The run capacitor.

A capacitor stores an electrical charge and releases it in a shove. Motors in an air conditioner need that shove to start, and a run capacitor keeps feeding them a smaller version of it while they run.

Physically it is a metal cylinder about the size of a soda can, sitting inside the electrical compartment. A dual run capacitor serves two motors at once, which is why it has three terminals rather than two: one for the compressor, one for the fan, and a common.

Why this part, in this city

Capacitors are rated for a temperature range and they age out of it. Phoenix runs them at the top of that range for five months a year, so they fail here years sooner than the same part fails in a milder climate. That is not a sign you were sold junk. It is the climate.

It is the single most common part failure through a Valley summer.

Reading the can

Capacitors are rated in microfarads, written as MFD or uF, and in volts. Both numbers are printed on the top. A dual shows two values, like 45 + 5.

A healthy one measures within about six percent of its rating. A failing one measures low, and a dead one measures nothing. That measurement takes a minute with a meter, which is why it is on the check-up list.

Do not open the panel

A capacitor holds its charge after the power is off. It does not care that the disconnect is pulled. People are genuinely hurt discharging one across a hand, and buying the wrong microfarad rating will cook the motor it was supposed to be starting.

For a part this cheap, it is not worth it. The price depends on which motor it serves and whether the unit is on the ground or a roof, and both are published before you book.