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}}] $