Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Current in Conductors
The amount of charge passing through a cross-section of a wire in time t is given by Q(t) = At^2 + Bt + C . Determine the dimensional formulae for A , B , and C .
Options
- AIT⁻¹ , I , IT
- BIT⁻² , IT⁻¹ , I
- CI , IT , IT^2
- DIT , I , IT^ -1
Correct answer
A. IT⁻¹ , I , IT
Step-by-step solution
According to the principle of homogeneity of dimensions, each term in the expression At^2 + Bt + C must have the same dimensional formula as the charge Q . The dimensional formula of charge Q is [IT] . For the first term: [At^2] = [Q] [A][T^2] = [IT] [A] = [IT⁻¹] For the second term: [Bt] = [Q] [B][T] = [IT] [B] = [I] For the third term: [C] = [Q] [C] = [IT] Thus, the dimensional formulae for A , B , and C are IT⁻¹ , I , and IT respectively.