The equivalent resistance of series ad parallel combinations of two cells are S and P respectively. IF S=nP , then find out the minimum possible value of n.

Explanation

IF the resistance be `r_1` and `r_2` then ,
`S=r_1+r_2` and `P=(r_1r_2)/(r_1+r_2)`
But S=nP
i.e., `r_1+r_2=n.(r_1r_2)/(r_1+r_2)`
or,`(r_1+r_2)^2=nr_1r_2`
or,`(r_1-r_2)^2+4r_1r_2=nr_1r_2`
or,`(r_1-r_2)^2=(n-4)r_1r_2`
As `(r_1-r_2)^2 ge 0,` therefore `n-4 ge 0` or , `n ge 4`
So, the minimum possible value of n is 4.