# what does voltage is dropped across the resistor mean?

#### elara

Joined Jan 12, 2016
15
When we speak of potential difference between "two points"- we speak of voltage - for example in a battery the difference of electrons between the negative and positive terminal is voltage, In other words, negative terminal has excess of electrons and positive has deficit of electrons and the difference between the two is voltage. So when electrons flow through the resistor once the battery is connected to a circuit, we measure the potential difference across this resistor and "confirm" that voltage has dropped (through voltmeter) but the rate of flow of current before the resistor and the after the resistor is the same (in a series circuit at least). In other words, there is no difference in electrons - so there is zero potential difference between these two points, hence there is no voltage. So what does this mean? Sorry if this is a dumb question.

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#### Papabravo

Joined Feb 24, 2006
18,405
The only time that the potential difference across a resistor can be zero is when the current is zero. This is basic Ohms Law. Any current that flows through a resistor, no matter how small, creates a voltage drop, which is proportional to the current. BTW, batteries and DC power supplies, both have internal resistance. This is why wall warts will put out a higher voltage than their label indicates, because the load has a high resistance and draws only a small amount of current. This is also why the voltage of such a wall wart will sag if the load is too small and tries to draw more current than the wall wart can provide.

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• Johann

#### elara

Joined Jan 12, 2016
15
The only time that the potential difference across a resistor can be zero is when the current is zero. This is basic Ohms Law. Any current that flows through a resistor, no matter how small, creates a voltage drop, which is proportional to the current. BTW, batteries and DC power supplies, both have internal resistance. This is why wall warts will put out a higher voltage than their label indicates, because the load has a high resistance and draws only a small amount of current. This is also why the voltage of such a wall wart will sag is the load is too small and tries to draw more current than the wall wart can provide.
But doesn't potential difference means the measure of difference of excess electrons between two points? So how is it that there is a potential difference when the electrons before and after the resistor are the same?

#### Papabravo

Joined Feb 24, 2006
18,405
You have it wrong. An Ampere of current is one Coulomb of charge per second flowing past a point in a circuit. What is the same on both sides of a resistor is the rate of charge flow, and not the absolute number of charges. So the charges build up on one side of a resistor, and only a certain number of them make it through. There's a heuristic description of the justification for voltage drop or potential difference.

#### bwilliams60

Joined Nov 18, 2012
1,430
Voltage drop is a measure of the amount of pressure that is lost across the resistor, not current flow. In a series circuit, electron flow is dependent on the amount of pressure pushing the electrons through a resistance. Each resistance you add will slow down the electron flow because there is a drop in pressure across each resistor. When you add up each of these voltage drops, they will equal source voltage. Keep in mind that even the conductors carrying current will have the tiniest bit of voltage drop as well.
The electron flow does not change because the initial voltage has already been established by the source and the load. The voltage dropped across the load has been established by the current flow and the resistance. It is all relative.

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• elara

#### elara

Joined Jan 12, 2016
15
You have it wrong. An Ampere of current is one Coulomb of charge per second flowing past a point in a circuit. What is the same on both sides of a resistor is the rate of charge flow, and not the absolute number of charges. So the charges build up on one side of a resistor, and only a certain number of them make it through. There's a heuristic description of the justification for voltage drop or potential difference.
I can't picture this in my head for some reason. Could you please elaborate? Are you saying the rate of charge flow is approximated and not absolute? In other words, the current before and after the resistor are relatively the same but not equal?

Voltage drop is a measure of the amount of pressure that is lost across the resistor, not current flow. In a series circuit, electron flow is dependent on the amount of pressure pushing the electrons through a resistance. Each resistance you add will slow down the electron flow because there is a drop in pressure across each resistor. When you add up each of these voltage drops, they will equal source voltage. Keep in mind that even the conductors carrying current will have the tiniest bit of voltage drop as well.
Ok. So far, I understood that the overall flow is reduced in the form of heat/energy due to electrons colliding with the atoms in the resistor. In other words, some of the charges (or the difference in potential) flowing from the battery are "neutralized" in the resistor. This potential energy is expended and can be referred to as voltage drop. But this leaves me to the definition of potential difference across two points? What does this mean when you are measuring across the circuit and not the battery?

