Electromotive force and potential difference

[Ravalanche]

hi everyone, i would like to ask some quick questions that i find confusing.
first, electromotive force is the energy supplied by a battery / power source, to ''push'' the charge through a circuit right? its unit is in Volts.
then, potential difference is defined as the work done to push 1 Coulomb of charge from point B back to point A. and its units is also in Volts.
So imagine a complete circuit. when a charge leaves the battery, let's say it contains 9 Joules of electrical energy / charge ( this is the E.M.F) then when it crosses a resistor. it drops from 9 Joules of Electrical energy to 6Joules. the drop is 3V, therefore potential difference is 3V.
now what do i call the remaining 6 Joules of electrical energy per charge? is it stilled called the EMF? I asked my teachers, they say its just simply called voltage. which i don't really understand what is the definition of voltage.

i've read wiki but it doesn't help , the term voltage is confusing. I'm not sure they are referring to EMF or P.d. thanks for the help in advance and i apologize for any mistakes in my statement as I am still learning.

 

[sankalpmittal]

hi everyone, i would like to ask some quick questions that i find confusing.
first, electromotive force is the energy supplied by a battery / power source, to ''push'' the charge through a circuit right? its unit is in Volts.
then, potential difference is defined as the work done to push 1 Coulomb of charge from point B back to point A. and its units is also in Volts.
So imagine a complete circuit. when a charge leaves the battery, let's say it contains 9 Joules of electrical energy / charge ( this is the E.M.F) then when it crosses a resistor. it drops from 9 Joules of Electrical energy to 6Joules. the drop is 3V, therefore potential difference is 3V.
now what do i call the remaining 6 Joules of electrical energy per charge? is it stilled called the EMF? I asked my teachers, they say its just simply called voltage. which i don't really understand what is the definition of voltage.

i've read wiki but it doesn't help , the term voltage is confusing. I'm not sure they are referring to EMF or P.d. thanks for the help in advance and i apologize for any mistakes in my statement as I am still learning.

Hiii !
Potential difference (PD)is defined as the amount of work done per unit positive charge (we assume positive but they are electrons !) on bringing it from infinity to the particular location.
We assume infinity because it defines a system to be simplified. It is also defined as the difference of potential energy or charge difference per coulomb of charge between two points in an electric circuit.

Electromotive force (EMF)is the potential difference existing between two terminals of the battery in a closed circuit , when no current is drawn from it. It is also defined as the amount of electrodynamic force (or energy supplied by battery) required to drive 1 coulomb of charge across a circuit. In other words you can also call it - Total Potential Difference.

EMF > PD , this condition is always true in a circuit.

See , suppose you have a closed circuit. In positive terminal you have 6 units of charge and in negative terminal you have 15 units of charge. The potential difference existing is 15-6 = 9 V which is electromotive force . So EMF = 9 V.

The difference in Voltages is equal to Work done on unit charge / Total Charges

V₂-V₁ = W/Q
OR
V=W/Q we assume PD

where V = V₂-V₁

Now

We knew EMF = 9 V

When driving a charge(electrons they are we just assume charge.) suppose due to a resister we do X J of work an there is PD - 3 V.
Then remaining = 9-3 = 6V. This drop is manifested in form of energy.

Always remember that EMF is total PD.

EMF = Total drop in voltage.
or
EMF = V₁+V₂+V₃ +...V_n

In your case , suppose energy used up = work done = 9-6 = 3 J
So V=W/Q
3=3/Q ==> Q=1 coulomb
You haven't assumed what amount of PD the circuit had when it was closed. Well if 6 J of energy remains then you cannot call it EMF. Its total voltage.

EMF = W/Q , total energy supplied is 9 J , So EMF = 9/Q say Q=1 or EMF = 9 V

If you assume that total voltage drop along a complete circuit is 9 V.

 

[Ravalanche]

Thanks for the detailed explanation. However, still I'm confused by the term voltage. What does voltage refer to? The p.d or emf?

 

[Delta2]

I think your confusion is because we use the term voltage for

1) Voltage between two points A and B $$V_{AB}$$ which is the potential difference between these Points. It is $$V_{AB}=V_A-V_B$$ where $$V_A$$ is the potential at point A and $$V_B$$ the potential at point B. Both potentials $$V_A,V_B$$ and voltage $$V_{AB}$$ are measured in units of volts. The potential at a point A $$V_A$$ is the amount of work needed (or provided by the electric field) to drive a unit charge from point A to infinity.

