A wire has a resistance R If its length is doubled and radius is reduced to half then its resistance will become? (A) 2R (B) 4R(Cy8R D) 16R

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Answer 1 · 2018-06-13T23:00:01

#"8R"#

Resistance of wire of circular cross section is given by

#"R" = "ρL"/"πr"^2#

For the same type of wire

#"R" ∝ "L"/"r"^2#

From above

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

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

#color(white)("R"_2) = "R" × (2 cancel("L"_1))/(cancel("L"_1)) × ((cancel("r"_1))/(1/2 cancel("r"_1)))^2#

#color(white)("R"_2) = "R" × 2 × 4#

#color(white)("R"_2) = "8R"#