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I've posted different question similar to this, yet still struggling to understand the theory. So here is another attempt to understand as to way two power sources(with different currents) connected in series cannot power a load without any harm? Or if it can, why can't the currents add up and the voltages?

schematic

simulate this circuit – Schematic created using CircuitLab

Although I've learned that current can flow to the load but at 5A(the lowest), why not 15A?

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  • \$\begingroup\$ What do you think the current through the load will end up being? \$\endgroup\$ – The Photon Nov 12 '14 at 5:21
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    \$\begingroup\$ Or put another way, with KCL in mind, what happens to the 5 A that flows through I2 but not through I1? \$\endgroup\$ – The Photon Nov 12 '14 at 5:21
  • \$\begingroup\$ Picture two ideal trains (fixed speed, no slip). One travels at 100 km/h, the other at 150 km/h. Now couple them. They remain ideal. At what speed does the combination travel? Under the required conditions there is no answer. \$\endgroup\$ – Wouter van Ooijen Nov 12 '14 at 7:39
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    \$\begingroup\$ Crossposted to physics.stackexchange.com/q/147037/2451 \$\endgroup\$ – Qmechanic Dec 20 '14 at 13:50
  • \$\begingroup\$ They'll fight.. \$\endgroup\$ – Pete Becker Dec 29 '14 at 16:32
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It is a basic rule. The physical basis for it is as follows. Current is just moving charges. Charges cannot accumulate. That is, objects generally cannot acquire a net charge. That is both a physical rule (rule of the universe) and also a rule for circuit analysis. So every time charges move into one side of a conductor, an equal number of charges has to move out on the other side.

So if I2 is dumping charge into the conductor at 10A, and I1 is clearing charge from the same conductor at 5A, that would imply that charge is accumulating in the conductor. Since that is impossible, it is impossible for two current sources to be in series unless they have the same current.

I hope you find this to be a satisfactory answer. I have tried to be accurate but intuitive. There are lots of analogies that could apply also (cars on a freeway, or skiers getting on a ski-lift or something). Let me know if you want me to offer something of that nature.

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  • \$\begingroup\$ It actually makes a lot of sense thank you, what might happen if this circuit was to be built? Also how can we relate this to parallel circuit and how current seems to accumulate there? \$\endgroup\$ – Pupil Nov 12 '14 at 6:18
  • \$\begingroup\$ A theoretical current source will increase the voltage across itself in an attempt to make the circuit draw the specified current. In the example circuit, the 10 Amp source will produce an infinite voltage, because the 5 Amp current source will only permit 5 Amps to flow. \$\endgroup\$ – Peter Bennett Nov 12 '14 at 7:41
  • \$\begingroup\$ There are many ways to build a current source. What will happen depends on the details. If they are current sources powered by some common VCC and delivering power to a load connected to "GND" then the one with the smaller limit will probably "win." But if the 10A current source is connected to a higher voltage or is somehow more powerful, it may cause the 5A source to fail/blow up, or whatever. This is just speculation. \$\endgroup\$ – mkeith Nov 12 '14 at 10:09
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    \$\begingroup\$ Actually, charges do accumulate, and objects do acquire net charge. \$\endgroup\$ – Chris Stratton Nov 12 '14 at 22:23
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    \$\begingroup\$ @ChrisStratton, that is true, but the extent that such accumulation effects normal circuit analysis is negligible. For circuit analysis purposes, you can assume that no conductors or circuit elements are allowed to have net charge. \$\endgroup\$ – mkeith Nov 12 '14 at 23:16
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The above answer given (by mkeith) is quite good. I think you can also see the problem logically.

By taking two current sources of different current values you are contradicting yourself.

1) By taking 10A current source you make a statement that you need 10A in a wire

But then again by your next action i.e.

2) By taking 5A current source you again state that you want 5A of current in the same wire(series-connection)

in a common wire, either statement-1 will be right or statement-2 will be right but not both. (because we know that one wire implies one path for current implies one current value)

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It violates KCL since if we take a point in between the centre of two current sources(i.e)node at the centre then by applying KCL convention it either results in -5 or +5A.Exactly speaking the current value is not equal to zero,this results in violation of KCL.Since Kirchhoff's law is a universally accepted one for lumped circuits this kind of physical connection is not at all possible.

