I = V / R
P = V^2 / R = I^2 R
Current is linearly proportional to voltage, so power is proportional to the
square of voltage and of current. For a fixed resistance, you can't change the
relationship between voltage and current.
Power loss is linearly proportional to the resistance of the conductor (e.g.
wire) and inversely proportional to the square of the voltage (or indirectly
current if you like), hence the use of very high voltages in long-distance power
transmission, as you indicated.
---- Clark Ward Jr <ki4gyt-at-gmail.com> wrote:
...
Actually, Power is proportional to the square of current... I^2 x R = P
which is why power companies use transformers to jack up the voltage to
tens of thousands of volts before sending it out over long distances to keep
from losing energy in the form of heat (power). Raise voltage, current goes
down, => I^2R goes down => less heat (power wasted)
...