At what value of teh resistances `R_(x)` in the circuit shown in Fig. Will the total resistance between points `A` and `B` be independent of the number of cells ?

Explanation

Total resistance of the circuit will be independent of the number of cells,

if `R_(x) = ((R_(x) + 2R) R)/(R_(x) + 2R + R)`
or, `R_(x)^(2) + 2R R_(x) - 2 R^(2) = 0`
On solving and rejecting the negative root of the quadratic equacation, we have,
`R_(x) = R (sqrt(3) - 1)`