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A few years ago my refrigerator stopped working but the outlet was fine. I could get the refrigerator working by plugging in a space heater in my bedroom but the space heater didn’t put out much heat. My electric stove and water heater was working fine. As where my lights and other small appliances.

What was wrong?

Basically, what happened is the power company was working on the line and disconnected the center tap on the utility transformer from the ground temporarily. 240 volts worked fine, and more less loaded half of 120-volt split phase worked normally, while the more loaded half of the phase only passed as much current as the less loaded portion of the split phase.
 
With split phase, if the center tap is disconnected, the maximum amperage that can flow is equal to what is on both sides of the phase. So the heavier load on phase “A” will only be able to pass as much current, and therefore voltage, as phase “B”. If you are pulling 34 amps on phase “A” and 10 amps on phase “B”, the center tap is returning the 24 amps not pulled on phase “B”. No center tap, then phase “A” can only pull 10 amps. As voltage is current times resistance, as the current reduces, so does voltage.
 
So the refrigerator wasn’t getting enough voltage to run, without space heater providing a return path to utility transformer. Split phase transformers rely on their center tap to balance out current between the split phases.

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