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
$R^{\prime }=\frac{r}{n}$, which is minimum resistance
$\therefore \frac{R}{R^{\prime }}=\frac{nr}{r/n}=n^2$