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

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(C) The effective resistance $R_{eff}$ for resistors connected in series is given by $R_{eff} = R_1 + R_2 + R_3$.Since conductivity $\sigma = \frac{1}

Vedclass · Accepted Answer

$\frac{\sigma_1 \sigma_2 \sigma_3}{\sigma_1 \sigma_2 + \sigma_2 \sigma_3 + \sigma_3 \sigma_1}$

Vedclass · Answer

(C) The effective resistance $R_{eff}$ for resistors connected in series is given by $R_{eff} = R_1 + R_2 + R_3$.Since conductivity $\sigma = \frac{1}{\rho}$ and resistance $R = \frac{\rho L}{A} = \frac{L}{\sigma A}$,for conductors of equal length $L$ and cross-sectional area $A$,we have $R = \frac{1}{\sigma}$.Substituting this into the series resistance formula: $\frac{1}{\sigma_{eff}} = \frac{1}{\sigma_1} + \frac{1}{\sigma_2} + \frac{1}{\sigma_3}$.Taking the common denominator: $\frac{1}{\sigma_{eff}} = \frac{\sigma_2 \sigma_3 + \sigma_1 \sigma_3 + \sigma_1 \sigma_2}{\sigma_1 \sigma_2 \sigma_3}$.Therefore,the equivalent conductivity is $\sigma_{eff} = \frac{\sigma_1 \sigma_2 \sigma_3}{\sigma_1 \sigma_2 + \sigma_2 \sigma_3 + \sigma_3 \sigma_1}$.

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

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