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The wiring to my garage is a single 20 amp breaker wired with AWG 14 gauge wire. When I turn on my table saw, it starts up but the reset button pops and the lights flicker. I have attached the saw to the first outlet coming into the garage to shorten the distance from the box, but I am seeing no difference.

Is the wire under powered for the 20 amp breaker?

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    In the interim, replace the 20 ampere breaker with a 15 ampere breaker. This will protect the wiring, and reduce the chances of starting a fire. – Tester101 May 3 '15 at 14:14
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Yes, the wire is undersized for 20 amps - 12 gauge copper is code minimum for 20 amps - if the run is long, 10 gauge can be a smart choice, if it's very long a larger size feed (30 - 60 amps at 240V) to a subpanel run on aluminum wire of much larger size quickly makes financial sense given the relative prices of aluminum and copper.

The cycle in effect is that the motor draws a large amount of current when it starts, and that drops the voltage on the undersized wire, and that makes the motor want more current to maintain power. Since heating goes up as the square of current, the motor overheats and shuts down. Keeping the voltage up with adequately sized feed wires keeps the current more reasonable.

Rewiring to a 240V subpanel in the garage may also offer the option of switching the saw to 240V operation, which will reduce the current by half (and the heating by 3/4) so it will start more easily. Depends on the saw motor, but most have that option.

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What kind of table saw is this? What are the listed power requirements?

You may have a problem with the wiring other than it's being 14 AWG. I assume this is copper wiring, right? I would look for loose connections, such as failing backwire push-in connections. (Less likely, the breaker may be failing. Or the wire to the breaker or to the neutral bar may be loose.) Somebody put a 20-A breaker on a circuit wired in 14 AWG. What else wrong did they do?

Immediately install a 15-A breaker and when you do check the tightness of the neutral at the neutral bar, first for this specific circuit and then for all the circuits. When we moved into our tract house 38 years ago there were flickering lights in a hall. The problem turned out to be a loose neutral in the panel. The insulation on the 12 AWG aluminum conductor was burned and the conductor damaged.

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