A resistance of R draw current from a potentiometer. The potentiometer wire, AB, has total resistance of `R_(0)`. 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 potentiometer wire.

Explanation

Derivation of expression of voltage across resistance R

Resistance between points A & C
`1/(R_1))=(1/R+1/((R_(0))/2))`
Effective resistance between points A & B.
`R_(2)=((R(R_(0))/2)/(R+(R_(0))/2))+(R_(0))/2`
Current drawn from the voltage source.
`1=V/((R(R_(0))/(R+(R_(0))/2)+(R_(0))/2)`
Let current through R be `I_(1)`
`I=(I((R_(0))/2))/(R+(R_(0))/2)`
Voltage across R
`V_(1)=I_(1)R`
`=(IR_(0))/(2(R+(R_(0))/2)).R=("RR"_(0))/(2(R+(R_(0))/2)) . V/(("RR"_(0))/(2R+R_(0)))+(R_(0))/2`
`=(2RV)/(R_(0)+4R)`