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Spec'ing a pot

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A rather rudimentary question, but I was wondering how one goes about spec'ing a pot?

I have a very small motor on which the control pot burned out. It is powered by a pair of C cell batteries for a total of 3 volts. In short circuit, it draw around 1A so the motor has a internal resistance of 1/3kohm. I only have 5kohm and greater pots on hand. To determine the operational series resistance, I paralleled a bunch of 10 ohm resistors. The range appears to be 1/2 ohm through 5 ohms.

If I acquired a 5 or 10 ohm pot, what wattage should I be looking for? At 5 ohms, .2W. At 1 ohm, 1W. At 0.01ohm, 0.01W. Something seems to simple about this but I can't lay my finger on it.
 
The effective resistance of the motor: R = E/I = 3V/1A = 3Ω, not 1/3kΩ. However, a DC motor is not like a resistor at all because of the back EMF generated by the motor when it is running.

You motor stalled (no back EMF) is likely to draw hugely more than 1A. It is usually not desirable to vary the speed of a motor by putting a variable rehostat in series with it. The speed regulation is horrible, the low-speed torque sucks, and you are wasting lots of power.

I'd be looking for a motor controller circuit that varies the speed of the motor using a conventional 5KΩ pot.
 
Unfortunately the application and the enclosure for the app precludes modification to fit a fancy circuit. My only choice is to replace the pot. The current pot looks like it might be 1/8 or 1/4W. Ie. undersized. Or atleast undersized based on my recollections.
 
Pots are rated in watts (E times I). The rating applies to the entire resistance element dissipating that power. If only a portion of the element is supporting current (dissipating heat) due to the wiper positioned away from an extreme end, the wattage should be derated linearly according to the wiper position. You don't want half of the resistance element dissipating the max rated power, for example, when the wiper is at the center, but rather half the rated power at worst. Good engineering practice is not to exceed one-half the power rating, and in my view, that rating should not be exceeded for any length of time if you want to guarantee the pot will work reliably.
 
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