Hello I have a HW problem and dont need you all to solve just want to make sure im correct about my approach.
So I have a charge q(t) = -15e^-4t mC entering a positive terminal of an element. And givin a time of 0<t<200mS. Find the current.

and current = dq/dt I would just plug and chug and take difference?

(-15e^-4(200mS)) - (-15e^-4(0)) / (200mS-0mS)

Because I am stuck thinking I have to take the derivative of the charge. But I think I might be overthinking this.

 

By doing this, you calculate the average current over that interval of time.

 

By doing this, you calculate the average current over that interval of time.

Yes you are correct, after doing abunch of calculus my brain immediately goes to taking derivatives when I see a (d) infront of anything now lol. But just taking the difference after plugging in the times would be the solution correct?

 

Hello I have a HW problem and dont need you all to solve just want to make sure im correct about my approach.
So I have a charge q(t) = -15e^-4t mC entering a positive terminal of an element. And givin a time of 0<t<200mS. Find the current.

and current = dq/dt I would just plug and chug and take difference?

(-15e^-4(200mS)) - (-15e^-4(0)) / (200mS-0mS)

Because I am stuck thinking I have to take the derivative of the charge. But I think I might be overthinking this.

Hi,

Think about what dq is and what dt is.
dq is the change in charge.
dt is the change in time.

Sometimes we think of this in terms of a discrete system instead of continuous. We replace each 'd' with the symbol for 'delta' so we end up with:
(delta q)/(delta t)

so a small change in 'q' over a small change in 't' which simply creates a fraction. The only catch is that if 'q' is curved with time, then the current is the average current only over the time period which is the 'delta t'. If it does curve, then it could be different fraction at another time. When it is a straight line though it is good for all time.

 

Hello I have a HW problem and dont need you all to solve just want to make sure im correct about my approach.
So I have a charge q(t) = -15e^-4t mC entering a positive terminal of an element. And givin a time of 0<t<200mS. Find the current.

and current = dq/dt I would just plug and chug and take difference?

(-15e^-4(200mS)) - (-15e^-4(0)) / (200mS-0mS)

Because I am stuck thinking I have to take the derivative of the charge. But I think I might be overthinking this.

The problem is very poorly stated.

The notion of charge as a function of time would apply to the total charge in some manner -- the total charge at time t on a capacitor plate, or the total charge that has passed a point since t=0. But saying that it represents the charge entering (i.e., immediate present tense) a positive terminal (i.e., passing a point) is not a description of charge, but a description of current directly.

This is underscored by the value of q(t) at t=0. It is -15 mC. What does that mean? It's one thing if it refers to the charge on a capacitor being -15 mC at t=0. But to say that it's the charge entering the capacitor at t=0 is nonsensical.

It's almost like whoever came up with this problem started with a different problem that gave the current as a function of time and asked you to find the total charge over some time period, and thought that they could make a new question by just swapping the role of current and charge.

Also, what are the units of the "-4" in exponential? It has to be inverse time, but is it inverse seconds? Inverse milliseconds? What?

 

The problem is very poorly stated.

The notion of charge as a function of time would apply to the total charge in some manner -- the total charge at time t on a capacitor plate, or the total charge that has passed a point since t=0. But saying that it represents the charge entering (i.e., immediate present tense) a positive terminal (i.e., passing a point) is not a description of charge, but a description of current directly.

This is underscored by the value of q(t) at t=0. It is -15 mC. What does that mean? It's one thing if it refers to the charge on a capacitor being -15 mC at t=0. But to say that it's the charge entering the capacitor at t=0 is nonsensical.

It's almost like whoever came up with this problem started with a different problem that gave the current as a function of time and asked you to find the total charge over some time period, and thought that they could make a new question by just swapping the role of current and charge.

Also, what are the units of the "-4" in exponential? It has to be inverse time, but is it inverse seconds? Inverse milliseconds? What?

Hi,

To me this looks like a simple charge function, a math expression that indicates a flow of charge from one place to another.
q(t)=-15*e^(-4*t) mC just seems to show how the charge flows over time.

This would seem to look like a capacitor discharging into a resistor with time constant 1/4 seconds. When we don't see units like that we usually assume time is in seconds. Only if mentioned do we change that, and then we might have to multiply 't' by some factor (or divide).

From that expression we should be able to get the electrical current function i(t).
In this case it would not be an average it would be the instantaneous current flow over time.

