Question

$n$ equal resistors are first connected in series and then connected in parallel. The ratio of the maximum to minimum resistance obtained in two cases is

• A. $ n : 1 $
• B. $ n^2 : 1 $
• C. $1 : n^2 $
• D. $ 1 : n$

Answer 1

Answer: (B)

Let resistance of each resistor is $r$.
When n resistors are connected in series, equivalent resistance is
$R = nr,$ which is maximum resistance.
When $n$ resistors are connected in parallel, equivalent resistance is
$R' = \frac{r}{n}$, which is minimum resistance
$ \therefore \, \, \frac{R}{R'} = \frac{nr}{r / n} = n^2$