The amount of charge passing through a cross-section of a wire in time t is Q(t) = At^2 + Bt + C . Assuming the numerical values of A , B , and C in SI units are 5 , 3 , and 1 respectively, find the value of the current at t = 5 s .

Step-by-step solution

Given the charge passing through the cross-section as a function of time: Q(t) = At^2 + Bt + C The current I is the rate of flow of charge, given by the derivative of Q(t) with respect to time t : I(t) = dQ dt = d dt (At^2 + Bt + C) = 2At + B Substituting the given numerical values A = 5 and B = 3 : I(t) = 2(5)t + 3 = 10t + 3 At t = 5 s , the current is: I(5) = 10(5) + 3 = 50 + 3 = 53 A