# Combining Passive Elements for Minimal Circuit

Discussion in 'Homework Help' started by ElectronicGuru, Nov 3, 2014.

1. ### ElectronicGuru Thread Starter New Member

Sep 26, 2014
22
1
I need to reduce the following circuit to its minimal representation:

where each inductor is 1 nH and each capacitor is 1 mF.

Here is my solution (sorry for the messy writing!):

This isn't a particularly challenging problem, but my question is if I can do the last step where I combine the two parallel inductors even though there is a capacitor between them. Something in my mind says I can, which is likely based on something I read (and have forgotten from where).

What allows/disallows me from doing this?

If I had two parallel current sources in place of the two inductors (separated by the capacitor), could I have combined the two sources into one?

2. ### blah2222 Well-Known Member

May 3, 2010
573
36
Might want to double-check how you handled the parallel inductors at the bottom left side of the circuit.

To your question about the inductors in parallel with the capacitor: are you able to move the inductor on the left of the capacitor to the right of the other inductor without breaking any connections? Try it out and see if that answers your question.

3. ### JoeJester AAC Fanatic!

Apr 26, 2005
3,661
1,528
Your solution is not entirely correct.

You are correct with respect to the capacitors.

Here is the drawing with each component labeled.

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4. ### ElectronicGuru Thread Starter New Member

Sep 26, 2014
22
1
Seems I was too quick: as you two pointed out, I erroneously combined those three bottom-left inductors. Here's my updated circuit with what I believe is the correct solution:

As for what you, blah2222, said about combining the conductors with the capacitor in-between, I believe I can because the same amount of current/voltage should be through/across each parallel branch, no matter the order. I'm still not sure about the hypothetical part of my question with the current sources instead of the inductors. I think you couldn't combine the current sources unless they were directly parallel. Is this correct?

BTW JoeJester, what program did you use to create those diagrams and do the circuit analysis?

Thanks to you both once again!

5. ### blah2222 Well-Known Member

May 3, 2010
573
36
You can combine parallel current sources as they are independent branches in the circuit which will just produce a summation at an entry/exit node. You cannot connect current sources in series for obvious reasons.

I am not sure what you mean by "directly parallel". Both sources would have their top terminals connected with one another as well as their bottom terminals connected together no matter how you arrange your circuit drawing. They are parallel, period.

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6. ### WBahn Moderator

Mar 31, 2012
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You can actually combine current sources that are in parallel branches even if they have other components in series with them individually. The reason is that a current source masks the presence of any components in series with it, just as a voltage source masks the presence of components that are in parallel with it.

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7. ### studiot AAC Fanatic!

Nov 9, 2007
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519
Just to confirm point for electronicguru.

Think of a more general circuit, say a battery and two impedences Z1 and Z2.

Does it matter whether you connect Z1 on the left hand side and Z2 on the right hand side or the other way round or even both on the same side?

As in my sketch?

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8. ### JoeJester AAC Fanatic!

Apr 26, 2005
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9. ### ElectronicGuru Thread Starter New Member

Sep 26, 2014
22
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I honestly have no idea why I'm getting confused on such basic principles. I'm going to review some of these concepts from my book. Haven't read it in a while. Thanks.

I remember reading about that "masking effect" a while ago. For those series components, would you simply place them in series with the single, combined current source?

Thanks for the sketch. For some reason, the idea of switching around the passive elements was okay for me, but moving around sources wasn't. No idea why I was stuck in that thinking. Thanks for the help.

10. ### WBahn Moderator

Mar 31, 2012
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No, because they don't have the combined current going through them so that would be misleading. But it also doesn't really matter because you can just remove them entirely from the circuit as they have no effect (unless you are being asked for the voltage specifically across one or more of them or you are being asked for total power dissipation in the circuit or something like that.