Question

When the diameter of a wire is doubled, its resistance becomes ______.

Options

• double

• four times

• one-half

• one-fourth

Answer 1

When the diameter of a wire is doubled, its resistance becomes one-fourth.

Explanation:

We know that,

R = `(rho L)/A`

Area (A) ∝ d²

If the diameter is doubled, the new diameter d' = 2d.

Then the new area A' becomes:

A' = π(r')²

A' = `pi((d')/2)^2`

A' = πd²

A' = 4A

Since resistance R is inversely proportional to area, we can express the new resistance R' as:

R' = `(rho L)/(A')`

R' = `(rho L)/(4 A)`

R' = `R/4`

∴ The resistance becomes one-fourth of its original value, so the correct answer is (d) one-fourth.