Question

Two metal wires of identical dimensions are connected in series. If ${\sigma }_1$ and ${\sigma }_2$ are the conductivities of the metals respectively, the effective conductivity of the combination is

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

Answer 1

The correct option is D $\frac{{\sigma }_1{\sigma }_2}{{\sigma }_1+{\sigma }_2}$


$R=R1+R2$

$\rho lA=\rho 1lA+\rho 2lA\rho =\rho 1+\rho 21\sigma =1\sigma 1+1\sigma 2\sigma =\sigma 1\sigma 2\sigma 1+\sigma 2R=R_1+R_2$ $\frac{\rho l}{A}=\frac{{\rho }_{1}l}{A}+\frac{{\rho }_{2}l}{A}$

$\rho ={\rho }_1+{\rho }_2$

$\frac{1}{\sigma }=\frac{1}{{\sigma }_1}+\frac{1}{{\sigma }_2}$

$\sigma =\frac{{\sigma }_1{\sigma }_2}{{\sigma }_1+{\sigma }_2}$