A resistance of RΩ draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance R₀Ω. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of the potentiometer.

When the sliding contact is in middle, a resistance of R₀/2 is connected in series with a parallel combination of R and R₀/2.
Hence, net resistance is given by:
Req = R₀/2 + (R₀/2)||R
Current flowing through the circuit is given by:
I = V/Req
Potential across R is given by:
VR = I(R₀/2||R)
VR = (V/Req)(R₀/2||R)
Solving,
VR = R/(4R + R₀)V