We know that, net resistance maximum when the number of resistance is connected in series and it is minimum when they are connected in series and it is minimum when they are connected in parallel. Let n number of identical resistors having resistances rΩ.
\(R_{max}==r+r+r+...+r=rn\) -------- equation (i)
The minimum resistance is given by
\(\frac1{R_{min}}=\frac1r+\frac1r+\frac1r+...+\frac1r=\frac nr\) -------- equation (ii)
Multiplying equation (i) and (ii), we get
\(\frac{R_{max}}{R_{min}}=n^2\)
Hence, the required ratio of Rmax to Rmin is n2 : 1
