Question

You are given n resistors, each of resistance r. They are first combined to get minimum possible resistance, then they are connected to get the maximum possible resistance. The ratio between rrurnmum to maximum resistance is

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

Answer 1

The Correct Option is D

Minimum possible resistance can be found in parallel arrangement and maximum possible resistance can be found in series arrangement.
Thus, $\hspace30mm \frac{1}{R_{min}} = \frac{1}{R} + \frac{1}{R} + ....+$ n times
$\hspace50mm = \frac{n}{R}$
$\Rightarrow \hspace30mm R_{min} = R / n$
and $\hspace30mm R_{max} = R + R + .......+$ n times
$\Rightarrow \hspace40mm R_{max} = nR$
$\therefore \hspace30mm \frac{R_{min}}{R_{max}} = \frac{R / n}{nR} = \frac{1}{n^2}$