Question

If M, L, T and I stand for mass, length, time and electric current respectively, the dimensional formula for capacitance is:

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

Answer 1

Answer: (C)

Capacitance $ C=\frac{Ch\arg e}{Potential}=\frac{q}{V}=\frac{Q}{W/q}=\frac{{{q}^{2}}}{W} $ Dimensions of $ \text{C = }\frac{{{\text{(Dimensions}\,\text{of}\,\text{charge)}}^{\text{2}}}}{\text{Dimensions}\,\text{of}\,\text{work}} $ $ =\frac{{{[IT]}^{2}}}{[M{{L}^{2}}{{T}^{-2}}]} $ $ =\frac{[{{I}^{2}}{{T}^{2}}]}{[M{{L}^{2}}{{T}^{-2}}]} $ $ =[{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}}] $