Question

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

• A. 18 : 1
• B. 9 : 1
• C. 6 : 1
• D. 2 : 3

Answer 1

Answer: (B)

Current density $J=\frac{i}{A}=\frac{i}{\pi r^2}$
$\Rightarrow \frac{J_1}{J_2}=\frac{i_1}{i_2}\times \frac{r_2^2}{r_1^2}$
But the wires are in series, so they have the same current, hence, $i_1=i_2$
So, $\frac{J_1}{J_2}=\frac{r_2^2}{r_1^2}$
$=9:1$