Question

If the diameter of a resistance wire is halved, then its resistance becomes ______.

Options

• four times

• half

• one-fourth

• two times

Answer 1

If the diameter of a resistance wire is halved, then its resistance becomes four times.

Explanation:

We know that,

R = `rho L/A`    ...(i)

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

A = `(pi d^2)/4`

∴ The equation (i) becomes:

R = `rho ((4 L)/(pi d^2))`

If the new diameter (d') is halved (d' = `d/2`):

R' ∝ `1/(d')^2`

R' ∝ `1/(d/2)^2`

R' ∝ `4/d^2`

∴ The new resistance (R') scales up exactly to 4 times the original value (R' = 4R).