# Superposition Theorem in Electric Circuits. Are there indeed more than one current?

1. Oct 17, 2011

### nik2011

Hello!

If we want to find i3, we can apply the superposition theorem to the circuit below.

It gives

For V2 set to 0: i3' = V1 / R1
For V1 set to 0: i3'' = V2 / (R1 || R2)
i3 = i3' - i3'' = V1/R1 - V2 / (R1 || R2)
i3 = 10 / 500 - 2.5 / 83.3 = -0.01A

My question is
Do the i3' and i3'' currents really exist. By exist I mean part of electrons flowing through V2 flow in one direction and the other part flow in the opposite direction? And when i3 is measured it is the net current of i3' and i3''.

Or only i3 exists so all electrons flow through V2 in the same direction. If so how does the superposition happens? E. g., do V1's electric field interact with V2's electric field "directly"?

Or it is this way, if we look at a single electron which flows through V2's branch the force applied by V1's field sums up with force applied by V2's field and the resulting force defines the electron's speed and direction? If so, how to calculate the values of the force applied by V1 and the force applied by V2?

So in general, what I want to know is how does superposition happens in electrical circuits?

Thank you!

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2. Oct 17, 2011

### sophiecentaur

Re: Superposition Theorem in Electric Circuits. Are there indeed more than one curren

I should strongly advise you against trying to use electrons for ordinary electrical calculations. What's wrong with Current? All the equations use it and it avoids all those dodgy models involving electrons that people carry in their heads. Forget "electric field" here. What counts is Potential difference. The same current will flow whatever shape / length the resistors and wires happen to be so the field (volts per meter) is irrelevant.

Kirchoffs Laws etc. work perfectly for situations like this.
V2 is a voltage source and that defines the current I4 through R2.
The PD across R1 is also defined by the difference between the two Voltage sources V1 and V2. So the Current I2 is determined by that. The voltage source V2 will source or sink just the right amount of current (I3) so that I4 is what you calculated already.
The only problem you might consider having would be if the tow 'batteries' were not ideal - but that would be specified and would involve, effectively, some more simultaneous equations.

3. Oct 17, 2011

### nik2011

Re: Superposition Theorem in Electric Circuits. Are there indeed more than one curren

sophiecentaur,

I agree using Kirchoffs Laws or the Superposition theorem is the best approach to analyse this circuit.

What I'm trying to do is to imagine what physical processes actually happen when two currents sums up.
I would be pretty happy with a simplified model if what actually is going on is a very complicated process.
Just to have some "image" of this process in my head.

Or a simplified explanation and a reference to the complex one would be just perfect :)

4. Oct 18, 2011

### sophiecentaur

Re: Superposition Theorem in Electric Circuits. Are there indeed more than one curren

Fair enough but you need to start off in a valid direction. Electric fields can hardly help and neither can very simplified models of electron flow.
The 'next level' of complication needs to be much more complicated if it is to hold water.

5. Oct 18, 2011

### nik2011

Re: Superposition Theorem in Electric Circuits. Are there indeed more than one curren

Could you name a couple of such model?
I found this Wikipedia's article http://en.wikipedia.org/wiki/Comput...ics#Finite-difference_time-domain_.28FDTD.29"
Though I don't understand a single word in it, to be honest. But just out of curiosity, do some of the things described in this article look like such models?

Last edited by a moderator: Apr 26, 2017