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I have some cheap potentiometers that I would like to use as variable resistors.

The potentiometers have a power rating lower than the amount of power I would like to be able to dissipate across the setup at a fixed voltage, so I have a plan.

Instead of using a single potentiometer set to resistance X and total voltage drop of V, I will put the two variable resistors in series and set both of them to a resistance 1/2 X. The voltage drop across each will now be 1/2 V.

The setup

Because the total current will stay the same thanks to an equal equivalent resistance, each variable resistors will get the same current as the original setup with only one variable resistor.

Because P = IV, each resistor should dissipate half the power with half the voltage drop. The total power will be the same, but because I have two potentiometers in series, given that I adjust them to the same resistance each time, I will be able to dissipate twice the total power ago a given total resistance.

Is there a flaw in my reasoning?

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The most likely flaw in your reasoning is probably that you think a potentiometer used as a rheostat can dissipate it's rated power at any setting of the wiper. It can't.

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Figure 1. The potentiometer resistance track. Source: Types of resistors.

The rated power is when the dissipation is spread over the full length of the resistance track. When used as a variable resistor (rheostat), as you are proposing, the maximum power dissipation is reduced in proportion to the amount of track in use. Effectively the power specification is telling you the maximum current the track can handle.

Let's say that the potentiometer in Figure 1 has a rated power of 0.125 W and a resistance of 250 Ω.

The maximum current it can handle is (from \$ P = I^2R \$) given by \$ I = \sqrt{\frac {P}{R}} = \sqrt{\frac {0.125}{250}} = 22\ \text{mA} \$.

At, say, a 40% setting the maximum power allowed would be \$ 0.125 \times 0.4 = 0.05 \ \text W \$.

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