug -- which could potentially be touched, giving someone a nasty surprise. And it's polite to fit it even if there isn't a plug and socket connection, because anyone working on the installation might think it OK to touch the motor terminals if they were isolated from the supply.
The resistor you refer to is a bleed resistor. it is a safety item to slowly bleed off the charge on the capacitor so that service technitians do not inadvertently electrocute themselves. Additionally many of these capacitors have enough charge on them to melt the internal connections to the capacitor if they are shorted. at a minimum this would destroy the capacitor and it could even cause the cap to burst. A bleed resistor (which is often internal to the capacitor) prevents that from occurring.