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 t

foass77W

foass77W

Answered question

2021-05-26

The current in a wire varies over time according to the relation I=55A?(0.65A/s2)t2.
How many electric charges 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.

Answer & Explanation

timbalemX

timbalemX

Skilled2021-05-27Added 108 answers

Step 1 
The charge flowing through a cross section in the time interval is given by
q=t1t2Itd 
Substitute (55A(0.65A/s2)t2) for I, 0s for t1, and 8.5s for t2 to find the charge. 
q=0s8.5s(55A(0.65A/s2)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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