A cylindrical metal wire of length $l$ and cross sections area $S$, has resistance $R$, conductance $G$, conductivity $\sigma$ and resistivity $\rho$. Which one of the following expressions for $\sigma$ is valid
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Conductivity $\sigma = \frac{1}{\rho }$ .... $(i)$
and conductance $G = \frac{1}{R}$
$ \Rightarrow \,\,GR = 1$ ..... $(ii)$
From equation $(i)$ and $(ii)$ $\sigma = \frac{{GR}}{\rho }$
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