Question

A wire X is half the diameter and half the length of a wire Y of the similar material. The ratio of resistance of X to that of Y is

Answer 1

Hello dear,

● Answer-

Rx : Ry = 2 : 1

● Explaination-

# Given-

Dx/Dy = 1/2

Lx/Ly = 1/2

# Solution-

Let ρ be resistivity of material.

Resistance of wire X,

Rx = ρLx / Ax

Rx = ρLx / (πDx^2/4)

Resistance of wire Y,

Ry = ρLy / Ay

Ry = ρLy / (πDy^2/4)

Dividing both,

Rx/Ry = (Lx/Ly) (Dy/Dx)^2

Rx/Ry = (1/2) × (2)^2

Rx/Ry = 2

Therefore, resistance of wire X is twice that of wire Y.

Hope it helps...