Charge and Current in a Wire: Why is the Current Zero at t=2s?

[twiztidmxcn]

hey

i'm doing this problem with charge and current in a wire and am having a bit of difficulty in the final part of the problem.

A total amount of charge (C) that enters a wire is given by Q = 4t - t^2, where t is greater than or equal to zero and in seconds.

A) graph this equation, t interval 0->4
B) Find current expression in terms of time
C) graph this, t interval 0->4
D) explain why I has value at t=2s that is observed.

I've done A-C already. I know that I = dQ/dt, took the derivative and graphed both equations for the given intervals. I know that at t=2s, the current is 0A. My question is, why is this?

I figure that it's due to the fact that at this point in time, the wire has the maximum amount of charge entering it that it can handle and then the current starts flowing the opposite direction. I think it possibly has roots in conductivity/resitivity, though I'm not fully sure.

Any help in the right direction would be much appreciated
thanks
-twiztidmxcn

 

[mezarashi]

I don't think there's anything too profound in that question, and I think you already have the right understanding. The wire can be connected to any sort of electrical component which we are unfortunately not given. But at t=2, the charge entering the wire has become charge leaving the wire, so you will see the reversal of current.

 

[lightgrav]

That function : Q(t) = 4[A] t - 1[A/s] t^2 , is contrived for this question.
There is no interesting physical situation that will provide charge like that
(except for a circuit intentionally designed and constructed to demonstrate it)
You will never see such a function again - it is an exercise.

Hint: What's happening with the Q function at this time?

 

[twiztidmxcn]

yea, randomly generated physics problems out of a book tend not to have any real interesting value beyond demonstration of equation usage

anyways, to the both of you who helped, thanks you

-twiztidmxcn

 

[plusaf]

yea, randomly generated physics problems out of a book tend not to have any real interesting value beyond demonstration of equation usage

anyways, to the both of you who helped, thanks you

-twiztidmxcn

please let me add this: the equation given in the beginning tells what the current flow for "the circuit" will be versus time.

the problem statement invites your mind to try to figure out what kind of circuit could produce that kind of charge flow.

:) that's irrelevant. the equation specifies the charge flow, and the reason it's zero is "because" that's a solution to the equation at t=2
:)

i think one other trap is the "charge entering the wire" statement. for this kind of problem, the charge, a bit more accurately, is flowing through the wire, according to the given equation. :) wires don't tend to accumulate charge... :) at least, not on their own, i'd say.

you're doing just fine!