What size bleeder resistor is best for a Run Capacitor, 440V AC, Microfarad 30, 60/50hz ?
The AC unit is a Trane Executive BTD736A100B0.
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I found a replacement capacitor for your unit on Repair clinic. It does not show a resistor connected to the terminals. Old AC units and even ceiling fans used bleeder resistors on start capacitors to drain them once they were removed from the circuit. Run capacitors normally didn't have them.
I am not associated in any way with Repair Clinic.
The bleed resistor is not needed. Bleed resistors serve only to gradually discharge voltage on the capacitor when it is not being used by the circuit, in this case, the motor. It will not affect the performance of the motor. The purpose of a bleed resistor is safety: a capacitor stores electrical energy even after the power is turned off, and that can put a high voltage >350 VDC with substantial current behind it on the associated wiring. You think there's nothing live because you disconnected the power, so you could get a bad shock. It might not last long enough to electrocute you, but you might flinch and cut your hand on something sharp. Standard practice for HVAC techs is to remove AC power, then short the capacitor terminals (say, with screwdriver) to discharge it before touching anything else. Since they are trained this way, there's no need for bleed resistors for most (~all) HVAC motor capacitors. Furthermore, your resistor was not installed correctly: the wire ends were wrapped around the terminals, rather than by crimped on quick disconnect terminals. That makes me think it was installed by someone who didn't know what s/he was doing. I would remove it. Replacing the capacitor is easy, but you do want to match three things: the capacitance (mFd), the voltage (VAC, you can replace with higher but not lower), and whether it is a start or run capacitor. (Many caps combine both into the same package.) BTW, it's best practice to store unused capacitors with a shorting wire across the terminals. This ensures there is no stored voltage, and signals same to anyone handling them.
I think you're looking for a resistor vaguely like TE's ROX series. Most manufacturers make them about the same size, so you should be able to infer wattage from physical dimensions: 0.5W is 10mm, 1W is 12mm, and 2W is 16mm.
Those stripes are standard "color codes" for resistors. But something is wrong. Yours seem to be Gray, Black, White, Silver. (and I am sure silver is last; silver/gold indicate tolerance.) That would indicate 80,000 megaohms or 80 Gohms.
80 G Ohms doesn't make any sense because it's not a standard size (first digits of 10 12 15 18 22 27 33 39 47 56 68 82 are standard sizes) and it seems way too high-value to discharge in any reasonable time. I wonder if the colors have been faded by the weather or overheating. It was horked on there in a pretty lame way, I wonder if an amateur picked a bad combination of value and wattage, and it overheated. Ohm's Law
Voltage drop = Current x Resistance
will tell you how much current it'll flow in-circuit. Watt's Law
Power = Voltage x Current
will tell you how much power the resistor must dissipate.