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An unloaded potentiometer is a linear divider: output equals supply times the fractional position. Adding a load puts resistance in parallel with the lower leg, pulling the output down. The error is worst at mid-travel, where the wiper's source impedance peaks at a quarter of the total resistance.
Loaded divider
Vout = V x (Rlower || Rload) / ((Rlower || Rload) + Rupper); source Z = Rlower x Rupper / Rtotal
Electrical results are planning estimates only. Verify against the applicable wiring rules (IEC 60364, BS 7671, NEC or local code) and have all installation work designed and checked by a qualified electrician.
At least 100 times the pot resistance to keep loading error under about 0.25%. Otherwise buffer the wiper with an op-amp follower.
Near the middle of travel, because that is where the wiper's source impedance is highest.