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Why do folks have such trouble with current sources?
In the following voltage-source circuits, most folks see easily the incongruity:

schematic

simulate this circuit – Schematic created using CircuitLab You just don't do this with voltage sources - you get heat and sparks and dead batteries or possibly explosions.
Your series-connected current sources are the current-source equivalent to this situation.
Current source "prefers" to see a dead short for a load.
Voltage source "prefers" to see an infinite resistance (open) for a load.

Current sources add nicely in parallel
Voltage sources add nicely in series

Current sources must have a place (a load) to shove electrons
Voltage sources only supply electrons if they have to.

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This will lead to disaster, or whacky behavior. You are asking to violate basic physics. Kirchoff says the sum of currents at a node is zero. The node between the two current sources is in a tough spot. Current is way of counting charge carriers passing a point. In one seconde, the 10A source pushes 10 coulombs of charge. The 5A source pulls 5 coulombs away. That doesn't add up, though briefly a positive charge may build up before the circuit malfunctions.

With real world devices, perhaps one current source will puff smoke and smell bad, leading to an open circuit, or perhaps the 5A source may "win" by limiting current to 5A with the 10A struggling, but acting like a piece of wire.

Note that a current source does nothing if not in a circuit - so there should not be any assumption about a current source always has its specified current flowing. A voltage may develop across it, in hopes of pushing charge to make current, but there's only so far a realistic current source can push.

Current source may be put in parallel, however. That is analogous to stacking voltage sources in series.

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  • \$\begingroup\$ "Note that a current source does nothing if not in a circuit" - actually, that's a model violation too, as current source must always have its current flowing. And the case of a 5A current source with its terminals connected to nothing is not all that different from the case of the 10A source with its only circuit completed by way of a 5A current source. Needless to say one can't actually build a current source, but only something that approximates one under limited conditions - for example something where the voltage will rise up to a limit in an attempt to push the specified current. \$\endgroup\$ – Chris Stratton Nov 12 '14 at 22:20
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Imagine that one has a loop of inelastic pipe which allows water to flow without friction except at one point, where flow is proportional to pressure difference.

On this loop one has two pumping engines; one will ensure that five gallons per minute of water will flow through it, and the other will ensure that ten gallon per minute will flow through it. Each engine will add or remove as much energy as required to make the proper amount of water flow.

If only the 10g/min pumping engine were present, the pressure difference between its upstream and downstream sides would be whatever was necessary to push five gallons of water per minute through the constriction. The tighter the constriction, the greater the required pressure difference, and thus the more energy the pumping engine would have to add.

If a 5g/min engine were added in parallel, pumping in the same direction as the 10g/min engine, it would increase by 50% the amount of water that needed to flow through the constriction, and thus increase by 50% the amount of energy needed to make that happen. The total amount of energy dissipated by the constriction would be increased to 2.25 times the earlier amount; the 10g/min engine would have to output 1.5 times as much energy as it had before, and the 5g/min engine would have to output half that amount (0.75 times as much energy as the 10g/min engine had been putting out).

If the 5g/min engine were added in parallel the other way, half the water pumped by the 10g/min pump would go through the 5g/min engine. This would mean that the constriction would only half to pass half as much water, and would thus only produce half as much back-pressure and dissipate a quarter as much energy as it had with just the 10g engine. The amount of energy the 10g/minute engine had to add to the water would be half of what was necessary when it was operating alone, and the 5g/minute engine would actually extract energy from the water.

The problem with wiring the engines in series is that any water which flows through one must flow through the other; if 10g/minute flows through the upstream engine but only 5g/minute flows through the downstream one, that would imply that 5g/minute must somehow be accumulating in the pipe between the engines. Since water is very slightly compressible, such a thing might be possible for a brief moment, but the more water accumulates there the greater the pressure of the water there. The 10g/minute engine would have to add a very-rapidly increasing amount of energy to the water, and the 5g/minute pump would have to extract almost all of that energy from the water. The amount of energy transfer would rapidly increase until such time as the increased pressure prevents the 10g/minute pump from handling its full 10g/minute, causes the 5g/minute pump to let through more than 5g/minute, or causes the pipe between the pumps to fail.

As with the water in the above example, "electron-stuff" is very slightly "compressible". It doesn't take a very large excess or shortage of electrons, however, to build up a really huge amount of "back-pressure". If electrons are entering something at a rate of 1 amp, they are going to have to leave at the same rate; at a current of 1 amp, even a microseconds' worth of excess electrons would be a lot.

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