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Nanyang
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Hi I'm new here and have this question I would like to ask. Sorry if I posted in the wrong section! My level of education is not high so please forgive me for this simple problem, though not simple to me.
Q: Why is it that in, for example, a series electric circuit that the electric current is constant?
I thought about this for very long (a year) when I am free and now, I kind of gave up trying to think of a solution independently.
note: this is not a homework
I asked my teacher about this and he said:
Note: I used div and grad to put my points forward, but I mostly self learned that and thus is not an excellent user of this mathematics. So do forgive any ugly mistakes made and if possible, correct it so that I can learn.
Sorry if this seems a little long, but these are some of the considerations I had over about one year thinking about this.
So do correct me where I'm wrong and hopefully help me understand why the current is constant in a series circuit.
Q: Why is it that in, for example, a series electric circuit that the electric current is constant?
I thought about this for very long (a year) when I am free and now, I kind of gave up trying to think of a solution independently.
note: this is not a homework
I asked my teacher about this and he said:
I thought of it and replied him saying:In a closed circuit with potential difference. There will be a net flow of charges in a specific direction. The collision of the electrons with the atoms of the conductor is represented by the resistance of the wire.
You can see current as a sea of electrons moving at a certain direction in general. According to Kirchhoff law, there should not be any charge accumulation anywhere in the circuit. The charges should move together. So the flow of electrons per unit time (current) in a series circuit is always constant.
Note: I used div and grad to put my points forward, but I mostly self learned that and thus is not an excellent user of this mathematics. So do forgive any ugly mistakes made and if possible, correct it so that I can learn.
So Kirchhoff nodal rule is div J = 0 which means that there is not net current through any closed surface formed on the wires. The closed surface can be infinitesimally small so that it's a point. So for any point on the circuit the net current flow is zero, thus the current is constant throughout the circuit for those charges that are moving, if there is no resistance.
I think this is something like a longitudinal wave and this wave should propagate at around c, assuming the apparatus is in a vacuum. Which means at an arbitrary time t, not all points on the circuit has charges moving.
But if I look at ohm's law, V=IR, if R is constant,
grad V = R grad I
E = - R grad I
So I is constant at all points in the circuit if E=0, where E is the electric field parallel to an infinitesimal displacement on the circuit. But electric fields extend to infinitely large distances, thus the parallel component of the electric field of the potential source is definitely not always zero on the circuit, as it is a closed loop. In other words, the charges, when going through the points where there is an electric field, accelerates and thus it's velocity changes.
Therefore, the current is not a constant as it goes around the circuit.
Now moving to the problem with the collisions of the electrons with the atoms of the conductor... More specifically the positive ions, since the metal loses negative electrons for conduction... etc... etc... etc... Anyway, the collisions occur because of the repulsion of the electrons of the atom and the free electrons that are flowing. To conserve momentum, the velocity gained by the electrons in orbit is slightly less than the velocity lost by the flowing electrons, and the orbiting electrons now taking a longer orbit.
Unless the previously flowing electron somehow enters the shells of the metal ion and the previously furthest electron is no longer orbiting the nucleus and now becomes a flowing electron, I cannot see how div J = 0.
Also, the positive nucleus gets attracted to the previously flowing negative electron and moves a little. Hence the 'missing' momentum from the previous consideration of the conservation of momentum is in the positive nucleus and therefore resistance is a property of the material, as the speed of the 'ejected' electron (that was previously orbiting before the flowing electron arrives near the ion) depends on the number of electrons orbiting as well as the mass of the nucleus. I don't know if this is true, but it's an idea.
If the flowing charges don't pass through, I think it will be something like a capacitor...where charges accumulates and the charge density changes with time, implying a non zero value for div J. Then the current is not the same at all points in the circuit.
Sorry if this seems a little long, but these are some of the considerations I had over about one year thinking about this.
So do correct me where I'm wrong and hopefully help me understand why the current is constant in a series circuit.
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