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The current in a wire varies with time according to the relation I=55A?(0.65A/s2)t2

How many coulombs of charge pass a cross section of the wire in the time interval between t=0 and t = 8.5s ?
Express your answer using two significant figures.
What constant current would transport the same charge in the same time interval?

1 Answer

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Final answer:

The total charge passing through the wire in the given time interval is 7.39 coulombs. A constant current of 0.87 amperes would transport the same charge in the same time interval.

Step-by-step explanation:

The charge passing through a cross-section of the wire can be found by integrating the current over the time interval. In this case, the current is given by the equation I=55A(0.65A/s^2)t^2. To find the charge passing through the wire, we need to evaluate the integral of this equation from t=0 to t=8.5s:

Q = ∫I dt = ∫55A(0.65A/s^2)t^2 dt = 7,39C

Therefore, the total charge passing through a cross section of the wire in the time interval between t=0 and t=8.5s is 7.39 coulombs.

To find the constant current that would transport the same charge in the same time interval, we can rearrange the equation Q = It to solve for I:

I = Q / t = 7.39C / 8.5s = 0.87A

Therefore, a constant current of 0.87 amperes would transport the same charge in the same time interval.

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