Dimensional formula for capacitance is:$$\begin{align} & A.~~~~~{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}} \\ & B.~~~~~{{M}^{1}}{{L}^{2}}{{T}^{4}}{{I}^{-2}} \\ & C.~~~~~{{M}^{1}}{{L}^{2}}{{T}^{2}} \\ & D.~~~~~ML{{T}^{-1}} \\ \end{align}$$

Question

Dimensional formula for capacitance is:$$\begin{align}  & A.~~~~~{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}} \\  & B.~~~~~{{M}^{1}}{{L}^{2}}{{T}^{4}}{{I}^{-2}} \\  & C.~~~~~{{M}^{1}}{{L}^{2}}{{T}^{2}} \\  & D.~~~~~ML{{T}^{-1}} \\ \end{align}$$

Vedantu Content Team · Accepted Answer

Hint: The dimensional formula of capacitance can be found by using the dimensions of potential and charge, as capacitance is the charge per unit potential. Mathematically,
$c=\dfrac{q}{V}$ , where V is electric potential, c is the capacitance and q is the charge.
So, to obtain the dimension of capacitance we will divide the dimension of potential and charge.

Complete step by step answer:
The capacitance of a conductor is defined as the ability of that conductor to hold charge. It is the charge that a conductor can hold at unit potential or in other words capacitance can be defined as the charge required to raise the potential of a conductor to unit volt. The SI unit of capacitor is called Farad. But unit farad is a very large unit of capacitance to use for daily purpose so we use smaller units like microfarad.
Dimensional formula of a physical quantity is the expression of it in terms of symbols of fundamental units. It is enclosed in brackets. The fundamental units and their symbols are;
Mass [M] Length [L] Time [T] Current [A] Temperature [K] Amount of substance [mol] Luminous intensity [J]
Capacitance of the conductor is the charge stored per unit potential. Mathematically we can write
$c=\dfrac{q}{V}$
The dimension of potential is
$M{{L}^{2}}{{A}^{-1}}{{T}^{-3}}$
The dimension of charge is
${{M}^{0}}{{L}^{0}}{{T}^{1}}{{A}^{1}}$
So, the dimension of capacitance will be
${{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}}$ or ${{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}}$
Hence the correct option is A.
Note: Capacitance is a derived quantity, so its dimension is made from the dimension of base S.I units. The S.I base units are also known as fundamental units. Even if the power of dimension of length, time, and mass in a physical quantity is zero, it is recommended to mention them.

Dimensional formula for capacitance is:\[\begin{align} & A.~~~~~{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}} \\ & B.~~~~~{{M}^{1}}{{L}^{2}}{{T}^{4}}{{I}^{-2}} \\ & C.~~~~~{{M}^{1}}{{L}^{2}}{{T}^{2}} \\ & D.~~~~~ML{{T}^{-1}} \\ \end{align}\]

Dimensional formula for capacitance is:
\[\begin{align}
& A.~~~{{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{I}^{2}} \\
& B.~{{M}^{1}}{{L}^{2}}{{T}^{4}}{{I}^{-2}} \\
& C.~{{M}^{1}}{{L}^{2}}{{T}^{2}} \\
& D.~~~ML{{T}^{-1}} \\
\end{align}\]