Charge entering element, current as a func of time

In summary, the current into the element as a function of time is given by q(t) = -7.5A * e^(t/τ), where τ is measured in seconds. This can be derived by taking the derivative of the equation q(t) = 7.5C * (1 - e^(t/τ)) with respect to time, and the resultant unit is A (amps), which is the rate of flow of charge.
  • #1
SteelDirigibl
40
0

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...
 
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  • #2
SteelDirigibl said:
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.
 
  • #3
yep... what am I missing?
 
  • #4
Perhaps you are missing the concept of a rate (using calculus).
 
  • #5
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?
 
  • #6
SteelDirigibl said:
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.
 
  • #7
so do I need to take the derivative?

-7.5C/τ*e(t/τ)

or

-7.5A*e(t/τ)
 
  • #8
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.
 
Last edited:
  • #9
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.
 
  • #10
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
 
Last edited by a moderator:

Related to Charge entering element, current as a func of time

1. What is charge entering an element?

Charge entering an element refers to the amount of electric charge that flows into a specific part of a circuit or system. This can be measured in coulombs and is typically represented by the symbol Q.

2. How is current related to time?

Current, represented by the symbol I, is the rate at which charge flows through a circuit. It is directly proportional to time, meaning that as time increases, the current also increases or decreases accordingly.

3. What is the function of time in determining current?

The function of time is to show how the current changes over a given period. It helps to visualize the pattern and behavior of current in a circuit, and can also be used to calculate the average or instantaneous current at a specific point in time.

4. How does the charge entering an element affect current?

The charge entering an element directly affects the current in the circuit. As more charge enters, the current increases, and as less charge enters, the current decreases. This relationship is described by the equation I = Q/t, where Q is the charge and t is the time.

5. Can current change over time in a circuit?

Yes, current can change over time in a circuit. This is because the flow of charge can be influenced by various factors such as the voltage, resistance, and capacitance in the circuit. These factors can change over time, causing the current to also change accordingly.

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