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.
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Normally it is a 20 amp using AWG 12/2 gauge wire. But it really depends on what size wire is on that circuit. If it is white AWG 14 gauge then use a 15 amp breaker. If it is yellow AWG 12 gauge then use a 20 amp breaker.
12 gauge underground wire or if you think you will ever add any devices to this circuit use 10 gauge.
The wire size depends on how much current it will conduct.
You listed no gauge wire. This is the required breakers.14 gauge - 15 amp12 gauge - 20 amp10 gauge - 30 amp8 gauge - 40 amp
The size of the wire is stated by its gauge under American Wire Gauge. Six gauge wire is size 6 AWG.