Work Done By Elelctric field in a circuit

[tonyjk]

hello, I've been searching the forum here, many websites and books and i just don't get it. The potential difference between two points in a circuit is the work done AGAINST the electric field so who's making the work in a circuit? isn't suppose to be the Electric Field? and in a circuit the electrons flows from lower potential to higher potential so electrons is moving with the direction of the electric field no? and when we say there's a drop of potential across a resistor is it means that the work done is negative? thank you

And i want to add something what is the relation between the energy gained or lost for an electron in a circuit and the work done by the electric field?

 

[andrewthorn]

It seems you do grasp the fundamentals. Within a simple circuit, electric field lines run along the length of a resistor from positive to negative, it can be thought of as field lines going from the positive to negative terminal of the cell. Therefore to move an electron from negative to positive, we are doing work against this field.

Also, where I believe you are getting slightly confused is by thinking about electron flow rather than conventional current, unfortunately circuit theory began before the discovery of the electron. Thinking in terms of positive charges can make things a little easier.

 

[sophiecentaur]

If you look at the Definitions of Work, Potential and Field (etc.) you find that Field is the gradient of Potential / Work done on a unit charge. There is no field inside a perfect conductor so there is little point in bringing electron movement into this. Electrons need (virtually) no energy to make them flow (albeit at a snail's pace) through a conductor. No work is involved because the Potential change is zero.

An Electric field does no work. It is a mis-use of terms to say that.

 

[tonyjk]

so what's the physical(real) meaning of a potential difference in a circuit?

 

[tonyjk]

is it a kind of energy per charge(gaining or losing?)

 

[Dale]

hello, I've been searching the forum here, many websites and books and i just don't get it. The potential difference between two points in a circuit is the work done AGAINST the electric field so who's making the work in a circuit?

This can either be some chemical which is doing work "against" the electric field at the molecular level, or a generator which is mechanically doing work "against" the electric field.

and in a circuit the electrons flows from lower potential to higher potential so electrons is moving with the direction of the electric field no?

That is just a convention. You very rarely need to actually think about the electrons, just think about the current for the most part and don't worry about the direction of the charge carriers.

and when we say there's a drop of potential across a resistor is it means that the work done is negative?

Yes, the work done ON the circuit BY a resistor is negative.

 

[tonyjk]

generator which is mechanically doing work "against" the electric field.

it's not the generator that "creates" the electric field in a circuit?

 

[sophiecentaur]

so what's the physical(real) meaning of a potential difference in a circuit?

Moving one coulomb of charge through a potential difference of one volt involves the transfer of one Joule of work / energy.
Bear that in mind at all times and it will help you to get things right.

 

[tonyjk]

Moving one coulomb of charge through a potential difference of one volt involves the transfer of one Joule of work / energy.
Bear that in mind at all times and it will help you to get things right.

thanks:D

 

[Dale]

it's not the generator that "creates" the electric field in a circuit?

Not really. Generators need an excitation, particularly larger or older generators. The excitation gives the generator a field to work against and thereby provide power to the circuit. Of course, that can be cumbersome to arrange, so modern small generators typically are "self excited" meaning that they have the exciter built-in as part of the design.

You can think of the exciter as providing a small field, the generator does work against that field and makes it bigger and adds power to the circuit. Then that power is used by the attached electrical devices to accomplish the purpose of the circuit.

 

[tonyjk]

aha ok! i didnt know that! thanks

 

[tonyjk]

sorry, but is it the electric field that moves the electrons so how come there's another force doing work on the electrons?

 

[sophiecentaur]

It's obvious that it takes a force to move an electron but a force doesn't "do work" because a force in itself is not an energy source (in strict terms). Also, which force / field are you discussing? There is virtually no field inside a wire and no work is done in there. In a resistive circuit, even, where would you say an overall field exists? Just across the terminals? The wires could be looped all over the place. So it is better just to think in terms of Potential, which is a scalar and doesn't care about the geometry.

 

[tonyjk]

So who's responsible for moving electrons in a circuit? Is it the force= thecharge x electric field?

 

[Dale]

sorry, but is it the electric field that moves the electrons so how come there's another force doing work on the electrons?

Short answer: the "other force" moves the charge in the opposite direction of the field, the field itself obviously can't do that.

