Question

There are two copper wires of length ratio 1 : 2 that have their cross-sectional areas in the ratio 1 : 4. What will be the ratio of their:

1. resistances?
2. specific resistances?

Answer 1

(a) The resistance of a wire is given by `R = ρl/A`. For the same material, ρ is the same.

`R_1/R_2 = (l_1/l_2) xx (A_2/A_1) = (1/2) × (4/1) = 2/1`

So the ratio of their resistances is 2 : 1.

(b) Specific resistance (resistivity) depends only on the material and temperature. Since both wires are copper and at the same temperature, their specific resistance is the same.

So the ratio of their specific resistances is 1 : 1.