Hello,

i would think we would use the simplest circuit possible which is one R and one C, but if you decide to use multiple R's then you would have to calculate the total energy lost in all resistors to find the total energy lost in the cap as it discharges from t1 to t2 through those resistances. Just seems harder to use more than one resistor anyway though. With a single R and single C the cap voltage starts out at some initial value v1 at t1 and discharges though the resistor until it reaches v2 at t2, and knowing v1 and v2 it is fairly simple to calculate the energy lost to the resistor.

 

If you think clearly about the original question, the whole circuit is only important to calculate the value of the equivalent resistance R - but that could be measured externally even without knowing the circuit (except that the circuit must satisfy the initial condition Io=Vo/Req). Total power dissipation is not relevant to solving the assigned problem, only the objective power is necessary. Whether the objective power is in a single resistor or in an equivalent resistance does not matter.

But now you are injecting something that was not in your original assertion:

But would that assume one knew the total energy stored in the capacitor at the beginning? It seems that the purpose of the assignment is to calculate that value as equal to the total energy dissipated in the resistor while the capacitor discharges. Where else would the energy in the capacitor go?

Now you say that it's "objective power." What is "objective power"? I just did a search and didn't find anything that defines "objective power" (except in relation to microscopes and other optical instruments).

As for the last question (Where else would the energy in the capacitor go?), it could go to a variety of places. It could go into another capacitor, or into a magnet, or charge a battery.

The best interpretation of the question, as I see it, is simply how much energy is lost (i.e., transferred to someplace else) by the capacitor during the discharge. As best as I can tell, it is supposed to be parameterized so that it is a function of time -- how much energy is lost between t=0 and t=dt. That will map nicely to what you are now calling "objective power", but it will not necessarily map to "total energy dissipated in the resistor".

 

Now you are arguing about terms taken out of their original context. That's no worth my time.

 

Now you are arguing about terms taken out of their original context. That's no worth my time.

Go look at my very first response to your suggestion. I was very clear that I was talking about the problems with using the "total energy dissipated in the resistor" was because you had no way of knowing what the rest of the circuit was doing with that effective resistance. If you meant something other than "total energy dissipated in the resistor" when you wrote it, then you could have cleared that up then.

 

If you are given the current as a function of t how would you find the total energy lost while a capacitor discharges?

i(t)=(-Qo/RC)(e^(-t/RC)) during the time interval [t,t+dt] and Qo being the initial charge stored in the capacitor.

Take a picture of the actual problem you see in the module and post it in this thread.