Which of the following combinations has the dimension of electrical resistance $( { \varepsilon _0}$ is the permittivity of vacuum and ${\mu _0}$ is the permeability of vacuum$)$ ?
  • A$\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} $
  • B${\frac{{{\mu _0}}}{{{ \varepsilon_0}}}}$
  • C$\frac{{{ \varepsilon_0}}}{{{\mu _0}}}$
  • D$\sqrt {\frac{{{\mu _0}}}{{{\varepsilon_0}}}} $
JEE MAIN 2019, Medium
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$\left[ {{\varepsilon _0}} \right] = {M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$
$\left[ {{\mu _0}} \right] = M\,L\,{T^{ - 2}}{A^{ - 2}}$
$\left[ R \right] = \,M\,{L^2}\,{T^{ - 3}}{A^{ - 2}}$
$\left[ R \right] = \left[ {\sqrt {\frac{{{\mu _0}}}{{{\varepsilon _0}}}} } \right]$
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