Long answer: A lot of people on these forums don't like the "plumbing" analogy, but I do. For a lot of practical purposes you can think as electricity running through wires in a similar way as water running through a pipe. In that analogy, pressure is analogous to voltage and flow is analogous to current.

So, let's say that we have a set of water pipes. Attached is a turbine (motor) which we want to drive to do some external work. At the turbine, the power is determined by the pressure (voltage) times the flow (current). The pressure difference (voltage difference) across the turbine (motor) is what drives the flow (current) through the turbine (motor), but how did we get that pressure (voltage) in the first place?

On some other part of the pipes (circuit) we installed a pump (generator). This pump (generator) takes energy from an external source and uses it to push water (charge) in the opposite direction of where it wants to go naturally, i.e. from the low pressure (voltage) to the high (pressure) side. If the pump (generator) didn't do that then the turbine (motor) would use the little bit of energy stored in the pipes (wires) and then all of the pressure (voltage) would be equal throughout the pipes (wires) and no more work would be done on the turbine (motor).

 

[tonyjk]

Just last question... In a circuit if there'sa dc source and a resistance the electrons flow from lower potential to higher potential and across the resistance its the same so we can say also that the resistance is doing work against the electric field?

 

[Dale]

No, the current flows through a resistor from a region of high potential to a region of low. I.e. The current is moving with the field through a resistor.

 

[tonyjk]

Yes so the electrons flow from lower to higher potential:p no?

 

[tonyjk]

And how about the work done across the resistor is it against the electric field?

 

[Dale]

Work is a scalar, it doesn't have a direction.

 

[tonyjk]

i was just reading the book Introduction to electrodynamics by David Griffiths they say that the force that is responsible for the flow of current inside a conductor is an electromagnetic force that does the job ( and they take the electric field)

 

[tonyjk]

and they say for the EMF the force inside a battery for example is the opposite of the Electric field so outside the battery the electric field is moving the electrons so how come the potential difference across a resistor for example is the work against the electric field?

 

[tonyjk]

The upshot of all this is that there are really two forces involved in driving current around a circuit: the source, fs, which is ordinarily confined to one portion of the loop (a battery, say), and the electrostatic force, which serves to smooth out the flow and communicate the influence of the source to distant parts of the circuit:
f=fs+E. (7.8)

so ok the emf does work against the electric field but outside like the resistor the potential difference is not the work done against the electric field no?

PS: the quote is from the book

 

[tonyjk]

we can say outside the EMF the force on the electrons is (the negative charge of the electron)* Electric Field so that's why it's the work done against the electric field?(because this force is opposite to the electric field)??

 

[sophiecentaur]

so ok the emf does work against the electric field but outside like the resistor the potential difference is not the work done against the electric field no?

I rather get the impression that will not be happy until you get an answer that is in exactly the terms that you want. This is getting in the way of your improving your understanding, I think.

It is true to say that each electron can be said to move as a result of the local electric field. However, this is hardly relevant in describing the charge flow and energy transfer in a circuit because what counts is the Volts and not thy Volts per Metre. The (dc) situation is precisely the same in a simple circuit however far apart the connecting terminals are held apart. The field across the terminals is irellevant.

 

[tonyjk]

I rather get the impression that will not be happy until you get an answer that is in exactly the terms that you want. This is getting in the way of your improving your understanding, I think.

haha:P no seriously i want to know why it's the work AGAINST the electric field(across a resistance for example) i just don't get it

 

[tonyjk]

for example the potential difference across a resistor is let's say 3V but the electrons is moving from the the lower potential to the higher potential and in the book they said that electric field moves the electrons inside the resistor so why this PD is the work done against the electric field? Can we say it's because the electric force is equal to ( the charge of the electrons(negative) X the electric field so this force is against the electric field?)

 

[sophiecentaur]

haha:P no seriously i want to know why it's the work AGAINST the electric field(across a resistance for example) i just don't get it

I just don't think that the "work done against an electric field" is a very relevant statement when dealing with circuits because the geometry is odd the fields are all over the place. That's why Electric Potential is a better approach. BUT we do often say that you do work "against a gravitational field" when we store up Potential Energy by raising something in the air. If that usage is acceptable then so could the use in electric situations. Your charge is, effectively 'going uphill' when you do work on a charge to make something happen at the other end of a circuit - where the charges will be "going downhill".

[Edit: reading your post, above, it seems that you, or someone, is putting things the wrong way round. A battery, not a resistor, does work "against" a field.]

