Question about how resistance works

In summary, the conversation discusses a simple circuit with a 4.5V battery and a 1kOhm resistance. The question is raised about how the electrons know to travel slower in the resistance. It is explained that the E-field and wire properties determine the motion of the electrons, and the power supply only provides a potential difference. The Drude model is mentioned as a useful explanation for this phenomenon.
  • #1
Tusike
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0

Homework Statement


Consider a simple circuit that looks like a rectangle (the cables), with 4.5 V attached on the bottom. The electrons are traveling from - to +, let's say I1 = 10A, which means they have an average velocity v1. Now put a 1kOhm resistance near the + side of the battery. I2 = 4.5mA anywhere in the circuit. My question is, how the hell does the electron that starts from the - end of the battery know that it shouldn't be traveling as fast? Isn't the E-field the same?


Homework Equations


None that I can think of.


The Attempt at a Solution


It's ready a theoretical question so I don't have an attempt. I know that they have to travel slower, because if not, they would clutter together at the resistance, and there's some law that doesn't allow it, I forget which (one of Maxwell's). I've always seen the potentials of a circuit represented by water falling down, so I tried applying the same here. Without the resistance = water falling in a tube, with a pump bringing it back up. With the resistance = near the bottom, make the tube really narrow, then after a few feet back to normal again. Applying what happens in the circuit in this situation, the water should start falling much slower than before; This can only be if the pump is pumping it slower. So does this mean that in the circuit, the battery's voltage is pumping the electrons slower or something like that?
Thanks for any help!
 
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  • #2
So what I'm imagining now is that when there is a resistance in the circuit, less electrons start from the - end, but still at the same speed as without the resistance. This results in the lower I2 observed. However, inside the resistance, aren't they supposed to travel slower? And they would clot up exactly (more electrons) so that the I inside the resistance equals the same as in the rest of the circuit. But as I mentioned before, clotting up is against a law, so I still don't understand.
 
  • #3
It's very unclear and usually wrong to say "less electrons" or "more electrons". You don't even need to apply Maxwell's equations here. You only need the microscopic Ohm's law:

[tex]\frac{1}{\rho}\vec{E}= \vec{J}= -ne\vec{v}[/tex]

where [tex]\rho[/tex] is resistivity, [tex]\vec{J}[/tex] is the current density, n is the number of electron per volume, and [tex]\vec{v}[/tex] is the drift velocity of electron.

We have the current: [tex]I=\int _{A} \vec{J}d\vec{A} = JA[/tex] where A is the cross-sectional area (assume that [tex]\vec{J}[/tex] is the same at every point on A). Since I is the charge passing through the cross-section in 1 second, and the total charge must be conserved, then in series, I = const, right? Therefore:

[tex]\frac{1}{\rho}\vec{E}A = -ne\vec{v}A = const[/tex]

So the E-field is not the same everywhere in general, as it depends on cross-sectional area and resistivity. Nothing can be concluded here, as the wire may get high resistance but be big and vice versa.

Similarly, for the drift speed, we have: [tex]nvA=const[/tex] so it depends on the properties of the wire, i.e. the number of free electron per volume n (one property about the material) and the cross-sectional area (one property about the size). Again, nothing can be concluded if the only thing we know is the resistance of the wire. But we understand that electrons at different places may get different drift speeds, so the power supply doesn't try to pump slower or faster - it only supplies with the E-field in the wire. The definition of power supply is a potential-difference source after all, right? The rest, i.e. how electrons at one point move, is up to the E-field at that point and the properties of the wire at that point. The electron doesn't foresee anything.

So the question is, how the hell the electron knows where and when to slow down or speed up? It doesn't. The E-field tells it to do so. From the first equation, you can see that the drift speed is proportional to the E-field. An interesting model which accounts for this is the Drude model. Find it on Wikipedia :wink:
 
  • #4
Thanks that's all I needed to know!
 
  • #5


I can explain how resistance works in this circuit using the principles of electricity and electromagnetism. In this circuit, the battery provides a potential difference of 4.5 volts, which creates an electric field in the circuit. The electric field is what drives the movement of electrons from the negative to the positive terminal of the battery.

When we introduce a resistance of 1kOhm in the circuit, it creates a hindrance to the flow of electrons. This resistance is caused by the collisions between the electrons and the atoms in the material of the resistance. These collisions slow down the electrons and reduce their average velocity, resulting in a lower current (I2 = 4.5mA) compared to the initial current (I1 = 10A).

To answer your question, the electrons do not "know" that they shouldn't be traveling as fast. It is the resistance in the circuit that causes them to slow down. The electric field is the same throughout the circuit, but the resistance affects the flow of electrons, resulting in a lower current.

In your analogy of water falling in a tube with a pump, the pump represents the battery providing the potential difference and the narrow part of the tube represents the resistance. As you correctly pointed out, the water will start falling slower in the narrow part of the tube due to the resistance, just like how the electrons slow down in the circuit.

In summary, resistance in a circuit is caused by collisions between electrons and atoms, which slows down the flow of electrons and reduces the current. The electric field remains the same, but the resistance affects the flow of electrons. I hope this helps to clarify how resistance works in a circuit.
 

1. How does resistance affect the flow of electricity?

Resistance is the opposition to the flow of electrical current. The higher the resistance, the more difficult it is for electricity to flow. This is because resistance converts some of the electrical energy into heat, reducing the amount of energy available to power devices.

2. What factors determine the amount of resistance in a material?

The amount of resistance in a material is determined by three main factors: the material's length, cross-sectional area, and resistivity (a measure of how well the material conducts electricity). The longer and thinner the material, and the higher its resistivity, the greater the resistance.

3. How is resistance measured?

Resistance is measured in ohms (Ω) using a device called an ohmmeter. This device applies a small known voltage to the material and measures the resulting current. The resistance is then calculated using Ohm's law: R = V/I, where R is resistance, V is voltage, and I is current.

4. Does temperature affect resistance?

Yes, temperature can affect resistance. In most materials, resistance increases as temperature increases. This is because higher temperatures cause the atoms in a material to vibrate more, making it more difficult for electrons to flow through. However, in some materials, such as semiconductors, resistance decreases as temperature increases.

5. How can we reduce resistance in a circuit?

There are several ways to reduce resistance in a circuit. One way is to use a thicker and shorter wire, as this will decrease the material's resistance. Another way is to use materials with lower resistivity, such as copper instead of iron. Additionally, keeping circuits at lower temperatures can also help reduce resistance.

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