(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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(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: $R = \frac{[ML^2T^{-3}I^{-1}]}{[I]} = [ML^2T^{-3}I^{-2}]$.

Class 11 Physics Units, Dimensions and Measurement Dimensions and Dimensional Formula

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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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A
$M^1L^2T^{-2}I^{-2}$
B
$M^1L^2T^{-1}I^{-1}$
C
$M^1L^2T^{-3}I^{-2}$
D
$M^1L^2T^{-3}I^{-1}$

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Units, Dimensions and Measurement

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Dimensions and Dimensional Formula

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The potential energy of a particle varies with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$,where $A$ and $B$ are constants. The dimensions of $AB$ are

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Different physical quantities are given in Column-$I$ and their dimensional formulas are given in Column-$II$. Match them appropriately.

Column-$I$ Column-$II$

$(a)$ Viscous force $(i)$ $[M^1 L^1 T^{-2}]$

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$(iii)$ $[M^1 L^{-1} T^{-2}]$

Column-$I$	Column-$II$
$(a)$ Viscous force	$(i)$ $[M^1 L^1 T^{-2}]$
$(b)$ Coefficient of viscosity	$(ii)$ $[M^1 L^{-1} T^{-1}]$
	$(iii)$ $[M^1 L^{-1} T^{-2}]$

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Which of the following pairs of physical quantities has the same dimensions?

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$A$ gas satisfies the relation $P V^{5/3} = K$, where $P$ is pressure, $V$ is volume, and $K$ is a constant. The dimensions of constant $K$ are:

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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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Different physical quantities are given in Column-$I$ and their dimensional formulas are given in Column-$II$. Match them appropriately.

Column-$I$ Column-$II$

$(a)$ Viscous force $(i)$ $[M^1 L^1 T^{-2}]$

$(b)$ Coefficient of viscosity $(ii)$ $[M^1 L^{-1} T^{-1}]$

$(iii)$ $[M^1 L^{-1} T^{-2}]$