Question

$n$ resistors each of resistance $R$ first combine to give maximum effective resistance and then combine to give minimum effective resistance. The ratio of the maximum to minimum resistance is

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

Answer 1

Answer: (B)

$n^2$

Answer 2

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