Question

We are given n resistors, each of resistance R. The ratio of the maximum to minimum resistance that can be obtained by combining them is

• A. $n^n$
• B. n
• C. $n^2$
• D. $lo{g}^n$

Answer 1

Answer: (C)

The correct option is C $n^2$
Maximum resistance can be obtained when the resistance are connected in series and minimum resistance can be obtained when the resistances are connected in parallel.
$R_{series}=R+R+R+...=nR$.
$R_{parallel}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+...=\frac{R}{n}$.
Therefore, $\frac{R_{series}}{R_{parallel}}=\frac{nR}{\frac{R}{n}}=n^2$.
Hence, he ratio of the maximum to minimum resistance that can be obtained by combining them is $n^2$.