Physics

The dimensional formula of capacitance is _____. Take $Q$ as the dimension formula of charge

${ M }^{ -1 }{ L }^{ -2 }{ T }^{ 2 }{ Q }^{ 2 }\quad$

SOLUTION
We know that Capacitance is given as:
$C=\cfrac { Q }{ V }$

The voltage is defined as the work done per unit charge.
$V=\cfrac { W }{ Q }$

$\implies C=\cfrac { { Q }^{ 2 } }{ W }$
$C=\cfrac { \left[ { Q }^{ 2 } \right] }{ \left[ M{ L }^{ 2 }{ T }^{ -2 } \right] } =\left[ { M }^{ -1 }{ L }^{ -2 }{ T }^{ 2 }{ Q }^{ 2 } \right]$

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Single Correct Medium Published on 18th 08, 2020
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