PS Avoid talking about electrons in matters like this or you are likely to fall over yourself as to which direction to think. If you accept the arithmetic identity that "minus a minus is a plus" then you can just talk of charges all the way through. Everything will work fine with ions, positrons and electrons that way.

 

[tonyjk]

Yes i know the battery does work against the electric field but there's also a potential difference across the resistance so its also a work done but by who? Is it the electric force= charge of the electron X electric field ?)

 

[sophiecentaur]

Yes i know the battery does work against the electric field but there's also a potential difference across the resistance so its also a work done but by who? Is it the electric force= charge of the electron X electric field ?)

Like I said before. I don't think the answer, on your terms, actually exists. I hope the following will help to reconcile the confusion.
Energy is supplied by the battery / generator. Would you say that the work done on the bicycle wheel is done by the links of the chain or by the cyclist? So would you say that the work done on the resistor is due to the other electrons or due to the battery? If there is no confusion when discussing mechanical energy transfer and work, why should there be confusion with an electric circuit?
Yes but which field are you referring to? The electron experiences a force because of the fields around adjacent ions and electrons. It has no idea about the 'field' across the terminals of the circuit. Is either field relevant, in the wider scheme of things?

 

[Dale]

work against the electric field

I am no longer sure that I know what you mean by "work against the electric field". Can you explain precisely, perferably in terms of equations, what you mean by that?

 

[Antiphon]

Forgive me for jumping in but if you have a charge in a field where the force points along a certain direction but you mechanically cause the charge to move opposite the force; that is doing work on the charge against the electric field.

 

[tonyjk]

Forgive me for jumping in but if you have a charge in a field where the force points along a certain direction but you mechanically cause the charge to move opposite the force; that is doing work on the charge against the electric field.

That's what i am saying

 

[tonyjk]

I am no longer sure that I know what you mean by "work against the electric field". Can you explain precisely, perferably in terms of equations, what you mean by that?

If you take an emf inside it there's a force fs opposite to the electric field E that does
Work against the electric field. In the circuit the electric field applies an Electric force opposite to the electric field this force is equal to the charge of the electron(negative) X electric field. And the work is the integral of those forces by the lenght

 

[Sefrez]

I am unsure if I am correct, but the way I see it is that you first need some form of resistance in order for a potential difference to exist. That is, without it, no work is needed in the first place to move charges. So in a simple circuit with an EMF and a resistor the EMF first moves charges against an electric field - this gives them potential. That is, they now want to "fall back". Not much different than lifting a mass and then being able to drop it. Though, remove gravity, or the resistor, and there is no longer this said potential.

Once the charges have been forced up the electric field they then fall to the lower potential. The potential difference must exist only over the resistor as it is what allowed for it to begin with. Any wiring that may be in this simple circuit can either be real and considered as some resistance it self (being accounted for in the resistor) or ideal and no resistance. In the second case, no work is needed to move charges. The battery does work only on the resistor. And like wise, the resistor does "negative" work. The charges that pass the resistor no longer have said potential.

Again, I am unsure if I am correct.

 

[sophiecentaur]

"Jumping in" is what this forum's all about. No need to aplologise. :-)

 

[tonyjk]

last question:P we say that across a resistor there's a drop of potential is it because when an electron loses it potential energy and it is convert to heat?thanks

 

[thunderhadron]

It is because when a resistor is connected to battery, Battery's Higher potential and lower potential plates makes the same situation with the resistor also. An electron gets energy difference there hence moves.

 

[sophiecentaur]

I know they love to tell you at School that electricity is all about electrons moving but the problem is, they move very slowly and the explanation is, ifaiac, a bit of a cop out. It is actually quite difficult to justify those last two posts in detail when you are dealing with AC. The same electrons are moving backwards and forwards inside the resistor for hours on end and another set of them are moving in and staying in the cables. None of them do what those two posts are implying. i.e. they don't 'have energy' then 'give it up'.
You should really stick to 'Charge' as your conceptual carrier of energy. OK it may be a bit abstract but it avoids falling over yourself and coming to dodgy conclusions.

 

[Dale]

haha:P no seriously i want to know why it's the work AGAINST the electric field(across a resistance for example) i just don't get it

OK, then based on your clarification, the work done across a resistance is NOT against the field. The work done in a battery or in a generator is against the field.

