Question

S.I. unit of electric capacity.
A. Stat Farad
B. Farad
C. Coulomb
D. Stat Coulomb

Answer 1

Hint: The ratio of change in charge to the change in electric potential difference is defined as the electric capacity in a system. It is denoted by C. It is also called the capacitance of a device.

Complete step-by-step solution -
The ratio of change in charge to the change in electric potential difference is defined as the electric capacity in a system. In other words, electric capacity is the amount of charge deposited for one unit of electric potential difference. It is denoted by C.
The unit of electric capacity will be the ratio of the unit of charge to the unit of electric potential difference.
The SI unit of charge is coulomb, denoted by C.
The SI unit of electric potential is volt, denoted by V.
Therefore, the SI unit of electric capacity is $\dfrac{\text{coulomb}}{\text{volt}}=\dfrac{C}{V}$, which is called farad. The unit farad is denoted by F.
An electric capacity of 1 Farad is equal to the deposition of 1 coulomb of charge for a potential difference of one volt.
Therefore, the SI unit of electric capacity is Farad (F).
Hence, the correct option is B.
Additional Information: The dimension of electric capacity is the ratio of the dimension of charge (Q) to the dimension of potential difference ($\Delta$V).
i.e. $\left[ C \right]=\dfrac{\left[ Q \right]}{\left[ \Delta V \right]}$.
The dimensional formula of charge is [AT].
The dimensional formula of electric potential is $\left[ M{{L}^{2}}{{T}^{-3}}{{A}^{-1}} \right]$.
Therefore, the dimensional formula of electric capacity is $\dfrac{\left[ AT \right]}{\left[ M{{L}^{2}}{{T}^{-3}}{{A}^{-1}} \right]}=\left[ {{M}^{-1}}{{L}^{-2}}{{T}^{4}}{{A}^{2}} \right]$.

Note: Let us discuss the other units mentioned in the options.
(i) Stat Farad : It is also a unit of electric capacity. However, stat farad is a CGS unit of electric capacity i.e. in the terms of centimetre, gram and seconds.
(ii) Coulomb : We have already used this unit in this solution and we know that it is the SI unit of charge.
(iii) Stat Coulomb : It is the unit of charge in the CGS system.