A) \[{{n}^{2}}\]
B) \[\frac{1}{{{n}^{2}}}\]
C) \[\frac{1}{{{n}^{3}}}\]
D) \[{{n}^{3}}\]
Correct Answer: B
Solution :
[b] Let R be the resistance of each of the n conductors. Effective resistance in series combination, \[{{R}_{s}}=R+R+....+n\,\,\,times\] Effective resistance in parallel combination, \[\frac{1}{{{R}^{p}}}=\frac{1}{R}+\frac{1}{R}+.....+n\] times \[=\frac{n}{R}\] or \[{{R}_{p}}=\frac{R}{n}\] \[\therefore \frac{{{R}_{p}}}{{{R}_{s}}}=\frac{R}{\frac{n}{nR}}\] \[=\frac{1}{{{n}^{2}}}\]
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