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.

Explanation

`Q(t) = At^2 + Bt + C`
` (a) At^2 = Q `
` rArr A = (Q/t^2) = I/t = [AT^-1]`
(b) Bt=Q
` rArr B=(Q/t) = I = [A]`
(c) C=[Q]
` rArr C= (A^1)(T^1). `
` (d) Current i = dQ/dT = d/dT(At^2 + Bt + C)`
` 2At + B = 2 xx 5 xx 5 + 3 =53A. `