Question

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

Answer 1

`"8R"`

Explanation:

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"`