`N` sources of current with different emf's are connected as shown in Fig. The emf of the sources are proportional to their internal resistancs, i.e., `E = alpha R`, where `alpha` is an assigned constatant. The lead wire resistance is neglible. Find:
(a) the current in the circuit ,
(b) the potential differences between points `A` and `B` dividing the circuit in `n` and `N- n` links.

Explanation

(a) Current, `i = (N xi)/(N R) = (N alpha R)/(N R) = alpha`, as `xi = alpha R` (given)
(b) `varphi_(A) - varphi_(B) = n xi - ni R = n alpha R = 0`