Rheostat power question

[ez24]

http://www.ebay.com/itm/100-Watt-100-Ohm-Ceramic-Disk-Rheostat-Variable-Resistor-/171725011843?pt=LH_DefaultDomain_0&hash=item27fb9bbb83

Does the power rating go down with the resistance?

For example if this can do 100 watts at 100 ohms, does this mean it is rated at 50 watts at 50 ohms, and 10 watts at 10 ohms and 1 watt at 1 ohm?

thanks

[richard.cs]

Yes, because it's able to dissipate a fixed amount of power per unit length so when you lower the resistance you also lower the length of the dissipating section and the power goes down.

Another way of looking at it is if you used it as a 100 Ohm resistor and it's safe at 100W then:

P=IV=I²R=V²/R

I²=P/R=[100 Watts]/[100 Ohms]
I=sqrt(1)=1Amp

And
V²=PR=[100 Watts]*[100 Volts]
V=sqrt(10000)=100Volts


So it'll be happy with 100V end to end and 1 amp flowing through it. If you now made it an arbitrary resistance by selecting say 58 Ohms, then 58% of the resistance wire is in circuit and that must dissipate the same power per unit length as it did before. The other 42% doesn't dissipate power but doesn't take heat away either - it's not very well connected (thermally) to the hot bit. It can now take 58 Watts, the resistance and the voltage are all different but the max current is still 1 Amp. Wherever you set it the maximum current doesn't change.