Question

The maximum and the minimum equivalent resistance obtained by combining $n$ identical resistors of resistance $R$ , are $R_{max}$ and $R_{min}$ respectively. The ratio $\frac{R_{max}}{R_{min}}$ is equal to

• A. $n$
• B. $n^2$
• C. $n^2-1$
• D. $n^3$

Answer 1

Answer: (B)

To get maximum equivalent resistance all resistance must be connected in series
$\therefore {\left(R_{eq}\right)}_{max}=R+R+R+\dots nR.=nR$
To get minimum equivalent resistance all resistances must be connected in parallel.
$\therefore \frac{1}{{\left(R_{eq}\right)}_{min}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\dots \frac{1}{n},\frac{1}{{\left(R_{eq}\right)}_{min}}=\frac{n}{R}$
$\Rightarrow {\left(R_{eq}\right)}_{min}=\frac{R}{n}\therefore \frac{{\left(R_{eq}\right)}_{max}}{{\left(R_{eq}\right)}_{min}}=\frac{nR}{R/n}=n^2$