Question

Resistance $n$, each of $r$ ohm, when connected in parallel give an equivalent resistance of $R$ ohm. If these resistances were connected in series, the combination would have a resistance in ohms, equal to

• A. $n^2 R$
• B. $R/ n^2$
• C. $R/n$
• D. $n R $

Answer 1

Answer: (A)

When $n$ resistance of $r$ ohm connected in parallel then their equivalent resistance is
$\Rightarrow \frac{1}{R}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}+\ldots \ldots \ldots . n$ times
$\therefore \frac{1}{R}=\frac{n}{r}$
$ \Rightarrow R=\frac{r}{n} $
$\Rightarrow r=n R$
When these resistance connected in series
$R_{s}=r+r+\ldots \ldots \ldots \ldots n$ times
$=n r=n \times n R=n^{2} R$