The dimensional formula of electric capacity (capacitance) is [M−1L−2T4A2]\left[M^{-1}L^{-2}T^{4}A^{2}\right][M−1L−2T4A2]. This is derived from the definition of capacitance as the ratio of electric charge QQQ to electric potential difference VVV, where:
- The dimension of charge QQQ is [AT]\left[AT\right][AT] (current times time).
- The dimension of electric potential VVV is [ML2T−3A−1]\left[ML^{2}T^{-3}A^{-1}\right][ML2T−3A−1].
Thus, the dimensional formula of capacitance C=QVC=\frac{Q}{V}C=VQ is:
[C]=[AT][ML2T−3A−1]=[M−1L−2T4A2]\left[C\right]=\frac{\left[AT\right]}{\left[ML^{2}T^{-3}A^{-1}\right]}=\left[M^{-1}L^{-2}T^{4}A^{2}\right][C]=[ML2T−3A−1][AT]=[M−1L−2T4A2]
where MMM is mass, LLL is length, TTT is time, and AAA (or III) is electric current.
