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

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

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[M L^{2} T^{- 2}]

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[M L^{2} T^{- 1} I^{- 1}]

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[M L^{2} T^{- 3} I^{- 2}]

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Solution

The correct option is C $[M L^{2} T^{- 3} I^{- 2}]$
Ohm's law: $R = \frac{V}{I}$
Also, $W = V q$ $⟹ V = \frac{W}{q}$ (where, $q = I t$ )
$⟹$ $R = \frac{W}{q I} = \frac{W}{I^{2} t}$

Dimensions of work done, $W = [M L^{2} T^{- 2}]$
$∴$ Dimension of resistance, $R = \frac{[M L^{2} T^{- 2}]}{I^{2} T} = [M L^{2} T^{- 3} I^{- 2}]$

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