Brain Teasers:

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rattus

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This is for all you mathematicians out there. Recently we have had questions arising about the relationships between capacitors, voltage, and energy. Now how many of you can do this?

1) Derive the equation for the charge/discharge current in an RC circuit? Assuming a constant voltage of course. It is not terribly hard.

2) Use this equation to derive the formula for stored energy on a capacitor. This is not very hard either.

Now, don't just plop down the answer. Show the steps. :twisted:
 
You Sure?

You Sure?

How can you charge and discharge a capacitor at a constant voltage?

Let's not forget to derive the quadratic equation while we are at it!
 
beanland, the circuit comprises (in series) a fixed voltage source, V, a switch, a resistor, R, and a capacitor, C. The switch closes at t = 0 which starts the charging process. This is a classic exam question requiring the use of a differential equation. I will get the ball rolling by providing the equation:

1) dV = Rdi + idt/C (units are volts)

dV, di, and dt are differentials. That is, they are infinitesimally small increments of V, i, and t. In this case, dV = 0 because the source voltage is constant. Then,

2) Rdi = - idt/C (volts)

3) di/i = -dt/RC (dimensionless)

Now who will solve eqn. 3 for i?
 
Rattus:

I have a brain teaser for you. (Of course, everyone else is welcome to answer.) Here it is:

A woman has 2 children. One is a boy. What are the odds that her other child is a boy?

Steve
 
What are the odds that the boy you mentioned would draw on the walls and try to blame his sibling? :lol:
 
rattus said:
Now who will solve eqn. 3 for i?
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I would, but I've had too much coffee this morning, and I don't think it's safe to drink and derive. :roll:
 
steve66 said:
...A woman has 2 children. One is a boy. What are the odds that her other child is a boy?...
Click to expand...

Steve -

I'll bite. Even money (or what ever is the current m/f birth ratio). The dice don't remember the last roll.

Of course that is different as to the odds that she has two boys (not knowing up front that one is a boy), which is 4 to 1.

But, I'm always interested in being educated

carl
 
Assuming we a charging the cap ... I(t) = (V/R)e^-(t/RC). Is that what you were looking for Rattus?

From the equation the current drops as time passes and the cap. charges. Also immediately after the switch is closed (t~0) the current is V/R as expected.
 
Since this thread is going haywire anyway, then think about this one! I have a nephew who's grandpa is my uncle!!!! No divorces, deaths, or second marriages involved! It's all legit. So how can this be?? (OBTW, I did not make this up, I really do have a nephew who's grandpa is my uncle!!!)
 
spsnyder,

Yes, that is the solution, but I am daring anyone to show the steps involved in solving,

di/i = -t/RC

for i.

It is not hard, but it is a bit tricky.
 
steve66 said:
A woman has 2 children. One is a boy. What are the odds that her other child is a boy?
Click to expand...
Your riddle has many answers, and therefore no answer (other than mine, of course - see below 8) :D ) is right. Here are the two most common answers:
  • The "gotcha" answer (probably the most common incorrect answer) simply states that the probability of having two boys is one out of four (25%).
  • The "OK, you got it" answer (the answer that the author of the riddle probably intended) is that the gender of the second child is independent of the gender of the first. So the probability that the second child is a boy is one out of two (50%).

However, each of these two answers presumes that the "event" of a child's gender has only two possible outcomes (boy and girl), and that the two are equally likely. That is not the truth. Here is why:
  • First, there is a third possible outcome, however rare: a hermaphrodite.
  • Secondly, there is a fourth possible outcome: the woman's children might be adults, and the second child might have undergone a certain voluntary surgical procedure. Thus, the actual gender of that child might be a matter of some controversy.
  • Next, looking at the world's history as a whole, the number of male children and the number of female children has not been exactly the same. I don't know which number is higher, but they are not equal. Therefore, the probability of each event is not 50%.
  • Finally, the biological characteristics of some couples tend to favor the birth of children of one gender over the birth of children of the other gender. Again, it is rare. But here again the probability of each event is not 50%.
But now for the "Truth," as only I have correctly perceived it. :wink:
  • You worded the question in such a way as to make it clear that this woman's two children have already been born. Therefore the gender of the second child is a question of fact, and not of probability. If the child is a boy, then the probability of the child being a boy is 100%. If the child is a girl, then the probability of the child being a boy is 0%.
 
ramdiesel3500 said:
I have a nephew who's grandpa is my uncle!!!!
Click to expand...
Here is one solution:
  • Your father had a brother. That person is your uncle.
  • Your uncle married, and had a son. The son is your first cousin.
  • Your wife has a sister. The sister married your first cousin.
  • Your wife's sister had a son. That child is your nephew.
  • Therefore, your nephew has, as his grandfather, your father's brother (i.e., your uncle).
 
Charlie b

BINGO!!!! (well almost!) In my particular case, my brother-in-law (wife's brother) married my uncle's (my dads brother's) daughter (my cousin).

So, in essence, you nailed it!!!! :D
 
I've always found this to be an interesting tidbit.

My father's youngest brother married my mother's youngest sister. My father was 4th of 9 children and my mother was the eldest of 4. We are 100% German ancestry. Here's what has always puzzled me.

My siblings and I are all quite tall and fair skinned however my cousins are all quite short with rather dark complexion.

Genetics, who can tell?

Bob
 
Rattus
You might as well give up on your post. This has turned into a sexual
discussion of family heritage.
 
Charlie:

I should of told you to assume both boys and girls are equally likely. :)

No one else bit, so I'll give you the answer.

The odds the other child is a boy is 1 in 3 or 33%.

Most people would (incorrectly) say the fact that one child is a boy has no effect on the other child, therefore the the odds are 1 in 2 or 50%.

The easy way to calculate this is to start with the 4 possibilities (each equally probable);

youngest is a boy, oldest is a boy
youngest is a boy, oldest is a girl
youngest is a girl, oldest is a boy
youngest is a girl, oldest is a girl

When I say one child is a boy, I am free to pick either the youngest or the oldest. As a result, you can't consider one child by themself. And the only posibility that is ruled out is the last one.

That leaves 3 equally probably events, with only one where the other child is a boy.

Steve
 
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