Question

The amount of charge passed in time t through a cross-section of a wire is Q(t) = At${}^2$ + Bt + C. (a) Write the dimensional formulae for A, B and C. (b) If the numerical values of A, B and C are 5, 3 and 1 respectively in SI units, find the value of the current, at t = 5 s.

Answer 1

$Q\left(t\right)=A{t}^2+Bt+C$

(a) $A{t}^2=Q$

$\Rightarrow A=\frac{Q}{t^2}=\frac{I}{t}=\left[A{T}^{-1}\right]$

(b) Bt = Q

$\Rightarrow B=\frac{Q}{t}=I=\left[A\right]$

(c) C = [Q]

$\Rightarrow C=A^1{T}^1$

(d) $\text{Current}i=\frac{dQ}{dT}=\frac{d}{dT}(A{t}^2+Bt+C)$

2 At + B = 2$\times 5\times 5+3=53A$