Sure, Derek; that's what I meant.
"a device of a given wattage which can run at 240V will draw half as much
current at that
voltage, and can therefore use wondering which is much lighter in
gauge."
I believe, but did not look up, that it is approximately a quarter as much copper by weight.
That's not how it works, but your confusion is understandable.
Power =
current *
voltage. A 1000w load at 120v requires 8.33 amps. A 1000w load at 240v requires 4.166 amps. Electrical conductors are rated at a particular
ampacity - a 12ga
wire can handle 20A, no matter the
voltage of the
circuit (subject to situational detratings, yada yada). A 120v
circuit can supply a maximum of 2400 watts of
power before the
current of of the
circuit exceeds 20A. A 240v
circuit can supply a maximum of 4800 watts of
power before the
current of the
circuit exceeds 20A. This is a linear relationship, and doubling the
voltage at a given
current doubles the
power.
The confusion comes when you combine
Ohm's law and
Joule's law and do derivatives like P = V^2/R, and now we see a square term. For a given resistance,
power indeed increases at the square of the
voltage. What gives? The confusion comes from the fact that the resistance doesn't stay constant as you increase the
voltage.
For example,
If you are designing a heater and wish that heater to dissipate 1000 watts, the resistance of your heater needs to be 14.4 ohms if it will be supplied by 120 volts (120v^2/1000 = 14.4). If your supply
voltage is 240v, the resistance of your heater will be 57.6 ohms (240^2/1000 = 57.6).
Understanding the reason electrical
power distribution runs at high
voltage requires a more accurate
circuit diagram. You have a supply
voltage, a load resistance, and you have a
wire resistance.
Using our heater example of 1000w, let's assume the
circuit wiring resistance is 1
ohm:
- At 120v, our
circuit resistance is 15.4 ohms - the 14.4
ohm resistance of the load, plus the 1
ohm resistance of the
wire. In this case, 6.5% of the
power is wasted in the
wire - 60 watts, and our 1000w heater will only put out 876 watts.
- At 240v, our
circuit resistance is 58.6 ohms - the 57.6
ohm resistance of the load, plus the 1
ohm resistance of the
wire. In this case, the
wire is a much lower percentage of the load
impedance, meaning less loss, and more
power delivery to the load. Now the
circuit loss is less than 2%. Only 17 watts are now lost in the
wire, and we get 968 watts to our load.