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#### Papabravo

Joined Feb 24, 2006
18,405
I can't picture this in my head for some reason. Could you please elaborate? Are you saying the rate of charge flow is approximated and not absolute? In other words, the current before and after the resistor are relatively the same but not equal?
...
No what I am saying is that the flow into an out of a resistor is identically the same, but there is more potential for flow on one side than the other. If the resistor could suddenly cut it's value in half, the flow would immediately double.

BTW it is OK not to get this stuff. It deals with a world that we cannot see touch and feel.

#### Alec_t

Joined Sep 17, 2013
12,807
Here's an analogy which may help. Think of an old-fashioned egg-timer with a volume of sand above a narrow passage. The number of sand grains going into the passage in unit time equals the number of grains coming out (the sand flow rate, analogous to current). There is a big pile of sand above the passage but not at the exit of the passage (analogous to potential difference).

• Johann and absf

#### crutschow

Joined Mar 14, 2008
29,779
At the atomic level the free electrons in a conductor are there independent of the voltage.
The atoms don't have "missing electrons" the electrons are just free to move from one atom to the next. Each atom always maintains a neutral charge.
The voltage just affects their rate of movement not the number of free ones.

#### kubeek

Joined Sep 20, 2005
5,772
...In other words, negative terminal has excess of electrons and positive has deficit of electrons and the difference between the two is voltage...
Here is your fundametnal flaw. Voltage does not necessarily mean an excess of electrons on one side. Yes, when you have excess electrons on one side you have an electric field, which turns into voltage difference, but the implication doesn´t necessarily work the other way. Electric field is what constitues voltage, and you can have two plates with same amounts of electrons that are at different voltage, just beacuse they are placed at different places in the the external electric field.

Battery does not have an excess of electrons on one pole. It has excess of electrons with higher potential that are willing to go to the other side, but the absolute amount on both poles is the same.

• elara

#### Papabravo

Joined Feb 24, 2006
18,405
A review of the chemistry of batteries might be helpful. In chemistry the use of square brackets implies "the concentration of". Concentrations in a solvent are usually expressed in moles per liter. One mole of any substance, or element, or ion is equal to Avagaro's number, which 6.02E23, which as you may be aware is bigger than a boatload!

http://www.science.uwaterloo.ca/~cchieh/cact/c123/battery.html

All of the ions in a DC circuit involving a battery and a resistive load are contained within the battery and the electrolyte. They do not leave the battery. All of the atoms in the wire and in the resistor are neutral atoms, there are no ions anywhere in sight. All of the electrons bound to atoms of the conductor have discrete energy levels. Above the highest energy level for the atoms of the conductor there is a band gap where no electrons have an energy level within the band gap. Above that energy level are numerous electrons from the battery that move along in the conductor with energy levels above the band gap. These energy levels are not discrete and form a continuum of energy levels. Most conductors have a very small band gap or none at all because the valence band and the conduction band overlap. Quantum mechanics also allows electrons to drop through the band gap to lower levels and tunnel through the bad gap (potential barrier) to higher levels. On a macro scale it is impossible to observe or measure this behavior.

As @kubeek has pointed out the battery contains an excess of electrons with enough potential energy to enter the wire, make it through the resistor, and proceed to the other electrode of the battery where chemistry dictates what happens next.

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• elara

#### BR-549

Joined Sep 22, 2013
4,928
The voltage drop across a resistor means there is current flowing thru it.

The electrons going in have more self repulsion, than the electrons coming out.

Electrons are repulsive to each other. Voltage squeezes them like a spring.

A resistor converts the self repulsion into heat.

#### JohnInTX

Joined Jun 26, 2012
4,667
No hijacking. No personal attacks. No arguing.

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#### hp1729

Joined Nov 23, 2015
2,304
Here is your fundametnal flaw. Voltage does not necessarily mean an excess of electrons on one side. Yes, when you have excess electrons on one side you have an electric field, which turns into voltage difference, but the implication doesn´t necessarily work the other way. Electric field is what constitues voltage, and you can have two plates with same amounts of electrons that are at different voltage, just beacuse they are placed at different places in the the external electric field.

Battery does not have an excess of electrons on one pole. It has excess of electrons with higher potential that are willing to go to the other side, but the absolute amount on both poles is the same.
Good discussion. What characteristic in the atom do we define as Voltage? "Potential difference" isn't very descriptive.
When we rub things together to generate static electricity what are we changing? We are pulling electrons from one body of atoms, creating a positive charge, and adding electrons to another body, creating a negative charge. Did I learn this wrong?
Does this same thing not happen at the atomic level as electricity flows from atom to atom?

