• # question_answer A piece of conducting wire of resistance R is cut into $2n$ equal parts. Half the parts are connected in series to form a bundle and remaining half in parallel to form another bundle. These bundles are then connected to give the maximum resistance. The resistance of the combination is A) $\frac{R}{2}\left( 1+\frac{1}{{{n}^{2}}} \right)$          B)        $\frac{R}{2}\left( 1+{{n}^{2}} \right)$ C) $\frac{R}{2(1+{{n}^{2}})}$   D)        $\left( n+\frac{1}{n} \right)$

[a] Resistance of each part $=\frac{R}{2n}$ For 'n' such parts connected in series, equivalent resistances, say ${{R}_{I}}=n\left[ \frac{R}{2n} \right]=\frac{R}{2}.$Similarly, equivalent resistance say ${{R}_{2}}$ for another set of n identical respectively in parallel would be $\frac{1}{n}\left( \frac{R}{2n} \right)=\frac{R}{2{{n}^{2}}}.$ For getting maximum of ${{R}_{1}}$& ${{R}_{2}},$ they should be connected in series & hence, ${{R}_{eq}}={{R}_{1}}+{{R}_{2}}=\frac{R}{2}\left( 1+\frac{1}{{{n}^{2}}} \right)$