$$n$$ equal resistors are first connected in series and then connected in parallel. What is the ratio of the maximum to the minimum resistance?

Solution :
When resistors are connected in series, then effective resistance of series combination
$$\eqalign{ & {R_S} = R + R + \ldots + n\,{\text{terms}} \cr & = nR\,.......\left( {\text{i}} \right) \cr} $$
When resistors are connected in parallel, then effective resistance
$$\eqalign{ & \frac{1}{{{R_P}}} = \frac{1}{R} + \frac{1}{R} + \ldots + n\,{\text{terms}} \cr & {\text{or}}\,\,\frac{1}{{{R_P}}} = \frac{n}{R}\,.......\left( {{\text{ii}}} \right) \cr & {R_P} = \frac{R}{n} \cr} $$
From Eqs. (i) and (ii), we get
$$\frac{{{R_S}}}{{{R_P}}} = \frac{{{n^2}}}{1}$$