Question

If n equal resistances are first connected in series and then connected in parallel, then the ratio of the maximum to the minimum resistance is ___.

• A. n
• B. $\frac{1}{n^2}$
• C. $n^2$
• D. $\frac{1}{n}$

Answer 1

The correct option is C $n^2$

A series connection gives maximum equivalent resistance, while a parallel connection gives the minimum equivalent resistance.
Equivalent resistance for resistances in series = $R_s=nR$
Equivalent resistance for resistances in parallel = $R_p=\frac{R}{n}$
Therefore : $\frac{R_{max}}{R_{min}}=\frac{R_s}{R_p}=\frac{nR}{\left(\frac{R}{n}\right)}=n^2$