If sigma_1,sigma_2,and sigma_3 are the conduc | vedclass

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(D) Conductivity $(\sigma)$ is the reciprocal of resistivity $(\rho)$. However,in the context of series connection of conductors (often referring to r

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(D) Conductivity $(\sigma)$ is the reciprocal of resistivity $(\rho)$. However,in the context of series connection of conductors (often referring to resistors),the resistance $R$ is given by $R = \rho \frac{L}{A} = \frac{L}{\sigma A}$.For three conductors of equal length $L$ and cross-sectional area $A$ connected in series,the total resistance is $R_{eq} = R_1 + R_2 + R_3$.Substituting $R = \frac{L}{\sigma A}$,we get $\frac{L}{\sigma_{eq} A} = \frac{L}{\sigma_1 A} + \frac{L}{\sigma_2 A} + \frac{L}{\sigma_3 A}$.Dividing by $\frac{L}{A}$,we get $\frac{1}{\sigma_{eq}} = \frac{1}{\sigma_1} + \frac{1}{\sigma_2} + \frac{1}{\sigma_3}$.Thus,$\sigma_{eq} = \left( \frac{1}{\sigma_1} + \frac{1}{\sigma_2} + \frac{1}{\sigma_3} \right)^{-1}$.

If $\sigma_1$,$\sigma_2$,and $\sigma_3$ are the conductivities of three conductors,what will be their equivalent conductivity when they are connected in series?

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