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You would need a source of power giving at least 500watts to heat a cup in reasonable time. You could obtain this from a lead acid cell such as a car battery. At 12v you would need a current of say 50 amps (this would give 600watts). So the heating coil should have a resistance of 12/50 ohms = 0.24 ohms. The connectors to and from the battery would need to be rated for 50 amps without heating up appreciably.

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