Question

A copper wire of length 1 m and radius 1 mm is joined in series with an iron wire of length 2 m and radius 3 mm and a current is passed through the wires. The ratio of current densities in the copper and iron wires is ______

Options

• 18 : 1

• 9 : 1

• 6 : 1

• 2 : 3

Answer 1

A copper wire of length 1 m and radius 1 mm is joined in series with an iron wire of length 2 m and radius 3 mm and a current is passed through the wires. The ratio of current densities in the copper and iron wires is 9 : 1.

Explanation:

Current density, J = `"I"/"A" = "I"/(pi"r"^2)`

∴ `"J"_1/"J"_2 = "I"_1/"I"_2 xx "r"_2^2/"r"_1^2`

But the wires are in series, so they have the same current,

hence, I₁ = I₂

∴ `"J"_1/"J"_2 = "r"_2^2/"r"_1^2 = 9 : 1`