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
$\therefore \left(R_{e q}\right)_{m a x}=R+R+R+\ldots nR.=nR$
To get minimum equivalent resistance all resistances must be connected in parallel.
$\therefore \frac{1}{\left(R_{e q}\right)_{m i n}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}+\ldots \frac{1}{n},\frac{1}{\left(R_{e q}\right)_{m i n \, }}=\frac{n}{R}$
$\Rightarrow \left(R_{e q}\right)_{m i n}=\frac{R}{n}\therefore \frac{\left(R_{e q}\right)_{m a x}}{\left(R_{e q}\right)_{m i n}}=\frac{n R}{R / n}=n^{2}$