The resistance of a 20 cm long wire is 5 ohms stretched to a uniform wire of length 40 cm. What is the resistance of the wire?

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Answer 1 · 2018-05-16T15:08:56

#"20 Ω"#

Resistance of a wire is given by the formula

#"R" = (ρ"L")/"A"#

or

#"R" = (ρ"L")/"A" × "L"/"L"#

#"R" = (ρ"L"^2)/"V"#

When a wire is stretched its volume (#"V"#) remains constant

#"R ∝ L"^2#

#"R"_2/"R"_1 = ("L"_2/"L"_1)^2#

#"R"_2 = "R"_1 × ("L"_2/"L"_1)^2#

#"R"_2 = 5 Ω × ((40 cancel"cm")/(20 cancel"cm"))^2 = "20 Ω"#