14-2 is rated for 15 Amp circuit. You can design a 15 Amp circuit to carry about 1440 Watts. The average outlet uses about 180 Watts and your pull chain is 60 Watts. You should have plenty of room on this circuit.
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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.
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