Question

Two wires of same shape whose resistivity ${\rho }_1$ and ${\rho }_2$ are connected in series. The equivalent resistivity of the combination will be :

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

Answer 1

The correct option is C $\frac{{\rho }_1+{\rho }_2}{2}$

Resistance in series
$R=R_1+R_2$
$\frac{{\rho }_{equi}{l}_{equi}}{A}=\frac{{\rho }_{1}l}{A}+\frac{{\rho }_{2}l}{A}$
${\rho }_{equi}\times 2l={\rho }_{1}l+{\rho }_{2}l$
${\rho }_{equi}=\frac{{\rho }_1+{\rho }_2}{2}$