Question

n equal resistors are first connected in series and then in parallel. The ratio of the equivalent resistance in the two cases is?

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{equivalent}\mathrm{resistance}\mathrm{of}n\mathrm{resistance}\mathrm{connected}\mathrm{in}\mathrm{series}=nR.....\left(1\right) \\ \mathrm{Equivalent}\mathrm{reistance}\mathrm{of}n\mathrm{parallel}\mathrm{resistance}=\frac{R}{n}.....\left(2\right) \\ \mathrm{Dividing}\left(1\right)\mathrm{by}\left(2\right),\mathrm{we}\mathrm{get} \\ \mathrm{Required}\mathrm{ratio}=\frac{nR}{{\displaystyle \frac{\mathit{R}}{\mathit{n}}}}=n^2:1 \end{gathered}$$