Oh. In that case, all the answers are zero.
My bad.

The first answer isn't necessarily zero. Negative current times negative voltage yields positive power, after all.

When a milliamp flows through a 5K resistor, and then you reverse the polarity and the current goes the other way for the same amount of time, no charge is transferred. Got it.

Yep. But that doesn't mean that no work was done on that resistor. Imagine an RC circuit in which the capacitor starts out with a certain charge on it. Then a voltage waveform is applied that puts some more charge on, takes all that and more off, and finally puts just enough back on to leave it at the same charge as before. How much charge was transferred off the cap? Zero. But non-zero energy was being dissipated in the resistor in each of those steps and that energy was supplied by the source that provided the voltage waveform.

 

@WBahn
In post #4 joeyd is talking about finding the current. In post #7 I suggest a way to find the integral of current and time by inspecting the graph. (Really, this one is so simple that I can do it.) In post #11 you show how to find the integral of current and time with calculus. Somehow, I am wrong. One doesn't need to know the integral of current and time to answer the questions because net change of charge is zero.

If the T.S. doesn't need to know the integral of current across time, why did three people tell him to do that?

 

Because the goal isn't to get an answer to this specific problem, but rather to understand the concepts needed to get the answer to an entire class of problems of which this is a special case. It is pretty clear that he doesn't understand the fundamental concepts. No one is saying that it is wrong to do it by inspection for this simple case, but if that is all he learns, then what happens when the next problem shows a half-sinusoid or something like that?

Now, whether it is better to start with simple special cases and move to the more general or start with the general and then use special cases can be debated all day long. But even if you want to use the special case approach at this stage, it needs to be connected to why the answer is what it is. Otherwise the person might walk away thinking that all that matters is that the waveform started at zero and ended at zero.

 

How far in that book did you get?

 

So...this only works with a rigorous method. If the first step is obvious to a person who only remembers the first week of Calculus class, you're doing it wrong. There is more than one thing to learn from this exercise and you can't learn the concept if the math is easy.

I disagree.
1) I can't do calculus past the first few days of the first semester, but I can see that the change in charge over a full cycle of a symmetrical wave is zero.
2) If two people are correct in saying, "find the integral" why is the third person to say that wrong?

I know. Because you can't understand the underlying concept if the math is easy.
I disagree.

 

I'm missing your point. Where was "the third person to say that" told they were wrong?

I said that which approach is better can be debated, so disagreeing just underscores that it can be debated.

 

@#12: There were two parts to the problem. The first must be integrated to get the correct answer -- for the correct reason. The second can be solved by inspection -- but this will not be obvious to someone who doesn't have a least a little bit of understanding of math beyond algebra.

BTW, the first part can be simplified -- you only need to solve for 1/2 the waveform, then double the answer. This is probably also obvious to you -- but possibly not to the OP. It is only after a bit of experience (which you have) that tricks like this become natural to discover.

But a first year EE should be able to solve these things the hard way -- and quickly -- or they are not going to get too far.

In fact, in my first post, I mentioned 'first principles'. No matter how many tricks one knows, its always important to know how to approach a problem from fundamentals. Often times, problems don't fit neatly into a 'rule-of-thumb' mold -- and you are stuck using the things you know to derive the things you don't know. Then again, failure is always an option.

 

So why take me to task for suggesting a method to find the integral? Both of you suggested the Thread Starter find the Integral. I only agreed.

Bottom line: Does he need to find the integral or not? If he needs it, I only agreed with you two. If he doesn't, all three of us are wrong.