A wire of registance 'R' is made thrice on itself. The new registance is what ?

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Answer 1 · 2018-04-09T02:57:06

#"9R"#

Resistance of a wire is given as

#"R" = "ρL"/"A"#

Multiply and divide RHS by #"L"#

#"R" = "ρL"/"A" × "L"/"L" = ("ρL"^2)/"AL"#

#"R" = ("ρL"^2)/"V" color(white)(..)[∵ "Volume = Area × Length"]#

When a wire is stretched its volume remains constant.

So,

#"R ∝ L"^2 color(white)(..)[∵ "ρ and V are constant"]#

#"R"_2/"R"_1 = ["L"_2/"L"_1]^2#

#"R"_2 = "R"_1 × ["L"_2/"L"_1]^2#

#"R"_2 = "R" × [(3cancel("L"_1))/cancel("L"_1)]^2#

#"R"_2 = "9R"#