Physics - Current Electricity Question with Solution | TestHub

In series combination,$\mathrm{S}=\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)$

In parallel combination,$\text{P}=\frac{{\text{R}}_1{\text{R}}_2}{\left({\text{R}}_1+{\text{R}}_2\right)}$

$\because \mathrm{S}=\mathrm{nP}$

$\therefore$$\left({\text{R}}_1+{\text{R}}_2\right) \; =\text{n}\frac{{\text{R}}_1{\text{R}}_2}{\left({\text{R}}_1+{\text{R}}_2\right)}$

$\therefore$${\left({\text{R}}_1+{\text{R}}_2\right)}^2=\text{n}{\text{R}}_1{\text{R}}_2$

For minimum value,${\mathrm{R}}_1={\mathrm{R}}_2=\mathrm{R}$
$$\begin{gathered} {\left(\text{R}+\text{R}\right)}^2=\text{n}\left(\text{R}\times \text{R}\right) \\ \Rightarrow 4{\text{R}}^2={\text{nR}}^2 \\ \text{⇒}\mathrm{n}=4 \end{gathered}$$