Can I compute resistive device power consumption at specific voltage knowing its power rated at some other voltage?

Question

Suppose I have a device containing a heating element and no thermostat such as some simple water heater. It's rated "3500 watts 220 volts" which I assume means that if it's plugged into a properly wired outlet supplying 220 volts it would produce 3500 watts of heat.

A real outlet will have some other voltage - maybe 215 volts, maybe 235 volts depending on the grid conditions and time of day.

I want to know the power of device plugged into a real outlet. I measure the voltage with a voltmeter and it reads 235 volts.

Then I try to apply Ohm's law which says that current is proportional to voltage.

The device manual says that at 220 volts the device power is 3500 watts and therefore draws 15,9 amperes current.

235 volts is 1,07 times greater than 220 volts so current at 235 volts would also be 1,07 times greater and it'll be about 17 amperes.

Then I multiply the real voltage (235 volts) by that computed current (17 amperes) and I get 3995 watts (almost 4 thousand watts).

Is this proper application of Ohm's law?

Answer 1

Yes, that's correct. You can combine the equations

$$P = I\cdot V \text{ and } I = \frac{V}{R}$$

to produce

$$P = \frac{V^2}{R}$$

Which means that in general for a constant resistive load, power is proportional to V².

So if the power at 220 V is 3500 W, then the power at 235 V would be

$$3500\text{ W} \cdot \left(\frac {235}{220}\right)^2 = 3994\text{ W}$$