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}}}

 

Answers (1)

 

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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