The dimensions of resistivity in terms of M, | vedclass

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(A) The formula for resistivity $\rho$ is given by $\rho = \frac{RA}{l}$.First,find the dimensions of resistance $R$ using Ohm's law: $V = IR$,so $R =

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$M L^3 T^{-1} Q^{-2}$

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(A) The formula for resistivity $\rho$ is given by $\rho = \frac{RA}{l}$.First,find the dimensions of resistance $R$ using Ohm's law: $V = IR$,so $R = \frac{V}{I}$.Since $V = \frac{W}{Q}$ (work per charge),the dimensions of $V$ are $[M L^2 T^{-2} Q^{-1}]$.The dimensions of current $I$ are $[Q T^{-1}]$.Thus,the dimensions of $R$ are $\frac{[M L^2 T^{-2} Q^{-1}]}{[Q T^{-1}]} = [M L^2 T^{-1} Q^{-2}]$.Now,substitute the dimensions of $R$,area $A$ $([L^2])$,and length $l$ $([L])$ into the resistivity formula:$[\rho] = \frac{[M L^2 T^{-1} Q^{-2}] \cdot [L^2]}{[L]} = [M L^3 T^{-1} Q^{-2}]$.

The dimensions of resistivity in terms of $M, L, T$ and $Q$,where $Q$ stands for the dimensions of charge,is:

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