How do I calculate the equivalent inductance in a circuit with diagonal wiring?

[Marcin H]

Homework Statement

Homework Equations

Adding inductors in series and parallel (same as resistors)

The Attempt at a Solution

This is the first time I ran into a circuit like this with diagonal wiring and I am not sure how to treat it. Do I add the inductors in the triangle in series? So for example, on the left would it just be 105uH? I don't think that is right. Then that would be in series with the 25uH. How do I do this?

 

[gneill]

Component arrangement on the page doesn't matter. The only thing that matters is how they connect to each other (the topology). You can feel free to re-draw the circuit with only horizontal and vertical lines and components if you wish, just so long as you maintain all the same connections.

 

[anachin6000]

As an indication, at the right end of the circuit 18 an 12 are connected in series and them together are in series with 38. the idea is tha the conductor lines between two connection points are ideal and you can modify their length and form as you wish.

 

[cnh1995]

First identify the series and parallel combinations. The circuit collapses into a very simple form then! You will automatically get rid of the diagonal wiring once you spot the series and parallel inductors.

 

[Marcin H]

First identify the series and parallel combinations. The circuit collapses into a very simple form then! You will automatically get rid of the diagonal wiring once you spot the series and parallel inductors.

I'm still not sure what would be in series and what would be in parallel. I want to say that the 60uH and 30uH inductors are in parallel, and once I get that would that equivalent be in series with the 25uH and 15uH?

 

[cnh1995]

I want to say that the 60uH and 30uH inductors are in parallel,

How are they in parallel? Do they have "common end points"?
Start from the rightmost side. What can you say about 18uH and 12uH?

 

[gneill]

I want to say that the 60uH and 30uH inductors are in parallel

Do they share the same two node connections? Can you draw a closed path that passes only through those two components (where wire doesn't count as a component) ?

 

[Marcin H]

Start from the rightmost side. What can you say about 18uH and 12uH?

Those are in series, so 30uH.

Do they have "common end points"?

So if they have a common endpoint, they are in series? Like the 18 and 12?

 

[cnh1995]

Remember these two points while checking whether two components are in series or parallel:
1)Parallel components have common endpoints.
2) While checking for series components, say R1 and R2, imagine some current flowing through R1. If the same current enters R2 after leaving R1, then R1 and R2 are in series.

 

[Marcin H]

Do they share the same two node connections? Can you draw a closed path that passes only through those two components (where wire doesn't count as a component) ?

Remember these two points while checking whether two components are in series or parallel:
1)Parallel components have common endpoints.
2) While checking for series components, say R1 and R2, imagine some current flowing through R1. If the same current enters R2 after leaving R1, then R1 and R2 are in series.

Ok, so whenever the current splits into different paths they are in parallel. So going through the 18 and 12 they would have the same current, but then the current would split at the bottom right corner. Current would go towards the 20 and 38. But then what happens?? It looks like current keeps splitting.

 

[cnh1995]

Parallel components have common endpoint"s", both the terminals are connected between two points.

 

[cnh1995]

Ok, so whenever the current splits into different paths they are in parallel. So going through the 18 and 12 they would have the same current, but then the current would split at the bottom right corner. Current would go towards the 20 and 38. But then what happens?? It looks like current keeps splitting.

18 and 12 will become 30uH. What can you say about this 30uH and the diagonal 20uH?

 

[Marcin H]

It looks like the current splits right? So would they be in parallel? (sorry for the crappy drawing)

 

[cnh1995]

so whenever the current splits into different paths they are in parallel.

After splitting at one terminal, if all the split currents reunite at the other terminal, then the components are in parallel.

 

[cnh1995]

It looks like the current splits right? So would they be in parallel? (sorry for the crappy drawing)
View attachment 95583

They are in parallel because their terminals are connected between two common points.

 

[Marcin H]

After splitting at one terminal, if all the split currents reunite at the other terminal, then the components are in parallel.

But what happens to the current after it goes through the 38? Wouldn't it split again?

 

[cnh1995]

But what happens to the current after it goes through the 38? Wouldn't it split again?

