Question

The dimensional formula of capacitance is

$[$0.77 Mark$]$

• A. $\left[M^2{L}^2{T}^4{A}^2\right]$
• B. $\left[M^{-1}{L}^{-2}{T}^{-4}{A}^2\right]$
• C. $\left[M^{-1}{L}^{-2}{T}^4{A}^{-2}\right]$
• D. $\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$

Answer 1

The correct option is D $\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$

$C=\frac{Q}{V}$
$\Rightarrow \left[C\right]=\left[\frac{Q}{V}\right]=\left[\frac{Q^2}{W}\right]$
$\Rightarrow \left[C\right]=\left[\frac{A^2{T}^2}{M{L}^2{T}^{-2}}\right]$
$\Rightarrow \left[C\right]=\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$