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

Rui Baldwin 2021-10-03 Answered

The current in a wire varies with time according to the relation I=55A?(0.65As2)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?
Express your answer using two significant figures.

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Expert Answer

grbavit
Answered 2021-10-04 Author has 109 answers
Step 1
The charge passing through a cross section in the time interval is given by
q=t1t2Itd
Substitute (55A(0.65As2)t2) for I, 0s for t1, and 8.5s for t2 to find the charge.
q=0s8.5s(55A(0.65As2)t2)dt
=[55tA]0s8.5s[0.65t32]0s8.5s
=467.5C133.1C
=334.1C
The amount of charge that pass a cross section in the given time interval is 334.1C.
Step 2
The constant current is given by the equation
I=Qt
=Qt2t1
Substitute 334.1 C for Q and 8.5s for t2 and 0s for t1 to find I.
I=334.1C8.5s0s
=39.3A.
The constant current that would transport the charge is 39.3A.
Answer:
The amount of charge that pass a cross section in the given time interval is 334.1C.
The constant current that would transport the charge is 39.3A.
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