Electronic – What’s the effect of shorting the wiper terminal with one of the ends of a trim pot

EDIT: I realized I didn't draw the schematic properly. Previously, the 100 Ohm resistor wasn't there.

I thought I'd done the math correctly for this, but clearly something conceptually isn't straight for me. I need a 5K potentiometer, but the sources I've looked through didn't have it in the package I'd like. I did see a 10K pot in the package though. So I thought by shorting the wiper terminal with one of the ends of the trim pot I'd be able to half the maximum possible resistance offerable by the pot.

$$\frac{1}{R_{total}} = \frac{1}{R_{wiper}} + \frac{1}{10000}$$
$$\frac{1}{R_{total}} = \frac{R_{wiper} + 10000}{10000 \cdot R_{wiper}}$$
$$R_{total}=\frac{10000 \cdot R_{wiper}}{R_{wiper} + 10000}$$

Since the highest resistance Rwiper can reach is 10K, the resulting highest value would be

$$R_{total}=\frac{10K \cdot 10K}{10K + 10K} = \frac{10K \cdot 10K}{2 \cdot 10K} = 5K$$

I could also make a graph by plotting the function of Rtotal.

By this point I was convinced. I tried to measure the resistance on a spare 10K pot lying around, but I saw that maximum value remained 10K. Why is this?

^{simulate this circuit – Schematic created using CircuitLab}