I’m starting a project and I’m 4th year mechanical.

Yes although I am in mechanical engineering I am trying to inquire about an electrical problem I have.


So one of the vital parts of this project I'm starting is the creation of heat due to circuitry. I know that heat is produced through a high resistance:      P= VR = RI^2. Similar to how a lightbulb produces so much heat. 
So first I'm wondering if the same thing is applicable through an arduino using a relay.
Second, I feel like a high voltage is important so would the arduino work?
If it does work, what metal can I use to produce that hear? And what should I really take into consideration?

Hi Damarius-Heating elements are usually made of wire that has a higher resistance then copper- often a material called nichrome, which is a mixture of nickel and chromium. How much heat (how many watts) do you want to produce? Since watts = volts multiplied by amps, you can use a high voltage and low current, or a low voltage and high current to get the same number of watts.  If you're running a high voltage you'll want more resistance in the heating element than if you were running a lower voltage.  To get a higher resistance use a longer length of smaller wire.  For a lower resistance the converse is true. Look for a chart that shows you the resistance per foot of different gauges of nichrome wire.  Note: You'll find that it is almost impossible to solder nichrome wire.  You can make a connection to it by using a crimp splice, or wrap the wire around a screw along with the wire you are connecting it to and tighten a nut down on it.   Another word of caution- the resistance of the wire will increase as it heats up.  You should be able to find charts that give this information too. -Rick

This is perfect information and to be honest I would have to do more calculation to figure out my target temperature in relation to heat. But what sort if board can I use?
Say I need 15V. The arduino can't handle that so do I have to custom build my own?

DamariusFirstly  you write P= VR = RI^2.RI^2 is right, but VR is not. It could  be VI or (v^2)/R.In any event you should follow Rick's advice. I don't really follow your question, but I think you are asking if the relay could switch a high voltage. If yes, the answer is: probably, but it does depend on the relay selected- voltage and current rating. The relay contacts (which you use to switch the current) would typically be isolated from the Arduino, so there would be no interaction although the Arduino would still need its power supply.

Damarius,Rick's advice on nichrome wire is good. If you want to control the heat output using an Arduino, you need to either use a relay to switch the power on and off as Aubrey mentioned or perhaps use a power MOSFET. I've written articles on relays and MOSFETs for my data sheet series which may help you with component selection.
https://www.eeweb.com/profile/elizabeth-simon...how-to-read-data-sheets-higher-power-fetsBest of luck on your project.

@aubrey Kagan my goal would be to increase an arduino input voltage. From what I understand the arduino only gives 5V to the circuit. I'm wondering if there is a component that could amplify that to maybe 10V or even 20V. ( Id have to do the math to know what I need/want)
@Everyone else thank you very much for your input I will take it all under consideration when I have more time to work on it. Its all very helpful stuff.