Charge entering element, current as a func of time

[SteelDirigibl]

Homework Statement

Over time (0s ≤ t < ∞), charge enters an element according to q(t) = 7.5C · (1 − e^(+t/τ)).

1. What is the current into the element as a function of time? (Find a symbolic answer!)
2. What is the unit of τ?
3. Prove that the unit of the result indeed is A.

The Attempt at a Solution

Do I need to take the integral of this to get current as a function of time? I don't suppose I cane just separate the coulomb int A*s and get the A by itself or is that not right?

And I don't know where else to go on this problem...

 

[MisterX]

Do I need to take the integral of this to get current as a function of time?

I suggest you look up the definition of electric current. You should know it already, though.

 

[SteelDirigibl]

yep... what am I missing?

 

[MisterX]

Perhaps you are missing the concept of a rate (using calculus).

 

[SteelDirigibl]

q(t) = 7.5C · (1 − e^(+t/τ)).

In this equation, the final output is in C, is it not? then would the units of tau be seconds also, so then to have this find current, can I multiply the whole thing by 1/t leaving me with amps as the resultant unit?

 

[MisterX]

so then to have this find current, can I multiply the whole thing by 1/t leaving me with amps as the resultant unit?

You're supposed to find the instantaneous current. Yes, if you divided by time, your answer would have the correct units. But that answer itself wouldn't be correct.

 

[SteelDirigibl]

so do I need to take the derivative?

-7.5C/τ*e^(t/τ)

or

-7.5A*e^(t/τ)

 

[MisterX]

What do you think and why? This is a very basic question. I don't think it's something with which you should struggle this much, if you are studying physics or engineering at the college level.

 

[SteelDirigibl]

i think that's right, because coulombs is the current coming in over an amount of time. (amps times however many seconds) so derivative would give instantaneous current at a given time.

 

[crixus]

current is rate of flow of charge.
So you need to take a derivative of the given expression.
exponentials are dimensionless t = unit of time so T = time too :)
as you take derivative you intitutively divide by DELTA t and take limit 0 so you have unit C/t = A