Solving Circuit: Find Total Capacitance & Understand Repercussions

[MathewsMD]

I've been trying to solve this circuit but cannot come up with any proper circuit that depicts this is in a simplified form that would help me solve for the total capacitance of the system. I just find it odd since current can go both "up" and "down" through the two middle capacitors and it seems like there would be repercussions to the circuit (are there any?). I've been trying to deduce the capacitance by creating different arrangements but it just seems like there are too many possible paths for the current to flow. Any help would be greatly appreciated!

 

[berkeman]

I've been trying to solve this circuit but cannot come up with any proper circuit that depicts this is in a simplified form that would help me solve for the total capacitance of the system. I just find it odd since current can go both "up" and "down" through the two middle capacitors and it seems like there would be repercussions to the circuit (are there any?). I've been trying to deduce the capacitance by creating different arrangements but it just seems like there are too many possible paths for the current to flow. Any help would be greatly appreciated!

Was there supposed to be an attachment?

 

[MathewsMD]

Was there supposed to be an attachment?

Hi,

Oh wow, sorry, I just realized it didn't attach properly. Yes, here it is:

 

[berkeman]

Ah, that helps. They are just trying to confuse you with the way they are drawing it.

Try this... Re-draw the circuit with the 4uF cap horizontally across the top, the 6uF cap horizontally across the bottom, and the two series caps horizontally across the middle. Be sure to keep the wires connected the same, so that the connections don't change. You end up with more of a horizontal rectangular circuit drawing.

Now, do you see some simplifications?

 

[MathewsMD]

Ah, that helps. They are just trying to confuse you with the way they are drawing it.

Try this... Re-draw the circuit with the 4uF cap horizontally across the top, the 6uF cap horizontally across the bottom, and the two series caps horizontally across the middle. Be sure to keep the wires connected the same, so that the connections don't change. You end up with more of a horizontal rectangular circuit drawing.

Now, do you see some simplifications?

I've tried to follow what you've said but doubt I fully understood what you meant...
Here's my following drawing but as you can already see, it is not the same circuit. I'm just not seeing how this can be easily decomposed yet.

Sorry for the hassle, but do you mind elaborating a little bit or showing a rough sketch please since I don't think I quite understood the transformation you wanted me to make?

 

[gneill]

Try this: Identify all the nodes and place a label on them (hint: Nodes a and b already have a label, and there's only one more. Remember that any contiguous wiring comprises the same node). Then make a list of all the components and the two nodes that they connect to. So for example the 4 μF capacitor connects to nodes a and b.

Now forget the original diagram and use the list to construct a new circuit diagram with the same node associations for each component. What do you come up with?

 

[MathewsMD]

Try this: Identify all the nodes and place a label on them (hint: Nodes a and b already have a label, and there's only one more. Remember that any contiguous wiring comprises the same node). Then make a list of all the components and the two nodes that they connect to. So for example the 4 μF capacitor connects to nodes a and b.

Now forget the original diagram and use the list to construct a new circuit diagram with the same node associations for each component. What do you come up with?

Hmmm...

Let me see if I did this right.

Despite doing this, I just don't see how this helps with the simplification exactly...

 

[gneill]

Can you share your list of components and node associations? (If you want you can combine the 7 and 5 μF capacitors into a single capacitor right away, since that combination is rather obvious from the original figure).

 

[MathewsMD]

Can you share your list of components and node associations? (If you want you can combine the 7 and 5 μF capacitors into a single capacitor right away, since that combination is rather obvious from the original figure).

Okay. Yes, I understand those 2 are in series. In the first image posted in the 7th post in this thread, I made black dots to represent nodes on the original image.

 

[gneill]

Okay. Yes, I understand those 2 are in series. In the first image posted in the 7th post in this thread, I made black dots to represent nodes on the original image.

Okay, well you've added dots to the top of the circuit, but they are still node b... remember, contiguous wire paths comprise a single node. You can trace a path from your dot to the terminal marked 'b' without passing through any components. So it's still node b.

So, how about writing out that list of components and which nodes they connect to?

