Most dead outlets are a tripped GFCI or breaker. Check those before anything else.
GFCI outlets cut power when they sense a fault, moisture or a worn device, and stay off until they're reset. Difficulty: Level 2: Getting Handy. Plan on 5 to 20 min.
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Press RESET firmly until it clicks.
If it won't reset, check the breaker panel for a tripped breaker.
If it resets and then trips again right away, unplug everything on it and try again.
Many outlets without buttons are protected by a GFCI somewhere else on the circuit, or by a breaker that tripped. Difficulty: Level 2: Getting Handy. Plan on 5 to 20 min.
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One GFCI outlet can protect other outlets down the line. Check and reset GFCIs in nearby bathrooms, the kitchen, garage, basement and outdoors.
Check the breaker panel. A tripped breaker sits in the middle or the OFF position. Push it fully OFF, then back ON.
Test the outlet with a lamp you know works or a plug-in tester.
Burning smells, scorch marks, buzzing and heat are signs of arcing or overheating, which can start a fire.
Unplug what you safely can, turn off the breaker for that circuit, and don't use the outlet until a licensed electrician checks it.
If the GFCI and breaker are fine but the outlet is still dead, or a breaker or GFCI keeps tripping, the problem is in the wiring or the device.
Opening outlets is Level 3 electrical work: breaker off and wires confirmed dead with a tester. If you aren't comfortable with that, call a licensed electrician.