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Are you referring to say an AC motor that draws 10 amps at 120volts but 5 amps at 240volts?
This is because of the phase difference of the two 'hot' legs but the power consumed (watts) is the same.
Is this what you meant: that higher voltage requires less current for the same Power?
Now with regards to ohms law, an increase in voltage results in an increase in current.
Current (I) = volts (E) / resistance (R)... I=E/R
As Voltage increases Current MUST increase as well.
In less words I was trying to say the greater the voltage the lower the current.
That's why transmission lines from the power company run such high voltages. Less current means less heat which causes loss
1200w toaster @120v = 10 amps
1200w toaster @1200v =1 amp
Way off topic now but all I was trying to say was there is far less currant (amperage) on a high voltage power line than there is on almost anything in your home.