Homework Help: Combinations of Capacitors

AznBoi · Feb 25, 2007

1. The problem statement, all variables and given/known data
Find the equivalent capacitance between points a and b for the group of capcitors connected as shown below.

http://img250.imageshack.us/img250/7816/40ha4.th.png [Broken]

2. Relevant equations
Series/Parallel combinations.

3. The attempt at a solution

I don't get how the two parallel capacitors, after being combined, are positioned in the circuit. Here's my attempt after combining a few capcitors.

http://img250.imageshack.us/img250/4610/401gx0.th.png [Broken]

ranger · Feb 25, 2007

I'm not sure I can follow your second diagram correctly without making a few assumptions (which may be wrong). Perhaps you can give each cap in the original circuit a label and label your attempt according to the original circuit.

AznBoi · Feb 25, 2007

ranger said: ↑

I'm not sure I can follow your second diagram correctly without making a few assumptions (which may be wrong). Perhaps you can give each cap in the original circuit a label and label your attempt according to the original circuit.

Yeah, I should have labled them. I just reduced the 3 parallel capacitors. I'm mostly unsure of where the 2 upper parallel capacitors will be set up. Will it just be a line like my attempt?

ranger · Feb 25, 2007

AznBoi said: ↑

Yeah, I should have labled them. I just reduced the 3 parallel capacitors. I'm mostly unsure of where the 2 upper parallel capacitors will be set up. Will it just be a line like my attempt?

What 3 parallel capacitors?

The upper part of the original circuit has more that two caps in parallel.

AznBoi · Feb 26, 2007

ranger said: ↑

What 3 parallel capacitors?

The upper part of the original circuit has more that two caps in parallel.

Sorry about that. Here is my whole attempt. I circled the capacitors that I combined and the black arrow is the result. I have a question. Are the capacitors that I pointed to all parallel? How do you tell the difference between parallel and series capacitors? They all seem to be on the same wire.. thanks.

http://img201.imageshack.us/img201/198/40kd8.th.png [Broken]

ranger · Feb 26, 2007

To simplify the case of whether components are in series or parallel (dont worry, whats applies here works for caps also). Think of them as being resistors. Consider this diagram (ignore the formulas):
http://upload.wikimedia.org/wikipedia/en/4/47/Cdr.GIF [Broken]
You see a current, I_T, entering the two resistor branch. Now are these two resistors in parallel or series? Why?
Knowing this, you will be able to answer the question you circled.

AznBoi · Feb 27, 2007

ranger said: ↑

To simplify the case of whether components are in series or parallel (dont worry, whats applies here works for caps also). Think of them as being resistors. Consider this diagram (ignore the formulas):
http://upload.wikimedia.org/wikipedia/en/4/47/Cdr.GIF [Broken]
You see a current, I_T, entering the two resistor branch. Now are these two resistors in parallel or series? Why?
Knowing this, you will be able to answer the question you circled.

Well from your provided diagram, it's pretty obvious that it is parallel because the total current is branched out into 2 separate onces and then coming back together. However, in this problem, the capacitors are like: [l] and it seems like they are in series because they don't exactly branch out, it is the same wire.. So are the capacitors that I circled for the first step in series? the ones on: [ and ]

ranger · Feb 27, 2007

Well taking the original diagram (upper left), the two caps are not in parallel. Lets say we trace a current coming from the node a. The current splits into three parts. One going left, down, and right. The current that flows left flows through two caps, so these two now have the same current flowing through them. The one that flows down flows into one cap, the one that flow right flows into two caps, so these two now have the same current flowing through them. All three currents then rejoin at the base of these 5 caps and flow into the second set....

So we have I_left[tex]\not=[/tex]I_down[tex]\not=[/tex]I_right, therefore these three bracnches must be in.....? How about two caps each in the upper left and right branch? So we have to consider two things, whether the branches are in series/parallel and whether the caps on the individual branches are series/parallel. Just tracing a current should be enough to figure this out.