First slide

Dimensions of physical quantities

Question

The dimensional representation of specific resistance in terms of charge $Q$ is

Moderate

A

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

$[{ML}^{2} T^{- 2} Q^{2}]$
C

${[MLT}^{- 2} Q^{- 1}]$
D

$[{ML}^{2} T^{- 2} Q^{- 1}]$

Solution

Since, $R = \frac{ρ l}{A}$ , where $ρ$ is a specific resistance.
$∴ [ρ] = [\frac{R A}{l}], R = \frac{V}{i}, V = \frac{W}{Q} [ρ] = [{ML}^{3} T^{- 1} Q^{- 2}]$

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