Question

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

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

Answer 1

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

Resistance of wire $R=\rho \frac{L}{A}$
So, resistance of first wire $R_1={\rho }_1\frac{L}{A}$
So, resistance of second wire $R_2={\rho }_2\frac{L}{A}$
Equivalent resistance $R_{eq}=R_1+R_2=({\rho }_1+{\rho }_2)\frac{L}{A}$
Or ${\rho }_{eq}\frac{L}{A}=({\rho }_1+{\rho }_2)\frac{L}{A}$
$⟹{\rho }_{eq}={\rho }_1+{\rho }_2$
So, option A is correct.