(B) The dimension of resistance $R$ is given by $[R] = [ML^2T^{-3}A^{-2}]$.Planck's constant $h$ has dimensions $[h] = [ML^2T^{-1}]$.Electric charge $

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(B) The dimension of resistance $R$ is given by $[R] = [ML^2T^{-3}A^{-2}]$.Planck's constant $h$ has dimensions $[h] = [ML^2T^{-1}]$.Electric charge $e$ has dimensions $[e] = [AT]$.Let the dimension of $R_H$ be proportional to $h^a e^b$.$[ML^2T^{-3}A^{-2}] = [ML^2T^{-1}]^a [AT]^b = [M^a L^{2a} T^{-a+b} A^b]$.Comparing the powers of $M, L, T,$ and $A$ on both sides:For $M$: $a = 1$.For $A$: $b = -2$.Substituting these values,we get the dimension of $R_H$ as $[h^1 e^{-2}] = [h/e^2]$.Thus,the dimension of $R_H$ is the same as $\frac{h}{e^2}$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

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The quantum Hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge,then the dimension of $R_H$ is the same as

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A
$\frac{e^2}{h}$
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$\frac{h}{e^2}$
C
$\frac{h^2}{e}$
D
$\frac{e}{h^2}$

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

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The quantum Hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge,then the dimension of $R_H$ is the same as

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