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Question

(C) The dimensional formula for resistance $R$ is derived from $R = \frac{V}{I} = \frac{W}{qI}$.Substituting the dimensions: $R = \frac{[ML^2 T^{-2}]}

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$\frac{h}{e^{2}}$

Vedclass · Answer

(C) The dimensional formula for resistance $R$ is derived from $R = \frac{V}{I} = \frac{W}{qI}$.Substituting the dimensions: $R = \frac{[ML^2 T^{-2}]}{[AT][A]} = [ML^2 T^{-3} A^{-2}]$.Now,let us check the dimensions of $\frac{h}{e^2}$.The dimensions of Planck's constant $h$ are $[ML^2 T^{-1}]$.The dimensions of charge $e$ are $[AT]$.Therefore,the dimensions of $\frac{h}{e^2} = \frac{[ML^2 T^{-1}]}{[AT]^2} = \frac{[ML^2 T^{-1}]}{[A^2 T^2]} = [ML^2 T^{-3} A^{-2}]$.Since the dimensions of $R$ and $\frac{h}{e^2}$ are identical,the correct option is $C$.

The dimensions of resistance are the same as those of $......$ where $h$ is the Planck's constant and $e$ is the charge.

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