Based on the information provided, it seems that there was a serious electrical issue when the power was turned back on after replacing the capacitor on your outside A/C unit. The sparks and smoking black smoke indicate a significant problem.
Several potential issues could have caused this:
Incorrect Installation: If the capacitor was not installed correctly, it could have caused a short circuit or damaged some of the electrical components, leading to sparks and smoke.
Wiring Problems: During the capacitor replacement, the wiring might have been improperly connected or touched other components, causing a short circuit.
Faulty Capacitor: It's possible that the replacement capacitor was defective or of the wrong specifications, which could have caused a malfunction when the power was restored.
Other Damaged Components: The initial issue that prompted the capacitor replacement might have been related to other faulty components in the A/C unit. Replacing the capacitor alone might not have solved the root problem, leading to further issues when the power was turned back on.
Regardless of the specific cause, the A/C unit's failure to work after the incident suggests that there has been substantial damage. In this situation, it is best to avoid attempting any further repairs or investigation yourself, as dealing with electrical systems can be dangerous without proper knowledge and training.
Your best course of action is to immediately turn off the power to the A/C unit and contact a professional HVAC technician or an electrician to inspect and repair the system. They have the expertise and tools to diagnose the issue accurately and safely make the necessary repairs to get your A/C unit up and running again. It is essential not to continue attempting to use the A/C unit until it has been properly inspected and repaired to avoid any further damage or safety hazards.