Question

Two wires of same material have their area of cross section is the ratio 1:2 and length is the ratio 1:3 carry equal current. What is the ratio of the potential difference across the wires.

Answer 1

Answer: $\dfrac{V_{A}}{V_{B}} = \dfrac{2}{3}$

Explanation:

Given that,

Ratio of the cross section = 1:2

Ratio of the length = 1:3

Let us consider two wires are A and B of same material and carrying equal current.

Using ohm's law

$V = I R$

$V = \dfrac{I\rho l}{A}$

Ratio of the potential difference across the wires

$\dfrac{V_{A}}{V_{B}} = \dfrac{I\rho l_{A}}{A_{A}}\times \dfrac{A_{B}}{I\rho l_{B}}$

$\dfrac{V_{A}}{V_{B}} = \dfrac{2}{3}$

Hence, the ratio of the potential difference is 2:3.