Which resistor to use?

I have a 75 gallon fish tank, and I want to use a water heater heating element to provide the temp control (http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=370512031785). This listing says it's 120 volts, 1750 watts. I'm deducing that the amps will be at about 15. The problem is that I want to control the temperature using an arduino relay that's rated at 10 amps only.

My question is what resistor should I use to drop the amperage to 10? Also, if you can help me with the math you used to figure it out would be great, so I don't need to keep bothering people next time I come across the same problem.

Thanks in advance for your help! :)

Two of those elements in series would probably work - note any resistor to drop the current will itself be a mains heater... Finding the right relay (or a lower power heater) would perhaps be a more elegant solution?

Just as an exercise...

15 Amps at 120 Volts would be 8 Ohms. 10 Amps at 120 Volts would be 12 Ohms so you need an additional 4 ohms.

The 4-ohm resistor would be dropping 1/3 the total voltage (120 * 1/3 = 40).

10 Amps at 40 Volts means that you need a 400 Watt resistor.

The heater will get the other 80 Volts so your 1750 Watt heater now is an 800 Watt heater.

If you put two of the 1750W heaters in series the current should drop to 7.5A making a total of 900W for both. Not much better.

Try a heftier relay.

Also, if you can help me with the math you used to figure it out would be great, so I don't need to keep bothering people next time I come across the same problem.

The relationship between Voltage, Resistance, and Current is defined by [u]Ohm's Law[/u]: I = V/R R = V/I V = I x R

(I is current in amps)

Power is calculated as P = V x I.

And with some algebra you can come up with: P = Voltage squared/Resistance P = Current squared x Resistance