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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Subjective Medium Published on 18th 08, 2020
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