# Two circuits connected by a single wire, will there be current in wire?

1. Aug 29, 2011

### jaumzaum

If 2 circuits are connected by a single wire, will there be current in the wire?

If there is current, it can only goes throgh one way (ex: right or left) . In a 2 circuits like the example,

[PLAIN]http://img594.imageshack.us/img594/838/imagemgpp.png [Broken]

Where c and d are generators, e/f/g resistors. The wire AB is inicially unplugged and then plugged. In which case of voltage of the generators/resistance of the capacitors There would be current i n AB and in which case there wouldn't be?

What would happen if c or d were capacitors?

Last edited by a moderator: May 5, 2017
2. Aug 29, 2011

### VortexLattice

You just need to calculate which side of the wire has higher potential. If they're equal, no current will flow. If one is higher, current will flow from there. But I don't think we can tell without values for those components which way it will flow.

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3. Aug 29, 2011

### jaumzaum

If c = 80V, d = 20V
e = 5 ohm
f = 5 ohm
g = 2 ohm

What would happen?

4. Aug 29, 2011

### xts

@Vortex
But, if you have all components values?

OK. Take: c: 4.5V, d: 9V, f: 100ohm, e: 300 ohm, g: 1000 ohm.

Could you tell us now what will be a currend A-B and which direction?

5. Aug 29, 2011

### xts

@jaumzaum: nothing happens. Maybe small current flows for a very short while just after you connect A and B - discharging their initial difference in potentials (that would be equivalent to an initially charged capacitor connecting those halves).
Current always flows along some loop - A-B do not form one.

6. Aug 29, 2011

### jaumzaum

Thanks xts

And why the current is small (or almost none) in AB? How can we calculate it? Will there be ac urrent until the 2 circuits get the same potencial difference?

7. Aug 30, 2011

### jaumzaum

Ok,

So nobody of the whole site knows how to solve this question?

8. Aug 30, 2011

### Staff: Mentor

There is no current. You can analyze with node voltage or loop current, my preference is node voltage.

9. Aug 30, 2011

### jaumzaum

Thanks Dalespam

I already know theres no current (its a question I've already s een before)

I want to know why

10. Aug 30, 2011

### Staff: Mentor

Just use standard analysis techniques like node voltage:
http://people.ee.duke.edu/~gary/ECE27/nvm.pdf [Broken]

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11. Aug 30, 2011

### Studiot

I think this is a trick question.

What happens if you redraw it thus?

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12. Aug 30, 2011

### jaumzaum

[PLAIN]http://img809.imageshack.us/img809/6809/imagemzs.png [Broken]

In G: R3.i1 + R1.i1 -V1 = 0 -> i1 = V1/(R1 + R3)
In H: -R2.i2 + V2 = 0 -> i2 = V2/R2
i1 = i2 + i3 -> i3 = V1/(R1 + R3) - V2/R2

But what that thing has to do with the other?

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13. Aug 30, 2011

### Staff: Mentor

It is the same circuit. Just write the current through AB in terms of the loop currents G and H. Everything will drop out and you will get 0.

Last edited: Aug 30, 2011
14. Aug 30, 2011

### jaumzaum

I didn't understand?

I'm still getting i3 = V1/(R1 + R3) - V2/R2

Couldn't you solve it? My test is in 2 days, and I have a lot of things I wanted to ask too

I would be thankful

[]s
John

15. Aug 31, 2011

### willem2

But the current through AB isn't equal to the current through the wire AB in the circuit in the origional post. (and it isn't 0 either). The wire AB was eliminated from the first circuit because the potential at A and B is obviously the same, but from the resulting circuit you can then no longer draw any conclusion about the current through this wire.

The current through the first AB wire is obviously 0 because there is no return path. If there was a current, electrons would pile up on one side, creating a potential difference, that would stop the current.

16. Aug 31, 2011

### meldraft

Kudos for the link, great document

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17. Aug 31, 2011

### Staff: Mentor

That is correct, but i3 is not the current through AB. Let's label the current from A to B as I and express I in terms of the loop currents G and H. By applying KCL at B we see I+H-H=0 so I=0. By applying KCL at A we see -I+G-G=0 so I=0.

18. Aug 31, 2011

### Staff: Mentor

Yes it is, it just isn't equal to I3.

19. Aug 31, 2011

### jaumzaum

Why couldn't the current be like this?

Where the darker the higher the current

As willem2 said, if there was a current, electrons would pile up to one side, reducin g the potencial difference and the current stops (that what happenned). But I was not able to draw the current reducing because I didn't have enoug h colors for that.

Anyway, couldn't it be like this?

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20. Aug 31, 2011