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) \[\left( n+\frac{1}{n} \right)\]
Correct Answer: A
Solution :
[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, \[{{R}_{eq}}={{R}_{1}}+{{R}_{2}}=\frac{R}{2}\left( 1+\frac{1}{{{n}^{2}}} \right)\]
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