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I = W/E. Current is equal to Watts divided by Volts. 1500/120 = 13 amps. A #14 is rated at 15 amps. A conductor can only be loaded to 80% for a continuous load so 80% of 15 equals 12 amps. Too small for the 1500 watt load. A #12 conductor is rated at 20 amps times 80% equals 16 amps for a continuous load. To answer your question, no, a #16 conductor will not handle a 1500 watt load.

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Q: Will 16gauge wire handle a 1500watt 120 volt heater?
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