Question

If $C$ is the capacitance and $V$ is the potential, the dimensional formula for $C{V}^2$ is

• A. $[M{L}^2{T}^{-1}]$
• B. $[M{L}^{-2}{T}^{-3}]$
• C. $[M{L}^2{T}^{-2}]$
• D. $[M{L}^{-2}{T}^{-2}]$
• E. $[M{L}^{-1}{T}^{-1}]$

Answer 1

Answer: (C)

$[C]=[M^{-1}{L}^{-2}{T}^4{A}^2]$
$[V]=[M{L}^2{T}^{-3}{A}^{-1}]$
$\therefore$ $[C{V}^2]=[M^{-1}{L}^{-2}{T}^4{A}^2]{[M{L}^2{T}^{-3}{A}^{-1}]}^2$
$=[M{L}^2{T}^{-2}]$