 

[tonyjk]

OK, then based on your clarification, the work done across a resistance is NOT against the field. The work done in a battery or in a generator is against the field.

Im not saying that i am right i just don't know the answer and I am trying to find the right one! so across a resistance is it against or not? thanks

 

[tonyjk]

i think across the resistance there's drop of potential it means that the potential energy of the electrons is converted to heat? despite that the electron moves from a lower potential to a higher potential right?

 

[Sefrez]

I know they love to tell you at School that electricity is all about electrons moving but the problem is, they move very slowly and the explanation is, ifaiac, a bit of a cop out. It is actually quite difficult to justify those last two posts in detail when you are dealing with AC. The same electrons are moving backwards and forwards inside the resistor for hours on end and another set of them are moving in and staying in the cables. None of them do what those two posts are implying. i.e. they don't 'have energy' then 'give it up'.
You should really stick to 'Charge' as your conceptual carrier of energy. OK it may be a bit abstract but it avoids falling over yourself and coming to dodgy conclusions.

I think potential is a bit arbitrary anyway. So of course you could assign it with AC current, it would just be constantly changing and likely a bad way to think about it. The main point to be made is that the source driving current performs work and it can only do so because of the resistance within the circuit performing "negative work," if you will. That is, no net work is required to move charges from here to there if there is no intermediate resistances.

i think across the resistance there's drop of potential it means that the potential energy of the electrons is converted to heat? despite that the electron moves from a lower potential to a higher potential right?

For the sake of defining potential for an electron, no, it does not move from a lower to higher potential. That goes against the purpose of defining potential. In order for an electron to do positive work (and thus produce heat) it must lose potential energy.

Maybe you are still thinking of electric fields and are getting confused as to what an electric field means for an electron? An electric field is defined such that its direction points away from positive charges and toward negative charges. In consequence, it also describes the direction a positive charged particle will experience a force in. That is, an ideal positive charged particle will have field lines directed radially outward and placing another positive charged particle near it - you will find that the force it experiences is also radially outward - just as the field lines indicate. Place an electron in this vicinity however, and you get the opposite result.

In summary, a positive charged particle gains potential energy when an external force does positive work on the particle. That is, when this external force moves the particle in the opposite direction of the field. For a negative charged particle (electron) potential energy is gained when an external force does positive work on it also. However, in order to do positive work, the negative charged particle must be moved in the direction of the electric field. Why? Because the positive charged particle creating the radial outward fields actually attracts the electron rather than repelling it as would be so with another positive charge.

So
ΔU = W = -We = -∫F . dD = -∫qE . dD
{ΔU = change in potential energy, W = external work, We = work done by electric field (or source creating electric field, if you will), F = force on charge by field, q = charge of particle including sign, E = electric field created by source, D = displacement}

Being as simple as I can, when an electron goes over a potential difference of ΔV (positive change,) its potential energy change is -qΔV where I have explicitly place its negative charge sign. So it's potential energy change is explicitly negative in sign.

 

[tonyjk]

Im not understanding that EMF has a force fs that does work against the electric field so how they will gain energy if they are moving against the electric field? and all around the circuit the electrons are moving against the electric field (inside the resistor) I am confused

 

[Dale]

Im not saying that i am right i just don't know the answer and I am trying to find the right one! so across a resistance is it against or not? thanks

It is not. The work done across a resistor is always with the field, according to your description of what you mean by "against the field".

Btw, you should not think about electrons, only about charge and current. In many cases (i.e. electrolytes, electrolytic capacitors, batteries) the charge carriers are positive or even both positive and negative. That may be the source of your confusion. Ignore the flow of electrons, just think about current.

 

[sophiecentaur]

Im not understanding that EMF has a force fs that does work against the electric field so how they will gain energy if they are moving against the electric field? and all around the circuit the electrons are moving against the electric field (inside the resistor) I am confused

You keep ignoring the one thing here that answers your question: it's the answer you get when you multiply a negative number (electronic charge) by a negative number (the direction of the force on it, due to the field times the displacement). This gives a positive value of work done ON the electron when the conventional charge is transported from the positive end to the the negative part of the circuit "AGAINST the field". When the electron flows in the direction 'it wants to go or downhill' (sorry, but it's the best way to describe it) the sign of the work done BY IT on the substance of the resistor is Positive.

The essence of all this seems to be a confusion between Electric Potential (based on a positive charge) and Potential Energy (which involves the sign of the charge involved).