Question

Dimension of electric current is.
A.$[{M^0}{L^0}{T^{ - 1}}Q]$
B.$[M{L^2}{T^{ - 1}}Q]$
C.$[{M^2}L{T^{ - 1}}Q]$
D.$[{M^2}{L^2}{T^{ - 1}}Q]$

Answer 1

Hint: To write the dimensional formula of a physical quantity, we use the symbols to represent
The fundamental quantities are setting up the mathematical relation of the physical quantity with their respective exponents.
The electric charge has the dimension electric current time

Complete answer:
 The coulomb is the SI unit of electric charge, which is defined as an ampere second. A charge is defined as the root of twice the Planck constant times.
Current ($I$): Rate of charge per unit time \[I = \dfrac{Q}{t}\]
where \[Q\] is the charge
and $t$ is time (S.I. unit $s$ [second])
Unit of current: \[\dfrac{{Coulomb}}{{second}}\]
The rate of flow of charge per unit time is defined as current.
current($I$): Rate of charge per unit time \[I = \dfrac{Q}{t}\]
Where $I$ stands for current $Q$ for coulomb and $t$ for time
A coulomb is a charge transferred by a current of one ampere in one second,
The dimension of $Q$ is defined \[\left( {current \times time} \right)\] \[ = \left[ {AT} \right]\]
The dimension of time \[t = T\]
Current \[I = \dfrac{Q}{t} = \dfrac{{\left[ {AT} \right]}}{{\left[ T \right]}} = \left[ A \right]\]

Finally, the answer is, option (A)
$[{M^0}{L^0}{T^{ - 1}}Q]$

Note:
Dimensional Analysis identifies the relationships between different physical quantities by identifying their base quantities like length, mass, time, and electric current and units of measure like miles vs. kilometers, or pounds vs. kilograms by tracking the dimensions as calculations or comparisons are performed.
The conversion of units from one-dimensional unit to another is often easier within the metric or SI system than in others, due to the regular $10$-base in all units.