Physics

If $$y = \dfrac { t } { \varepsilon _ { 0 } L V }$$ where t is time, $$L$$ is length, $$V$$ is potential and $$\varepsilon _ { 0 }$$ is permittivity, then dimension of $$y$$ is same as that of:


SOLUTION
since

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

$$\left[ t \right] =\left[ T \right] $$

$$\left[ V \right] =\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -3 }{ A }^{ -1 } \right] $$

$$\left[ l \right] =\left[ L \right] $$

from given equation: $$y=\cfrac { t }{ { \varepsilon  }_{ 0 }LV } $$

from RHS  $$\cfrac { \left[ T \right]  }{ \left[ { M }^{ -1 }{ L }^{ -3 }{ T }^{ 4 }{ A }^{ 2 } \right] \left[ L \right] \left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -3 }{ A }^{ -1 } \right]  } $$

$$=\cfrac { \left[ T \right]  }{ \left[ { T }^{ 4-3 }{ A }^{ 2-1 } \right]  } =\cfrac { \left[ T \right]  }{ \left[ T \right] \left[ A \right]  } $$

$$=\left[ { A }^{ -1 } \right] $$
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