Which one of the following is the correct dimensional formula for the capacitance, whose unit is the farad F? Here M, L, T and C stand for the units of mass, length, time and charge respectively.

Question

Accepted Answer

(1) [F]=[C²M⁻¹L⁻²T²]. C=Q/V, so the dimensions of capacitance are those of charge divided by those of potential. Potential is work per unit charge: [V]=([ML²T⁻²])/([C])=[M L²T⁻²C⁻¹]. Hence [C_cap]=([C])/([ML²T⁻²C⁻¹])=[C²M⁻¹L⁻²T²]. So the farad has dimensions [C²M⁻¹L⁻²T²].

Which one of the following is the correct dimensional formula for the capacitance, whose unit is the farad F? Here M, L, T and C stand for the units of mass, length, time and charge respectively.

Step-by-step solution

Why the other options are wrong