View attachment 95584

It would, and it will continue to split. But in the end, all the split currents will reunite at the other terminal. Incoming current has to be equal to outgoing current. Isn't this what KCL is all about?

 

[SammyS]

As an indication, at the right end of the circuit 18 an 12 are connected in series and them together are in series with 38. the idea is tha the conductor lines between two connection points are ideal and you can modify their length and form as you wish.

This is NOT correct.

Yes, at the right end of the circuit, the 18 and 12 are connected in series, but that combination is in parallel with the 20. The combination of these three is in series with the 38.

etc, etc.

 

[Marcin H]

It would, and it will continue to split. But in the end, all the split currents will reunite at the other terminal. Incoming current has to be equal to outgoing current. Isn't this what KCL is all about?

True. I am confused now. You said:

After splitting at one terminal, if all the split currents reunite at the other terminal, then the components are in parallel.

Does this mean that the combined 30 is in parallel with the 20 and 38? Why is sammy saying they are in series?

 

[cnh1995]

Does this mean that the combined 30 is in parallel with the 20 and 38?

Combined 30 is in parallel with 20. Their parallel equivalent is in series with 38. This series-parallel stuff goes on and the circuit reduces to a single equivalent inductance between the given terminals.

 

[SammyS]

gneill has a very good explanation of determining which circuit elements are in series, and which are in parallel.

I'll take a stab at it.

If exactly two elements share a node, then those two elements are in series. Any current (or charge) passing through such a node, must come from one of the two elements and then pass into the other.

If two nodes are connected to each other by two or more elements, then those elements are in parallel with each other. They all have the same potential across them.

 

[Marcin H]

Combined 30 is in parallel with 20. Their parallel equivalent is in series with 38. This series-parallel stuff goes on and the circuit reduces to a single equivalent inductance between the given terminals.

this diagonal stuff is really messing me up. That makes sense once you have the parallel equivalent in series with the 38. But I still don'nt really get why

gneill has a very good explanation of determining which circuit elements are in series, and which are in parallel.

I'll take a stab at it.

If exactly two elements share a node, then those two elements are in series. Any current (or charge) passing through such a node, must come from one of the two elements and then pass into the other.

If two nodes are connected to each other by two or more elements, then those elements are in parallel with each other. They all have the same potential across them.

I still don't understand this. :/ How can I redraw this, so it looks like a standard circuit? I think someone said that I can redraw this into a normal looking circuit, maybe that will help me see what's in series and what's in parallel.

This kinda helped in the sense that I know how to do it now, but I don't really understand why it is like that... :/

 

[SammyS]

this diagonal stuff is really messing me up. That makes sense once you have the parallel equivalent in series with the 38. But I still don'nt really get why

I still don't understand this. :/ How can I redraw this, so it looks like a standard circuit? I think someone said that I can redraw this into a normal looking circuit, maybe that will help me see what's in series and what's in parallel.

This kinda helped in the sense that I know how to do it now, but I don't really understand why it is like that... :/

Do you know what a node is?

 

[Marcin H]

Do you know what a node is?

That's another thing... My teacher didn't explain that really well. I always thought, from physics, that the dots where nodes, but now I learned that you can combine nodes into essential nodes and stuff like that, but it didn't really make too much sense.

 

[Marcin H]

That's another thing... My teacher didn't explain that really well. I always thought, from physics, that the dots where nodes, but now I learned that you can combine nodes into essential nodes and stuff like that, but it didn't really make too much sense.

I am currently in an intro to comp E and EE class. first time dealing with circuit analysis.

 

[cnh1995]

When two or more components are in series, same current flows through all of them, as said in earlier posts.

this diagonal stuff is really messing me up. That makes sense once you have the parallel equivalent in series with the 38. But I still don'nt really get why

Look at the two ends of 30uH and 20uH. They are connected between same two points i.e. the diagonal points in this case. So, between those same points, you can put the equivalent of 30||20 i.e. 12uH. Now, again assume some current through that 12uH. That same current will flow through 38uH, without splitting. This means 12 and 38 are in series. They are not in parallel because their ends are not connected between same two points, as are of 30 and 20 in the above picture.