Fig. illustrates a potentiometric circuit by means of which we can very a voltage `V` applied to a certain device possessing a resistance `R`. The potentiometer has a length `l` and a resistance `R_(0)` and voltage `V_(0)` is applied to its terminals. Find the voltage `V` fed to the device as a funciton of distanace `x`. Analyse separately the case `R gt gt R_(0)`.

Explanation

Total resistanace `= (l - x)/(l) R_(0) + (R. (x R_(0))/(l))/(R + (x R_(0))/(l))`
`= (l-x)/(l) R_(0) + (x R R_(0))/(l R + x R_(0))`
`= R_(0) [(1-x)/(l) + (x R)/(lR + x R_(0))]`
Then `V = V_(0) (x R)/(lR + x R_(0)) //(1 - (x)/(l) + (xR)/(x R_(0) + lR)) = V_(0) R x//{lR + R_(0) x (1 - (x)/(l))}`
For `R gt gt R_(0), V = V_(0) (x)/(l)`