In your example where the charge voltage drops from 9 to 6 it is actually that the charge is moved between one point with potential 9Volt and another point with potential 6volt. The potential difference between these points is 9V-6V=3V.

 

[Ravalanche]

so you are saying that if at a particular point, a charge has let's say again 6 Joules of electrical energy, then I can say that the potential at that particular point is 6volts?
or should I say the voltage at that point is 6volts?

 

[Delta2]

so you are saying that if at a particular point, a charge has let's say again 6 Joules of electrical energy, then I can say that the potential at that particular point is 6volts?
or should I say the voltage at that point is 6volts?

Both are correct but more accurate and correct is the first that is to say that the potential at that point is 6volts.

 

[Ravalanche]

alright, thanks alot.
cheers.

 

[sophiecentaur]

Thanks for the detailed explanation. However, still I'm confused by the term voltage. What does voltage refer to? The p.d or emf?

The term Voltage (although we use it all the time) is too sloppy to use in a formal argument. People also use that horrid term "Amperage" (ugh!) when they mean Current. (Also 'footage', meaning length - but never 'pintage' for amount of beer consumed?)
Potential difference is the only really meaningful term and it is strictly defined in terms of energy transferred by a charge. Hence when there is a PD of 1, volt, every coulomb that flows, transfers 1 Joule of energy.
1V = 1Joule per Coulomb
PD is, OF COURSE always a difference in potential between two points. 'Voltage' may be used as shorthand to refer a PD relative to Ground.
emf is a term which refers to an 'ideal' potential which would be available from a source of electrical power if there were no losses of energy inside the source. Once current starts to flow - supplying energy to a circuit, there is always energy lost inside any source (internal resistance) So, as has been said already, you can sometimes measure this 'emf' if you take no current. It may not be actually possible in all instances, though, because you can't actually 'get inside' the works.

 

[Ravalanche]

haha, yeah its true, I see the term voltage everywhere when dealing with electricity, its kinda confusing though, but thanks to you guys I finally got it.
btw, another side question, thought i would post here instead of starting a new thread.
anyway, how does current actually flow? we say that current is the flow of charge right? and we group these charges into couloumbs with consist of electrons. But I know that its not that simple. Can someone please share their knowledge on how does current actually ''move''? current flows opposite to the direction of electron flow, in electronics, holes also move in the opposite direction, does that mean current = holes?

 

[sophiecentaur]

I always try to think of Current in the abstract / bulk sense and not to consider the actual mechanism at a lower level. This is because current can actually take different forms. At the end of the day, in electric circuits, it has to involve electrons moving into the end of wires at one end and leaving the other end. But one couldn't rule out a circuit in which part of the current path consisted only of positive ions flowing through some exotic fluid - or even positrons flowing through a vacuum or a tube of 'ionised' anti hydrogen. Who know the future of electrical circuitry?

In metals, there are many electrons (some people call them Valence electrons and there is at least one per atom) that are very mobile within the material. They are in constant random thermal motion, at normal temperatures, with a very high RMS velocity. When a current 'flows' there will be a net movement of all these electrons, at a 'drift speed' of only a mm or so per second. So it is not a helpful model to think of a 'stream of electrons' moving through the metal, any more than it is useful to think of a few tens of thousand immigrants flowing into a country when the airports, roads and railways are carrying possibly millions of travellers in and out every year. The 'net' migration figure is only a small part of what's really going on and wouldn't help you plan a transport system. So I don't like the 'water' analogy and nor do I really think much of the 'bicycle chain' analogy, in which a stream of well identified electrons are responsible for the 'flow' of charge. When the total net flow of electrons is added up, you can say that a certain charge has passed and we use the Coulomb as our unit. I reckon that's enough.

Conventional Current is a useful, intermediate, level at which to discuss a huge range of situations. You only need to 'change gear' and discuss mechanism (such as the "hole" conduction, you mentioned) as and when it becomes relevant. After all, it doesn't help an Engineer who's designing a turbine to get down to the level of individual gas molecules at the same time as calculating the best blade profile. Bulk properties are very often best dealt with at t heir own level.

If not, then why not look at the fundamental particles of which the actual electrons are made?
Ohm's law with Quarks could be a bit of a headache.

 

[Ravalanche]

I always try to think of Current in the abstract / bulk sense and not to consider the actual mechanism at a lower level. This is because current can actually take different forms. At the end of the day, in electric circuits, it has to involve electrons moving into the end of wires at one end and leaving the other end. But one couldn't rule out a circuit in which part of the current path consisted only of positive ions flowing through some exotic fluid - or even positrons flowing through a vacuum or a tube of 'ionised' anti hydrogen. Who know the future of electrical circuitry?

