In the circuit shown in figure. AB is a uniform wire of length L and resistance R. P is a sliding contact. Take the ratio of lengths PB to AB as `alpha`.
(a) Find the ratio `(V_(0))/(V)` in terms of `R_(0),R` and `alpha`
(b) Predict the value of `(V_(0))/(V)` when `R_(0) rar infty`. Use the result obtained in (a) to show that your prediction is correct.
(c) Find the ratio `(V_(0))/(V)` when `R_(0) = 2R and alpha = (1)/(2)`

Answer

(a) `(alpha)/((1-alpha)((alphaR)/(R_(0))+1)+alpha)`
(b) `alpha`
(c) `(4)/(9)`