Question

Two wires of same dimensions but resistivities ${\rho }_1$ and ${\rho }_2$ are connected in series. The equivalent resistivity of the combination is:

• A. ${\rho }_1+{\rho }_2$
• B. $\frac{1}{2}\left({\rho }_1+{\rho }_2\right)$
• C. $\sqrt{{\rho }_1{\rho }_2}$
• D. $2\left({\rho }_1+{\rho }_2\right)$

Answer 1

The correct option is A ${\rho }_1+{\rho }_2$

$\text{Step 1: Calculation of resistance of both wires}$

We know that Resistance, $R=\rho$ $l/A$

As, the physical dimensions are same then Length $l$ and Area $A$ are constant

So, $R_1={\rho }_1$ $l/A$

$\&$ $R_2={\rho }_2$ $l/A$

$\text{Step 2: Equivalent resistance and resistivity}$

For series combination $R_{eq}=R_1+R_2=({\rho }_1+{\rho }_2)l/A$

Compare this with $R_{eq}=\left({\rho }_{eq}\right)l/A$

So, ${\rho }_{eq}={\rho }_1+{\rho }_2$

Hence, Option A is correct