In metals, there are many electrons (some people call them Valence electrons and there is at least one per atom) that are very mobile within the material. They are in constant random thermal motion, at normal temperatures, with a very high RMS velocity. When a current 'flows' there will be a net movement of all these electrons, at a 'drift speed' of only a mm or so per second. So it is not a helpful model to think of a 'stream of electrons' moving through the metal, any more than it is useful to think of a few tens of thousand immigrants flowing into a country when the airports, roads and railways are carrying possibly millions of travellers in and out every year. The 'net' migration figure is only a small part of what's really going on and wouldn't help you plan a transport system. So I don't like the 'water' analogy and nor do I really think much of the 'bicycle chain' analogy, in which a stream of well identified electrons are responsible for the 'flow' of charge. When the total net flow of electrons is added up, you can say that a certain charge has passed and we use the Coulomb as our unit. I reckon that's enough.

Conventional Current is a useful, intermediate, level at which to discuss a huge range of situations. You only need to 'change gear' and discuss mechanism (such as the "hole" conduction, you mentioned) as and when it becomes relevant. After all, it doesn't help an Engineer who's designing a turbine to get down to the level of individual gas molecules at the same time as calculating the best blade profile. Bulk properties are very often best dealt with at t heir own level.

If not, then why not look at the fundamental particles of which the actual electrons are made?
Ohm's law with Quarks could be a bit of a headache.

i see, i used to think of electrons as sort of like a chain with beads but closely packed,so when one ''vibrates'', the others will obtain its energy and thus transfering it from one another. still, thanks a lot for the info, that helped alot.

 

[sophiecentaur]

i see, i used to think of electrons as sort of like a chain with beads but closely packed,so when one ''vibrates'', the others will obtain its energy and thus transfering it from one another. still, thanks a lot for the info, that helped alot.

There are all sorts of models. Some of them take you further than others. I think that the 'school' model is potentially counter productive. So many 'Science' teachers know so little about this but feel duty bound to promote this model.

 

[antistrophy]

There are all sorts of models. Some of them take you further than others. I think that the 'school' model is potentially counter productive. So many 'Science' teachers know so little about this but feel duty bound to promote this model.

What model would you suggest for relating voltage and current to things already familiar to a high school student?

 

[Ravalanche]

meanwhile, can a single coulomb of charge be extremely high in electrical energy ( potential given a single point ) while the velocity of it is low ( current? since current is charge per second, its sort of like speed?). is this possible? high voltage but low current. Its hard to imagine though. because if it possesses high electrical energy, wouldn't that also mean it has high kinetic energy so that it moves fast too?

 

[sophiecentaur]

Rate of charge transfer is not the same as speed. The units are not the same and the analogy is not good.
This will rankle with some readers but I recommend using the maths as your model as soon as you can. Semi-mechanical analogies are no more valid. They are worse, in fact.

 

[Ravalanche]

analogies gives u a better idea, but it does not fully describe the real situation right?

 

[NascentOxygen]

hi everyone, i would like to ask some quick questions that i find confusing.

You need not be confused between the terms "electromotive force", "potential difference", and "voltage" -- these terms are synonymous. All are measured in volts. The term "potential difference" is most descriptive, though "voltage" is good shorthand and is understood by everyone to mean "voltage difference". Where just "voltage" is spoken of, there exists an accepted reference point conventionally considered zero volts (or ground).

i don't really understand what is the definition of voltage.

That's an easy one: voltage is that which is measured in volts.

You will wear yourself out trying to imagine a distinction between the terms EMF, potential difference, and voltage. There is no difference.

 

[cabraham]

Actually, emf has a distinct meaning vs. "voltage drop" or "pd". Consider a 12V battery powering an 11 ohm lamp, with a 1 ohm cable. The total resistance is 12 ohms, & the current is 1 amp.

Tee 12V across the battery terminals is an "emf" because charges transiting inside the battery are gaining energy.

But, the 1 volt across the cable is not an emf, but rather a drop. Voltage drop & emf are not the same. In the cable, charges are losing energy.

They have the same units, i.e. volts. A drop is energy per charge lost. An emf is energy per charge gained.

But both the voltage drop & the emf can be called a "potential difference". PD is a broad term, whereas "drop" & "emf" are specific.

I hope this helps.

Claude

 

[NascentOxygen]

Actually, emf has a distinct meaning vs. "voltage drop" or "pd".

It might in your mind, but that's your interpretation.

