Question

A piece of wire has a resistance of 0.45.
calculate the resistance of another wire of the same material with a third of the length and half the cross-sectional area.

Answer 1

formula of resistance is given by, R = ρl/A , where ρ is specific resistance or resistivity, A is cross sectional area of wire and l is length of wire.

given, resistance of a piece of wire , R = ρl/A = 0.45 ohm....(1)

a/c to question,

we have to find resistance of another wire of the same material i.e., resistivity of wire = ρ, length of wire, l' = l/3 and half of cross sectional area so, A' = A/2

now, resistance of another wire, R' = ρl'/A' = ρ (l/3)/(A/2) = (2/3) ρl/A

from equation (1),

R' = 2/3 × 0.45 = 0.30 ohm

hence, resistance of another wire is 0.30 ohm