#### WBahn

Joined Mar 31, 2012
26,398
When we speak of potential difference between "two points"- we speak of voltage - for example in a battery the difference of electrons between the negative and positive terminal is voltage, In other words, negative terminal has excess of electrons and positive has deficit of electrons and the difference between the two is voltage. So when electrons flow through the resistor once the battery is connected to a circuit, we measure the potential difference across this resistor and "confirm" that voltage has dropped (through voltmeter) but the rate of flow of current before the resistor and the after the resistor is the same (in a series circuit at least). In other words, there is no difference in electrons - so there is zero potential difference between these two points, hence there is no voltage. So what does this mean? Sorry if this is a dumb question.
A charge (electron) accelerates in response to an electric field. In a resistor (which means in most materials) a charge (electron) moving through the material wants to slow down and just stay put (wiggling around its current position due to thermal energy). This is much like friction. So to get the electron to move from one end of the resistor to the other, we need an electric field that is constantly accelerating the electrons which are then constantly giving up that energy to the friction-like effects and slowing back down. Recall that a voltage drop is the result of an electric field. So the bottom line is that we need an electric field across the resistor to give the electrons enough energy to make it through the resistance (with that energy being converted to heat in the process).

As a mechanical analogy, imagine a block of wood sliding on a long wooden board. The "voltage" across the board is the difference in height from one end of the board to the other (which is, in fact, a measure of the gravitational potential difference across the board). The "resistance" of the board is the degree of roughness between the block and the board. The "current" is the block of wood sliding down the board. The goal is to raise one end of the board just the right amount so that the block slides down the board at a constant speed. If the board and block are highly polished and lubricated, the high end of the board doesn't have to be lifted much at all. But if the two surfaces are very rough (think fine sandpaper) then one end of the board has to lifted a lot to find the angle that will result in the block sliding down at a constant speed.

• elara

#### hp1729

Joined Nov 23, 2015
2,304
A charge (electron) accelerates in response to an electric field. In a resistor (which means in most materials) a charge (electron) moving through the material wants to slow down and just stay put (wiggling around its current position due to thermal energy). This is much like friction. So to get the electron to move from one end of the resistor to the other, we need an electric field that is constantly accelerating the electrons which are then constantly giving up that energy to the friction-like effects and slowing back down. Recall that a voltage drop is the result of an electric field. So the bottom line is that we need an electric field across the resistor to give the electrons enough energy to make it through the resistance (with that energy being converted to heat in the process).

As a mechanical analogy, imagine a block of wood sliding on a long wooden board. The "voltage" across the board is the difference in height from one end of the board to the other (which is, in fact, a measure of the gravitational potential difference across the board). The "resistance" of the board is the degree of roughness between the block and the board. The "current" is the block of wood sliding down the board. The goal is to raise one end of the board just the right amount so that the block slides down the board at a constant speed. If the board and block are highly polished and lubricated, the high end of the board doesn't have to be lifted much at all. But if the two surfaces are very rough (think fine sandpaper) then one end of the board has to lifted a lot to find the angle that will result in the block sliding down at a constant speed.
< > You must read Forrest Mimms. </ > He likes to show electron as rest until a voltage is applied. I find that misleading. Electrons are always in motion from atom to atom. When we apply a voltage the motion gets organized in a negative to positive direction.

#### WBahn

Joined Mar 31, 2012
26,398
I've never read Forrest Mimms in any depth, though I did purchase a number of his books from Radio Shack when I was in high school -- never did get around to actually reading them, though.

You might note that I specifically referred to their constantly wiggling around. It adds nothing to the discussion getting bogged down talking about Fermi levels and electron mobility and such for a discussion at this level.

#### profbuxton

Joined Feb 21, 2014
419
I have never read such convoluted answers to to the question in my days. Can't anyone answer in simple terms?

• ronnietucker and Johann

#### Johann

Joined Nov 27, 2006
190
Its like water flowing through a narrow part of a pipe: The same amount of water that enters the one side of the narrow piece is leaving the other side of the narrow piece, BUT there is a pressure difference between input and output (only as long as the water flows!). Same with electric current (flow) and electric potential (pressure).