We have two wire `A` and `B` of the same mass and the same material. The diameter of the wire `A` is half of that `B`. If the resistance of wire `A` is `24 ohm` them the resistance of wire `B` will be

Options

A. 12 ohm
B. 3.0 ohm
C. 1.5 ohm
D. None of the above

Answer

C

Explanation

`m_(A) = m_(B) rArr V_(A)d = V_(B)d rArr A_(A) I_(A) = A_(B)I_(B) rArr A_(A)/A_(B) = I_(B)/I_(A) xx A_(B)/I_(B) = (A_(B)/A_(A))^(2) = (d_(B)/d_(A))^(4)`
`rArr 24/R_(B) = 16 rArr R_(B) = 24/16 =1.5 Omega`