Which of the following combinations has the d | vedclass

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(D) The dimensional formula for permittivity of vacuum is $[\varepsilon_0] = M^{-1}L^{-3}T^4A^2$.The dimensional formula for permeability of vacuum is

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$\sqrt {\frac{{\mu _0}}{{\varepsilon _0}}} $

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(D) The dimensional formula for permittivity of vacuum is $[\varepsilon_0] = M^{-1}L^{-3}T^4A^2$.The dimensional formula for permeability of vacuum is $[\mu_0] = MLT^{-2}A^{-2}$.The dimensional formula for electrical resistance is $[R] = ML^2T^{-3}A^{-2}$.Now,consider the expression $\sqrt{\frac{\mu_0}{\varepsilon_0}}$:$\sqrt{\frac{\mu_0}{\varepsilon_0}} = \sqrt{\frac{MLT^{-2}A^{-2}}{M^{-1}L^{-3}T^4A^2}} = \sqrt{M^2L^4T^{-6}A^{-4}} = ML^2T^{-3}A^{-2}$.This matches the dimension of electrical resistance $[R]$.Therefore,the correct option is $D$.

Which of the following combinations has the dimension of electrical resistance? (Here,$\varepsilon_0$ is the permittivity of vacuum and $\mu_0$ is the permeability of vacuum.)

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