Question

Resistances $n$, 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)

Equivalent resistance of $n$ resistances each of $r$ ohm in parallel is given by
$\frac{1}{R}=\frac{1}{r}+\frac{1}{r}+.....+ntimes=\frac{n}{r}$
So, $r=nR$
When these resistances are connected in series, effective resistance is
$R=r+r+......+n$ times $=nr$
$\therefore$ $R=n(nR)=n^{2}R$