Question

A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is ______.

Options

• 9 : 1

• 1 : 9

• 4 : 1

• 3 : 1

Answer 1

A wire of resistance R₁ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is 9 : 1.

Explanation:

Resistance, R₁ = `rho"L"_1/"A"_1`

R₂ = `rho((3"L"_1)/("A"_1//3))`

= `9rho"L"_1/"A"_1`

∴ `"R"_2/"R"_1 = (9rho"L"_1/"A"_1)/(rho"L"_1/"A"_1)`

= 9