Question

1.A piece of wire of resistance R is cut into five equal parts. These parts are then connected
in parallel. If the equivalent resistance of this combination is R, then the ratio R/R is
(a) 1/25 (b) 1/5 (c) 5 (d) 25

Answer 1

☆ Wire is cut into 5 equal parts. Since all dimensions are same for pieces, Resistance of each wire is equal and has value = $\:\sf{\dfrac{R}{5}}$.

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☆ Resistance is proportional to length of wire and inversely proportional to area of cross - section. If length is ⅕th, then Resistance is also ⅕th of the original value.

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☆ When these five are connected in parallel combination, then net resistance becomes ⅕th again. So R1 = $\:\sf{\dfrac{R}{5}}\:\times\:{\dfrac{1}{5}}$$\:\sf{=\:{\dfrac{R}{25}}}$

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☆ $\:\sf{Ratio\:=\:{\dfrac{R1}{R}}\:=\:{\dfrac{1}{25}}}$

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$\:\:\:\:\:\:\therefore\:{\underline{\sf{Hence,\: the\:correct\:option\:is\:{\sf{\bf {(a)\:{\dfrac{1}{25}} }}}}}}.$

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