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1.Units, Dimensions and Measurement
medium
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)
Solution
$\begin{array}{l}
\left[ {{\varepsilon _0}} \right] = {M^{ – 1}}{L^{ – 3}}{T^4}{A^2}\\
\left[ {{\mu _0}} \right] = M\,L\,{T^{ – 2}}{A^{ – 2}}\\
\left[ R \right] = \,M\,{L^2}\,{T^{ – 3}}{A^{ – 2}}\\
\left[ R \right] = \left[ {\sqrt {\frac{{{\mu _0}}}{{{\varepsilon _0}}}} } \right]
\end{array}$
\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]
\end{array}$
Standard 11
Physics
