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

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Quantrex Academy · Accepted Answer

Correct answer: B. 53 A

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) = \dfrac{dQ}{dt} = \dfrac{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 \text{ s}

, the current is:

I(5) = 10(5) + 3 = 50 + 3 = 53 \text{ A}

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