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. $nR$

Answer 1

Answer: (A)

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