Question

Two wires of the same metal, have the same area of cross section but their lengths in the ratio of 3: 1, What should be the ratio of current flowing through them respectively, when the same potential difference is applied across each of their length​

Answer 1

Given:-

wires having same metal and same cross-section area.

$\text{Ratio of their lengths=}\dfrac{L_{1}}{L_{2}}=3$

To Find:-

Ratio of current flowing through them.

Explanation:-

$\text{According to question, resistivity}(\rho_{1})=\rho_{2}\\\\\text{cross-section area, }A_{1}=A_{2}\\\\\text{From Ohm's law, }\\\\\text{current, I}=\dfrac{Voltage(V)}{Resistance(R)}\\\\\text{Since, voltage is also same}\Rightarrow\dfrac{I_{1}}{I_{2}}=\dfrac{R_{2}}{R_{1}}\\\\\Rightarrow\dfrac{I_{1}}{I_{2}}=\dfrac{\rho_{2}\times L_{2}\times A_{1}}{A_{2}\times\rho_{1}\times L_{1}}=\dfrac{L_{2}}{L_{1}}=\dfrac{1}{3}$