Electric Current (Physics II Question)?

Question

I'm having problems with an online homework problem for my Phys II class. When I try to type what I get as a response, I get a notice that says my answer is off by 10%.
The question is:
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The quantity of charge q (in coulombs) that has passed through a surface of area 1.92 cm^2 varies with time according to the equation q = 4t^3 + 5t + 6, where t is in seconds.

(a) What is the instantaneous current through the surface at t = 0.92 s?

(b) What is the value of the current density?
______ kA/m2
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I know the equations for the problem, but when I substitute the numbers, i don't get the right answer.
Can somebody give me a short explanation?
I would really appreciate it.

I got part (a)...
I took the derivative, and got 12t^2+5, and plugged in the value for t to get 15.157.

for part b i tried doing
j=i/A
j=15.157/A
where A = 3.68E-4
but the answer i get isn't correct.

Answer 1

did u convert area from cm^2 to m^2

Answer 2

You accidentally squared the area again. I think you might've thought that was the length of one side, instead of using it as the area.
Your equations are correct otherwise.
You have to convert the surface area of 1.92 cm^2 to m^2.
then do
j=i/A
j=15.157/.000192 = 78.942 kA.

Answer 3

I can't see why you got A= 3.68E-4

We don't know the shape of the area, so consider it a rectangle
1.92 cm x 1 cm, so area = 1.92 cm^2
or 1.92E-2 m x 1E-2 m, so area = 1.92E-4 m^2

Answer 4

akm69 gave a good answer but the fuse (part b) should be 5A, not 3A. A current of 3.48A would 'blow' the 3A. You should always select the fuse-rating which the next-highest one up from the normal current.