Question

If current (I) is regarded as the fourth dimension in the fundamental dimensioning system containing (M,L,T), then the dimensional formula of charge (Q) in terms of current and other fundamental dimensions is :-
A. $\left[ {L{T^2}} \right]$
B. $\left[ {{L^0}{T^0}} \right]$
C. $\left[ {{L^{ - 1}}{T^0}} \right]$
D. $\left[ {LT} \right]$

Answer 1

Hint: Every physical quantity has its dimensional formula in terms of M, L, T & A.
where,
M = Mass
L = Length
T = Time
A = Current (Ampere)

But in this question, I is regarded as the fourth dimension in place of A for current to express the dimension of charge.

Complete step by step solution:
In this question, I is used as the fourth dimension instead of A for current to express the dimensional formula of charge (Q).

We know that,
Charge = Current × Time

Since the dimension of current and time is I and T respectively, therefore dimension of charge
$Q = \left[ I \right] \times \left[ T \right]$
$Q = \left[ {IT} \right]$

Hence the correct option is D. $\left[ {IT} \right]$

Formula used : $Q = I \times T$

Note: We can also find out the dimensional formula of any quantity by its unit without knowing its formula.
For Example : Velocity has $m{s^{ - 2}}$ as its unit then its dimensional formula will be $\left[ {L{T^{ - 2}}} \right]$ because meter and second are unit of length and time respectively.