Suntan Power of a Potentiometer
A Potentiometer with a power rating of (say) 0.5W will have a maximum voltage that can exist across the pot before the rating is exceeded.
All power ratings are with the entire resistance element in circuit, so maximum dissipation reduces as the resistance is reduced (assuming series or "two terminal" rheostat wiring).
Let's look at the 0.5W pot, and 10k is a good value to start with for explanation.
If the maximum dissipation is 0.5W and the resistance is 10k, then the maximum current that may flow through the entire resistance element is determined by ...
P = I² R ... therefore
I =P / R ... so I = 7mA
In fact, 7mA is the maximum current that can flow in any part of the resistance element, so if the 10k pot were set to a resistance of 1k, current is still 7mA, and maximum power is now only 50mW, and not the 500mW we had before.
