Which of the following combinations has the dimension of electrical resistance ( ε 0 is the permittivity of vacuum and μ 0 is the permeability of vacuum)? (a) √((ε₀)/(μ₀)) (b) (ε₀)/(μ₀) (c) √((μ₀)/(ε₀)) (d) (μ₀)/(ε₀)

Answer: (c). (1)/(√(μ₀ε₀)) = c gives μ₀ε₀ = 1/c². [μ₀] = [MLT⁻²A⁻²], [ε₀] = [M⁻¹L⁻³T⁴A²]. (μ₀)/(ε₀) = [M²L⁴T⁻⁶A⁻⁴] ⇒ √((μ₀)/(ε₀)) = [ML²T⁻³A⁻²] This is the dimension of resistance ( R = V/I); its value is about 377 Ω. So the answer is (c) √(μ₀/ε₀).

Which of the following combinations has the dimension of electrical… | JEE Main 2019 (12 Apr, Shift 1)

Q81JEE Main 2019 · 12 APR · SHIFT 1Easy

Units & Dimensions

Which of the following combinations has the dimension of electrical resistance ( $\epsilon$ 0 is the permittivity of vacuum and $\mu$ 0 is the permeability of vacuum)?

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Answer: (c)

$\dfrac{1}{\sqrt{\mu_0\varepsilon_0}} = c$ gives $\mu_0\varepsilon_0 = 1/c^2$ .
$[\mu_0] = [\mathrm{MLT^{-2}A^{-2}}]$ , $[\varepsilon_0] = [\mathrm{M^{-1}L^{-3}T^{4}A^{2}}]$ .
$\dfrac{\mu_0}{\varepsilon_0} = [\mathrm{M^2L^4T^{-6}A^{-4}}] \Rightarrow \sqrt{\dfrac{\mu_0}{\varepsilon_0}} = [\mathrm{ML^2T^{-3}A^{-2}}]$
This is the dimension of resistance ( $R = V/I$ ); its value is about $377\ \Omega$ .
So the answer is (c) $\sqrt{\mu_0/\varepsilon_0}$ .

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