The current in a conductor varies in time as shown in the figure. (a) How many c

Question

The current in a conductor varies in time as shown in the figure. (a) How many coulombs of charge pass through a cross section of the conductor in the interval t = 0 to t = 5.0 s?

What constant current would transport the same total charge during the 5.0-s interval as does the actual current?

The current in a conductor varies in time as shown in the figure. (a) How many coulombs of charge pass through a cross section of the conductor in the interval t = 0 to t = 5.0 s? What constant current would transport the same total charge during the 5.0-s interval as does the actual current?

Explanation / Answer

)

Q = ?I(t)dt

(where I(t) is the current with respect to time).

In the interest of making this shorter, the integral is just the area underneath the curve:

You have a rectangle (the lower part) with a trapezoid on top (on the right side).

The area is thus: 2 * 5 = 10 for the rectangle

and (3 + 2) / 2 * 4 = 5*2 = 10 for the trapezoid

So the total area is 10 + 10 = 20...since each square is 1.25A * 1s = 1.25C)

The amount of coulombs passed through is 20 * 1.25 = 25 C

b) This is simple and is just asking you what the average current is:

I-avg = Q-total / t = 25 / 5 = 5 A

Which is somewhere in between the lowest: 2*1.25 = 2.5A and the peak which is at 6 * 1.25 = 7.5 A.

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