The current in a wire varies with time according to the relation
I = 4 + 3t²
Where I is in amperes and t is in seconds. The number of coulombs of charge that pass a cross section of the wire between t = 3 s and t = 5 s is

Question

Quizplus · Accepted Answer

To find the amount of charge that passes a cross-section of the wire between time t = 3s and t = 5s, we need to integrate the current with respect to time over that interval:

Q = ∫[3s to 5s] I dt

Q = ∫[3s to 5s] (4 + 3t) dt

Q = [4t + (3/2)t^2] [3s to 5s]

Q = [(4(5) + (3/2)5^2) - (4(3) + (3/2)3^2)]

Q = [20 + 37.5] - [12 + 13.5]

Q = 32 Coulombs

Therefore, the number of coulombs of charge that pass a cross section of the wire between t = 3 s and t = 5 s is D) 106.

The Current in a Wire Varies with Time According to the Relation