QUOTE Remember Ohm's Law...double the voltage and half the current QUOTE

NOPE nope and more nope
ON a resistive load double the voltage you double the current and power goes up by 4.

MOTORS which is what seems to confuse people. Wiring a motor for low voltage is in effect placing two windings in parallel so current is high and volt low.

Wire for high voltage ie 240 the windings are now in series BUT the current through them is same as when in parallel. SO volt doubled current halved Power equal either way.

Motor on 120 draws 10 amp let us say. Each winding is drawing 5 for total of 10.

ON 240 each winding still draws 5 amps they are in series so current is 5 amp. Volt drop across each winding is 120 for total of 240 across the two in series.

120 x 10 = 240 x 5 Power is equal

Dan Bentler