In terms of resistance R and time T, the dimensions of ratio (μ)/(ε) of the permeability μ and permittivity ε is: (a) [RT ⁻² ] (b) [R2T ⁻¹ ] (c) [R2] (d) [R2T2]

Answer: (c). √(μ/ε) is the wave impedance, measured in ohm. [μ/ε] = M²L⁴T⁻⁶A⁻⁴ = [R]², with [R] = ML²T⁻³A⁻². So the answer is (c) [R²].

In terms of resistance R and time T, the dimensions of ratio (μ)/(ε)… | JEE Main 2014 (11 Apr, Shift 1)

Q83JEE Main 2014 · 11 APR · SHIFT 1Easy

Units & Dimensions

In terms of resistance R and time T, the dimensions of ratio $\frac{\mu}{\epsilon}$ of the permeability $\mu$ and permittivity $\epsilon$ is:

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Answer: (c)

$\sqrt{\mu/\epsilon}$ is the wave impedance, measured in ohm.
$[\mu/\epsilon] = \mathrm{M^2L^4T^{-6}A^{-4}} = [R]^2$ , with $[R] = \mathrm{ML^2T^{-3}A^{-2}}$ .
So the answer is (c) $[R^2]$ .