Hi guys. I've a test in the morning can anyone tell me if this is correct?

 

Ask if the answer makes sense.

Does it agree with what you know it needs to be at t = 0?

Does it agree with what you know it needs to be at t = ∞?

 

Well I guess I'll never know. I'm so roasted for this exam and I can tell you it AIN'T for the lack of studying. Bloody thing.
Sorry Wbahn... are you saying if I place values in it. Does it work out? Is that what you mean? I've no idea how to test it.

 

Well I guess I'll never know. I'm so roasted for this exam and I can tell you it AIN'T for the lack of studying. Bloody thing.
Sorry Wbahn... are you saying if I place values in it. Does it work out? Is that what you mean? I've no idea how to test it.

In your solution if you set t = 0 you will get that the voltage across the capacitor (the top relative to the bottom, which is the only orientation consistent with your equations) is 0 V. That makes sense because the capacitor starts off uncharged.

Now, what should the final charge be on the capacitor after a long time as passed? The capacitor will look like an open circuit and so you have a voltage divider with two equal resistors and you get a voltage of E/2.

But what does your solution say? As t goes to infinity (gets arbitrarily large), the exponential term is killed off leaving you with -E/2.

So your solution doesn't make sense because it yields at least one value that you know is incorrect.

Always, always, ALWAYS ask if the answer makes sense.

 

I've this thing in an hour... any chance of a quick solution? Or some good tips on where I went wrong?

 

I've this thing in an hour... any chance of a quick solution? Or some good tips on where I went wrong?

You want a good tip? Here's a good tip.

TRACK YOUR UNITS!

I simply do not know any way to get you to grasp the notion that tracking your units will result in better grades.

You made a mistake that messed up the units.

But because you won't track your units, you didn't catch it.

Instead, you blindly wasted time slugging away when it was guaranteed that your answer would be wrong.

Then, you couldn't even be bothered to ask if the units on your final answer work out.

RC has units of time. So your exponential has units of time-squared. But we KNOW that the exponential function, like ALL transcendental functions, MUST have arguments that are dimensionless.

So where in your work might you have caught this mistake?

Well, it actually turns out you made at least three mistakes, but two of them cancelled out (though a decent grader would have nailed you for each one).

Consider


Do you agree with this?

Next, consider



First, how did the 2 in the denominator on the right stay in the denominator when you took it to the left? This mistake undid the mistake in the prior step, but hopefully you can see that it was by pure look. You deserve NO credit for getting this mistake to go away.

Imagine if you went to have your diseased left kidney removed and the surgeon accidentally wrote down that it was your right kidney that needed to be removed. Then when marking your body before surgery he read that your right kidney needed to be removed but accidentally marked your body such that your left kidney ended up being removed. So, in the end, he removed the correct kidney. But, if you found out about this, would you be so pleased with his work that you would trust yourself to his care again? Or would you report him to whatever authority has jurisdiction because he probably shouldn't be allowed to practice medicine if he is going to be that careless?

Next consider that a careless surgeon is generally limited to killing people one at a time, but a careless engineer can kill people in job lots.

Next look at what happened to the RC in the top equation. It was in the denominator. This was good because we know that t has units of time and that RC has units of time and that ln(u) better not have units at all. Everything is good.

But now look at the bottom equation. You have RC multiplied by t so you have units of time-squared on the left but still something that must be dimensionless on the right.

If you had been tracking your units, like I have been preaching to you forever, you would have caught that something was wrong right here and you could have stopped right here and looked at the prior equation and confirmed that the units were correct and then immediately spotted the mistake you made and corrected it before moving on. But you refuse to listen, so you proceeded to waste your time and effort producing an answer that had zero chance of being right.

So how much time got chewed up with this that you could have been putting to better use studying for this exam?

All because you still don't feel that it is worth taking the time to track your units properly.

Well, if it results in a poor exam score that wasn't necessary, perhaps you will start to listen.