Let the resistances of the two parts be R 1 and R2, and the total resistance of the resistance wire of the sliding rheostat be R, then there are
R 1+R2=R
Total resistance of parallel circuit
R joint =R 1R2/(R 1+R2)
R 1+R2≥2√(R 1R2). Since R 1+R2 is a constant value, when R 1=R2, R1R2 takes the maximum value. At this time,
R joint =R/2
That is, when the slider is in the middle, the resistance is the greatest.