Is it safe if there are 3 wires black white bare copper at your breaker panel but only 2 wires at the wall socket outlet?

for USA, Canada and other countries running a 60 Hz supply service.Some appliances, especially older ones, don't have a ground wire. Also, a lot of wiring circuits in older houses were installed without using a ground wire to each socket outlet. They just ran a hot and a neutral wire. The neutral wire is grounded at the breaker panel.

On the breaker panel the 3rd wire - colored green or just bare - is the Ground wire. It is there to protect circuits - different to the one you are looking at - which need to have a ground wire as well as a neutral. On such circuits, in case of a fault condition in the appliances connected to them, a short circuit is sent to ground so that the circuit breakers on the hot wires should then trip to break the power supply to such circuits and stop a house fire or someone getting killed by electricity.

This is not a full answer to your question. You still have to think about which types of appliances - having plugs with only 2 prongs on their flexible cords - are still quite safe to use and which types are definitely not safe to use with that type of socket outlet - and in that situation, what should be done to make them safe?

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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.