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(A) The electrical resistance is given by $R = \frac{\rho l}{a}$.Rearranging for resistivity,we get $\rho = \frac{R a}{l}$.The dimensional formula for

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$[M^{-1} L^{-3} T^3 A^2]$

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(A) The electrical resistance is given by $R = \frac{\rho l}{a}$.Rearranging for resistivity,we get $\rho = \frac{R a}{l}$.The dimensional formula for resistance $R$ is $[M L^2 T^{-3} A^{-2}]$.The dimensional formula for area $a$ is $[L^2]$.The dimensional formula for length $l$ is $[L]$.Substituting these into the formula for $\rho$:$\rho = \frac{[M L^2 T^{-3} A^{-2}] [L^2]}{[L]} = [M L^3 T^{-3} A^{-2}]$.Electrical conductivity $\sigma$ is the reciprocal of resistivity $\rho$,so $\sigma = \frac{1}{\rho}$.Therefore,the dimensional formula for $\sigma$ is $[M^{-1} L^{-3} T^3 A^2]$.

The electrical resistance $R$ of a conductor of length $l$ and area of cross-section $a$ is given by $R = \frac{\rho l}{a}$,where $\rho$ is the electrical resistivity. What is the dimensional formula for electrical conductivity $\sigma$,which is the reciprocal of resistivity?

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