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14/3 copper with ground on a 25 amp breaker

Before I get chastised for recommending that 14 gauge wire be protected with a 25 amp breaker, which would be in violation of standard wiring requirements, Sec. 240.4(G) of the NEC tells us that the standard wiring requirements, i.e. 15 amps on 14 gauge wire, does not apply to motors. Table 430.52 tells us that an inverse-time circuit breaker (that's a standard type breaker) can be set to 250% of the FLC of the motor and 430.22 tells us that the branch circuit conductors are sized at 125% of FLC.

The question does not say that 10 amps is the FLC. The nameplate rating of a motor is not the FLC. FLC is determined by using the tables in Sect. 430. The name plate rating is used only for sizing current overloads, called "heaters". For my answer I have assumed 10 amps is the FLC.

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