Question

Write the dimensional formula of capacitance.

• A. $\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]$
• B. $\left[M^{-2}{L}^{-4}{T}^5{A}^3\right]$
• C. $\left[M^{}{L}^2{T}^{-2}{A}^0\right]$
  
• D. None of these

Answer 1

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

Since charge on a capacitor with capacitance $C$ is given by $q=CV$,

therefore, $C=\frac{q}{V}$.

Hence, $\left[C\right]=\frac{q}{V}=\frac{\left[AT\right]}{\left[M{L}^2{T}^{-3}{A}^{-1}\right]}=\left[M^{-1}{L}^{-2}{A}^2{T}^4\right]$