The amount of charge passing through a cross-section of a wire in...

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.