Question

Two wires of equal length and equal diameter and having resistivities ${\rho }_1$ and ${\rho }_2$ are connected in series. The equivalent resistivity of the combination is

• A. $\frac{{\rho }_1+{\rho }_2}{2}$
• B. ${\rho }_1+{\rho }_2$
• C. $\frac{{\rho }_1+{\rho }_2}{{\rho }_1+{\rho }_2}$
• D. $\sqrt{{\rho }_1{\rho }_2}$

Answer 1

The correct option is (A) $\frac{{\rho }_1+{\rho }_2}{2}$

We know,

Resistance is given as

$R=\frac{\rho L}{A}$

Now we can write

$R_1=\frac{{\rho }_{1}L}{A}$

$R_2=\frac{{\rho }_2{L}_2}{A}$

For the series combination we know,

$R_{eq}=R_1+R_2=\frac{({\rho }_1+{\rho }_2)L}{A}$

Or, we can write

$\frac{{\rho }_{eq}2L}{A}=\frac{({\rho }_1+{\rho }_2)L}{A}$

Therefore,

${\rho }_{eq}=\frac{{\rho }_1+{\rho }_2}{2}$

Hence, Option $\text{A}$ is the correct answer