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}+.....+n\,times=\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 $