Now as to the 200ms spec, I am not sure if they want us to calculate the current at t=200ms or the total charge transferred, but it does sound something like the total charge transferred because they also mention t=0. That means they want us to consider the range of t=0 to t=0.2 seconds.
They could want the total charge over that period, or the total energy, or the average current, etc.

 

Hi,

To me this looks like a simple charge function, a math expression that indicates a flow of charge from one place to another.
q(t)=-15*e^(-4*t) mC just seems to show how the charge flows over time.

This would seem to look like a capacitor discharging into a resistor with time constant 1/4 seconds.

IF q(t) represented the charge ON a capacitor, then that would be a reasonable interpretation. But that is not what the question says it is. (as paraphrased by the TS). It is stated explicitly that IS the charge entering the positive terminal of this device (whatever it is).

To show how this makes no sense, what if we simply had

q(t) = -15 mC

and insist that this IS the current flowing into the positive terminal of the device. What is the current?

The question makes no sense, because it makes no sense to say that -15 mC of charge is flowing into a terminal AT an instant in time. This would require an impulse function delivering infinite current of just the right amount of infinity to result in -15 mC of charge entering. But then what about the next instant in time? It's a mathematical absurdity.

Let's see if we can make this even more apparent.

Let's say that I give you a function of time that is the volume of water.

v(t) = 100 gal

and tell you that this is the water entering a tank at time t. Not the amount of water IN the tank at time t, but the amount of water ENTERING the tank at time t.

How much water is in the tank after one minute.

It makes no sense, because "water entering the tank at time t" is a description of the FLOW of water, not the VOLUME of water, so it needs to have units of volume/time, such as gallons per minute.

Whatever function describes the amount of charge entering the positive terminal of a device needs to be a function that describes the flow of charge, not the amount of charge, so it need to have units of charger/time, not charge.

When we don't see units like that we usually assume time is in seconds. Only if mentioned do we change that, and then we might have to multiply 't' by some factor (or divide).

I don't know about you, but I don't think engineering should involve guessing or mind reading. This is how we slam space probes into planets or how airliners full of passengers run out of fuel in midflight. Both because people were to damn lazy to use units in their work and relied on others reading their minds and guessing what what meant, and in both cases guessed wrong.

 

IF q(t) represented the charge ON a capacitor, then that would be a reasonable interpretation. But that is not what the question says it is. (as paraphrased by the TS). It is stated explicitly that IS the charge entering the positive terminal of this device (whatever it is).

To show how this makes no sense, what if we simply had

q(t) = -15 mC

and insist that this IS the current flowing into the positive terminal of the device. What is the current?

The question makes no sense, because it makes no sense to say that -15 mC of charge is flowing into a terminal AT an instant in time. This would require an impulse function delivering infinite current of just the right amount of infinity to result in -15 mC of charge entering. But then what about the next instant in time? It's a mathematical absurdity.

Let's see if we can make this even more apparent.

Let's say that I give you a function of time that is the volume of water.

v(t) = 100 gal

and tell you that this is the water entering a tank at time t. Not the amount of water IN the tank at time t, but the amount of water ENTERING the tank at time t.

How much water is in the tank after one minute.

It makes no sense, because "water entering the tank at time t" is a description of the FLOW of water, not the VOLUME of water, so it needs to have units of volume/time, such as gallons per minute.

Whatever function describes the amount of charge entering the positive terminal of a device needs to be a function that describes the flow of charge, not the amount of charge, so it need to have units of charger/time, not charge.



I don't know about you, but I don't think engineering should involve guessing or mind reading. This is how we slam space probes into planets or how airliners full of passengers run out of fuel in midflight. Both because people were to damn lazy to use units in their work and relied on others reading their minds and guessing what what meant, and in both cases guessed wrong.

Hi,

I see what you mean about the static value, but I did not read it that way because it would not make sense to READ it that way, unless it was a trick question. Common sense for me, I guess. You can still ask for more detail if you like of course, and maybe something will come out of it. I can't remember the last time any of us asked for the dimensions of 't' in an expression like that though. I do like to state it myself though when giving some sort of formula.

As to the other about time 't' in an exponential like A*e^(-4*t), it would be absurd to think that 't' was in units other than seconds, I think. In fact, did we ever see that anywhere with expressions that deal with these kinds of electronic functions? I am assuming that you meant that 't' could be in milliseconds, microseconds, days, months, years, etc. It is true it could actually be in days, but that would be very uncommon and again it seems that common sense says it is in seconds. If there is something missing, then that could change that, but in its absence, I'd say we stick to 't' in seconds.

I am thinking you maybe got a little too pedantic with this problem?
More detail is always welcome though.