Which is the ground wire and which carries 120V on an old 240V welder that needs a new plug at the end of the power cord if the wire colors under the outer insulation are white green and black?

Answer 1

If you only have 3 wires you don't have the fourth wire for 120V. Since this is a 240V only device it doesn't need it. Black and white are your hots and green is ground.

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As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.

Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized.

IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.

Answer 2

The green wire is the ground wire, the white wire is neutral, and the black wire carries 120V. Connect the green wire to the ground terminal, the white wire to the neutral terminal, and the black wire to one of the hot terminals on your new plug for the welder.