Question

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

(1) \([\mathrm{F}]=\left[\mathrm{C}^{2} \mathrm{M}^{-2} \mathrm{~L}^{2} \mathrm{~T}^{2}\right]\)

(2) \([\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]\)

(3) \([\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{2}\right]\)

(4) \([F]=\left[C^{2} M^{-1} L^{-2} \ T^{2}\right]\)

Answer 1

Correct option is : (4) \([F]=\left[C^{2} M^{-1} L^{-2} \ T^{2}\right]\) 

\( C=\frac{q}{V}=\frac{q \cdot q}{V \cdot q}=\frac{q^{2}}{W D}=\frac{C^{2}}{M L ^{2} T^{-2}}=C^{2} M^{-1} L^{-2} T^{2}\)