# 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

Jun 13, 2018

$\text{8R}$

#### Explanation:

Resistance of wire of circular cross section is given by

${\text{R" = "ρL"/"πr}}^{2}$

For the same type of wire

${\text{R" ∝ "L"/"r}}^{2}$

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"