why 3 phase electricity instead of 4 or 5, etc?
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You can make a 3 phase system using only 3 wires. If you want a 4 phase system you need at least 4 wires, similarly 5 phases also need 4 wires. But you want the least amount of wires and then 3 phase is best, or in some application a single phase 2 wire system is used. The problem with a single phase system is that you can not start an electric motor using a simple single phase. With a single phase you can generate a magnetic field going up and down but you need it to also go side to side to get the motor to spin, so you need more phases. And that means you need more wires.
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