 

[MathewsMD]

Okay, well you've added dots to the top of the circuit, but they are still node b... remember, contiguous wire paths comprise a single node. You can trace a path from your dot to the terminal marked 'b' without passing through any components. So it's still node b.

So, how about writing out that list of components and which nodes they connect to?

There are two paths it can go from the top junction, though, right? Does not that mean it can be considered as a node? I'm sorry but do you mind providing some sort of visual aid on how you would go about solving this since I'm beginning to become a little confused with the wording.

 

[gneill]

There are two paths it can go from the top junction, though, right? Does not that mean it can be considered as a node?

It's a node, but it's the same node as terminal b since there's a contiguous wire path from there to b.

I'm sorry but do you mind providing some sort of visual aid on how you would go about solving this since I'm beginning to become a little confused with the wording.

Identify the contiguous wire "islands" where components connect. They will be your nodes:

 

[MathewsMD]

It's a node, but it's the same node as terminal b since there's a contiguous wire path from there to b.



Identify the contiguous wire "islands" where components connect. They will be your nodes:

Thank you for the drawing! It definitely clarifies what you meant by the nodes. Now, despite that, I still seem to have some trouble actually drawing the circuit. I've come up with the follow circuit but it is still incorrect. Any further ideas?

 

[gneill]

List your components and node associations. The 6 μF capacitor connects to nodes...

 

[MathewsMD]

Does someone please mind showing me the solution for this? I keep trying but can't seem to figure it out. I'd just like to learn the steps on how to simplify it. Any drawings would be extremely helpful! :)

 

[gneill]

Does someone please mind showing me the solution for this? I keep trying but can't seem to figure it out. I'd just like to learn the steps on how to simplify it. Any drawings would be extremely helpful! :)

We can't do your homework for you here. Providing complete solutions is against the rules. We can only give hints, suggestions to follow, and point out errors or misconceptions.

Drawings have been provided! Suggestions have been provided! Try them!

 

[MathewsMD]

We can't do your homework for you here. Providing complete solutions is against the rules. We can only give hints, suggestions to follow, and point out errors or misconceptions.

Drawings have been provided! Suggestions have been provided! Try them!

Haha sorry. It's just a random question I found online and it's been stumping me. Sorry, but even after going through the drawings, I still don't quite see how this can be simplified further. Sure, you've made the middle to capacitors an equivalent one by combining them since they're in series. When you talk about nodes, I'm just slightly confused and don't still exactly understand what you're trying to convey. I've redrawn them but just don't seem to see what you're trying to tell me. It just looks like the current can go through multiple paths in the drawn series and I feel like every time I redraw it is changing the circuit itself. Hence the reason for me asking for more possible images to work with incase I'm drawing/interpreting them wrong.

 

[gneill]

Haha sorry. It's just a random question I found online and it's been stumping me. Sorry, but even after going through the drawings, I still don't quite see how this can be simplified further. Sure, you've made the middle to capacitors an equivalent one by combining them since they're in series. When you talk about nodes, I'm just slightly confused and don't still exactly understand what you're trying to convey. I've redrawn them but just don't seem to see what you're trying to tell me. It just looks like the current can go through multiple paths in the drawn series and I feel like every time I redraw it is changing the circuit itself. Hence the reason for me asking for more possible images to work with incase I'm drawing/interpreting them wrong.

Perhaps you might want to do a bit of web browsing, looking up the definition of what a node is?

The drawings already provided have specifically identified the nodes in your circuit. From that can you identify which nodes each individual component connects to? Make a list of components and the nodes that they connect to (assume that the equivalent capacitance for the 7 μF and 5 μF capacitors is one of the components). You should see a pattern.

 

[berkeman]

Thank you for the drawing! It definitely clarifies what you meant by the nodes. Now, despite that, I still seem to have some trouble actually drawing the circuit. I've come up with the follow circuit but it is still incorrect. Any further ideas?

Try this -- keep the left and right A and B nodes where they are, and mentally rotate the middle part clockwise 90 degrees. Then redraw the circuit in that new configuration, with all capacitor legs horizontal...