Dimensions of resistance in an electrical cir | vedclass

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(C) According to Ohm's law,$V = RI$,which implies $R = \frac{V}{I}$.Dimensions of potential difference $V$ are given by $V = \frac{W}{q}$,where $W$ is

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

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(C) According to Ohm's law,$V = RI$,which implies $R = \frac{V}{I}$.Dimensions of potential difference $V$ are given by $V = \frac{W}{q}$,where $W$ is work and $q$ is charge.Dimensions of work $W = [ML^2T^{-2}]$ and charge $q = [IT]$.Therefore,dimensions of $V = \frac{[ML^2T^{-2}]}{[IT]} = [ML^2T^{-3}I^{-1}]$.Now,substituting this into the expression for resistance: $R = \frac{[ML^2T^{-3}I^{-1}]}{[I]} = [ML^2T^{-3}I^{-2}]$.

Dimensions of resistance in an electrical circuit in terms of dimension of mass $M$,of length $L$,of time $T$,and of current $I$ would be:

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