# 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) ? Option 1) $\sqrt{\frac{\mu_{0}}{\varepsilon _{0}}}$ Option 2) $\frac{\varepsilon _{0}}{\mu_{0}}$ Option 3) $\frac{\mu_{0}}{\varepsilon _{0}}$ Option 4) $\sqrt{\frac{\varepsilon _{0}}{\mu_{0}}}$

Unit and Dimension -

Ohm.mt - S.I Unit

$ML^{3}T^{-3}A^{-2}\rightarrow$ Dimensions

- wherein

specific resistance

Dimension of $\varepsilon _{0}=\left[M^{-1}L^{-3}T^{4}A^{2}} \right ]$

Dimension of $\mu_{0}=\left[MLT^{-2}A^{-2} \right ]$

$R=\frac{V}{I}=\frac{W}{q\cdot I}=\frac{\left[ML^{2}T^{-2} \right ]}{\left[AT\cdot A \right ]}$

$R= \left[ML^{2}T^{-3}A^{-2} \right ]$

Check option (1) $\sqrt{\frac{\mu_{0}}{\varepsilon _{0}}}=\frac{\left[MLT^{-2}A^{-2} \right ]^{1/2}}{\left[M^{-1}L^{-3}T^{4}A^{2} \right ]^{1/2}}$$=\left[ML^{2}T^{-3}A^{-2} \right ]=[R]$

Option 1)

$\sqrt{\frac{\mu_{0}}{\varepsilon _{0}}}$

Option 2)

$\frac{\varepsilon _{0}}{\mu_{0}}$

Option 3)

$\frac{\mu_{0}}{\varepsilon _{0}}$

Option 4)

$\sqrt{\frac{\varepsilon _{0}}{\mu_{0}}}$

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