16-3 Quiz Help

Question 1:
First convert Q to Coulombs. Use the formula C=Q/V to find the capacity. Since Q is in coulombs and V is in volts, this gives your capacity a unit of C/V which is the equivalent to a "Farad". However, they ask for the answer in nF. To convert your answer that you found for C in Farads to nF, simply divide the value by 10E-9. The answer is going to be negative because it does not matter what material is in between the plates...we obviously did the problem without knowing so it is therefore not necessary.

Question 2:

This question has two parts. The first part is exactly the same as in question 1. You are given Q which you need to convert to coulombs, and you are given V. Use the formula C=Q/V to find the value for the capacity. Next, they want to know the distance between two plates given the area. For this part you use the formula C=(1/4*pi*k)*(A/d), where you just determined C from the first part, A is given to you in the problem, and k is a constant. You solve for d and that is your answer. The answer is positive because the electric field can be quoted in either N/C OR V/M.

Question 3:

I'm not sure of the concepts behind this question, but I believe that distance and stored electrical energy are opposites, as in if one increases then the other decreases. I'm sure this can be determined by looking at the equation relating the two given in the notes. Since the distance between the plates is increased by a certain factor, that means that the stored electrical energy is decreased by the same factor. For example, if your distance increased by a factor of two, that would mean you multiply the distance by 2. If the stored electrical energy is then decreased by the same factor, you would divide your value by two instead of multiplying. Overall, since the stored electrical energy is changed by the same factor as the distance but in the reverse manner, just do (1/factor given) to get your answer. The answer is also negative because the result would not be the same if the power supply was disconnected.

Question 4:

This is almost the same as question three. Since the distance was decreased by a certain factor, that means that the stored electrical energy in the capacitor was increased by the same factor. Basically, the answer is the number provided in the question. The answer is negative because both the voltage and the capacitance change.

Have a good weekend!

hey...i tried to set the right equation to find d, but im not getting it...and for the area, am i suppose to square it because it is in m^2 or just plug it in like that...i need help in setting the right equation...pls tell me what im doing wrong?

No, you don't square the area. The units are already in m^2 so everything has been calculated for you.
As far as the formula goes, you are given C, pi, k. It will be easiest if you first calculate out the first part of the question (1/4*pi*9E9), where k = 9E9 first. You can then divide both sides by this value which I believe calculates out to be 8.8419E12 (this value is the same for everyone since this first part just consists of constants and what not.)

So now, You take your C value and divide it by the 8.8419E12
You are now left with this:
C/8.8419E12 = A/d
You have C and you have A . Multiply both sides by d to get rid of the fraction, and then divide to get d by itself. It's basically going to end up looking like this:
d = (A) / (C/8.419E12)
Hope this doesnt get too confusing since I didn't plug in C or A values, but I just wanted to help you understand the algebra aspect of it. Hope that helps!

I'm still having trouble getting number 2. I'm not sure where you are getting that constant from. (the 1/4 * pi * k) part.

my Q is 7.855uC which comes to 7.855e-6. my V is 1588 and my A is 1.01.

Maybe i'm doing the syntax wrong? i'm not sure.

I'm sorry but I don't understand te reasoning behind the answer to question 4.

A parallel plate capacitor is charged and disconnected from any power source. The distance between
the plates is decreased down to the fraction 0.5324 of its original value. By which factor does the stored
electrical energy in the capacitor change (see sheet 34) ? Indicate with a positive (negative) sign
whether during the distance change only the capacitance (both the voltage and capacitance) change.

So I tried to do it mathematically and this is what I got:

d=d
d'=.5324d

I'll use the formula (U'=.5*C'*V^2)/(U=5*C'*V^2)
- the .5 and V^2 cancel out
- I replace with (A/(4pi*k))*(1/d)

The equation looks like this now:
U'=(A/(4pi*k))*(1/d') for the numberator and
U=(A/(4pi*k))*(1/d) for the denominator
- the A/(4pi*k) cancels out and what is left is:
U'/U=d/d'

Then I plugged in the numbers and I got:
d/d'=1/.5324=1.878

So according to what I got, it means that the electrical energy in the capacitor changed by a factor of this. But that wasn't the correct answer and I would like to know why the answer is just .5324.

guest111 wrote:I'm still having trouble getting number 2. I'm not sure where you are getting that constant from. (the 1/4 * pi * k) part.

my Q is 7.855uC which comes to 7.855e-6. my V is 1588 and my A is 1.01.

Maybe i'm doing the syntax wrong? i'm not sure.

The error may just be in your calculations.. Not really sure.
C = Q/V = 7.855e-6/1588 = 4.9464E-9
C = (1/4*pi*k)(A/d)
4.9464E-9 = (1/4*pi*9E9)(1.01/d)
4.9464E-9 = (8.8419E-12)(1.01/d) divide both sides by 8.84E-12
559.432 = (1.01/d)
d= (1.01)/(559.432) = _________ your answer!

I'm not sure if I quite understand the reasoning behind number 4 myself, but if you look at the example in the notes given on sheets 30-32, part C..it asks "by which factor is the energy stored changed if the distance between the plates is increased by a factor of two?" According to the answer they given, If the distance is increased by a factor of two, then the stored energy or "U" will decrease by the same factor, as indicated by the answer given for part C on sheet 32 where it denotes 1/2. Therefore, it is suggesting that they have an inverse relationship. I'm not certain as to why this is the case, maybe the professors or TA's will know the reasoning, but for this question it just seems to work. And so for our question 4, it says the distance decreases by some factor x (this question is the exact opposite of that from the notes), so distance would be decreased by 1/x, and if stored energy is the opposite, it would increase by just x, hence why the number is the same as that given.

I'm still having trouble getting number 2. I'm not sure where you are getting that constant from. (the 1/4 * pi * k) part.

my Q is 7.855uC which comes to 7.855e-6. my V is 1588 and my A is 1.01.

Maybe i'm doing the syntax wrong? i'm not sure.

You get (1/4*π*k) from sheet 28 of your notes which you might want to look at to see where your mistake is.

I am still getting #1 wrong
can I know what was the power in your answer, was it E-19 ?

There shouldn't be a power. You are dividing C/10^-9

I am having a problem with number one. I have converted to micro C to C then divided by Volts. that answer I divided the 10^-9. But it still isn't working. I have tried dividing 10e_9 after converting to coulombs as wells.

Did we ever learn about n? I don't really remember doing anything with n or hearing it on the cd.. did i miss it somewhere?

Conversion requires you multiply the uC value by 10^-6.
Afterwards, use the equation provided and properly divide the now-proper units value by the provided voltage value. So basically what you're doing is C/V.

The value from there should be something like X.XX*10^-9 F. At this point, convert the F unit value to nF by dividing it by 10^-9. The final value should be something along the lines of X.XX nF.

Hope that helps.