Solved: CALC The current in a wire varies with time

Chapter 25, Problem 7E

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QUESTION:

Problem 7E

CALC The current in a wire varies with time according to the relationship I = 55 A – (0.65 A/s2)t2. (a) How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and t = 8.0 s? (b) What constant current would transport the same charge in the same time interval?

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QUESTION:

Problem 7E

CALC The current in a wire varies with time according to the relationship I = 55 A – (0.65 A/s2)t2. (a) How many coulombs of charge pass a cross section of the wire in the time interval between t = 0 and t = 8.0 s? (b) What constant current would transport the same charge in the same time interval?

ANSWER:

Solution 7E

Step 1:

a) We have to find out the amount of charge flowing in a particular time through a circuit.

It is provided, I = 55A - (0.65 A/s2) t2

But, we know that, I = dQ/dt

Therefore, we can write, dQ = I . dt

Integrating both the sides, we get, total charge,  

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