But, the 1 volt across the cable is not an emf, but rather a drop.

Try putting your tongue across it. Yup, that's a potential difference.

Voltage drop & emf are not the same.

I didn't mention voltage drop, though it's really nothing more than "voltage" with the substitution of "drop" for the negative sign. Nothing new there. It's still a potential difference.

 

[cabraham]

It might in your mind, but that's your interpretation.

Try putting your tongue across it. Yup, that's a potential difference.

I didn't mention voltage drop, though it's really nothing more than "voltage" with the substitution of "drop" for the negative sign. Nothing new there. It's still a potential difference.

I already stated that an emf & a voltage drop are both a potential difference, pd. As far as the tongue goes, it is a pd, but NOT an emf. The emf is the energy gained by charges inside the battery. You're not listening to what I'm saying.

Again for the record, a PD is a very broad term. The emf produced by the battery is a PD. The voltage drop in the cable is a PD as well. PD is the broad term.

Voltage drop is a PD incurred by charges losing energy, such as in the cable resistance. EMF is a PD incurred by charges gaining energy as in the redux action in the battery.

Voltage drops & emf are both a type of PD. But emf is not the same as a drop. That is what I wish to clarify.

One more point. If the battery is being recharged, then the 12V across its terminals are not an emf. The recharger is outputting the emf, & the battery PD is a drop. Just thought it deserves mention. Comments/questions welcome.

Claude

 

[sophiecentaur]

analogies gives u a better idea, but it does not fully describe the real situation right?

A GOOD analogy may give you a better idea but there are many possible analogies that are not worth following. What's wrong with good old maths as the analogy? If one says that maths is just too hard and not worth bothering with then perhaps the analogy that one finds acceptable is actually not complex enough to be a worthwhile model.

 

[NascentOxygen]

I already stated that an emf & a voltage drop are both a potential difference, pd.

That's all the OP needs to know. They are all voltages, anything else is just playing with semantics. It will be clear in student exercises what the questioner has in mind, e.g., a generator has a no-load terminal voltage of ...", or a "relay produces a back EMF of ...", and so on.

The emf is the energy gained by charges inside the battery.

There is nothing special about batteries. For historical reasons the term EMF is firmly (and quaintly) entrenched in engineering associated with vintage technology such as electrochemistry, motors and generators, transformers, relays and solenoids.

Voltage drop is a PD incurred by charges losing energy, such as in the cable resistance. EMF is a PD incurred by charges gaining energy as in the redux action in the battery.

I regret not being au fait with photovoltaic laboratories, but do researchers in solar cells speak of their creations generating an "EMF" in sunlight?

One more point. If the battery is being recharged, then the 12V across its terminals are not an emf. The recharger is outputting the emf, & the battery PD is a drop. Just thought it deserves mention.

So if we have two car batteries connected by a resistor, you want to say at the terminals of one you can measure an EMF and the terminals of the other a PD? Really? But you can't identify which is the EMF and which is the PD without the use of a meter?

So you want the converse of a voltage drop to be an EMF? What do you have against "voltage rise"? Much more self-explanatory and more sensible all around.

 

[sophiecentaur]

So you want the converse of a voltage drop to be an EMF? What do you have against "voltage rise"? Much more self-explanatory and more sensible all around.

What's wrong with Potential Difference? The sign of the difference tells you 'which way is up'. If you need an 'implied sign' by the word you use -i.e. drop or rise then one day it will confuse you when you need the right answer for a complicated situation.

We grew out of 'push and pull' ages ago when dealing numerically with forces so why not let the maths notation do the job for you when dealing with electrical potential?

 

[cabraham]

That's all the OP needs to know. They are all voltages, anything else is just playing with semantics. It will be clear in student exercises what the questioner has in mind, e.g., a generator has a no-load terminal voltage of ...", or a "relay produces a back EMF of ...", and so on.

There is nothing special about batteries. For historical reasons the term EMF is firmly (and quaintly) entrenched in engineering associated with vintage technology such as electrochemistry, motors and generators, transformers, relays and solenoids.

I regret not being au fait with photovoltaic laboratories, but do researchers in solar cells speak of their creations generating an "EMF" in sunlight?

So if we have two car batteries connected by a resistor, you want to say at the terminals of one you can measure an EMF and the terminals of the other a PD? Really? But you can't identify which is the EMF and which is the PD without the use of a meter?

So you want the converse of a voltage drop to be an EMF? What do you have against "voltage rise"? Much more self-explanatory and more sensible all around.

So just what is your point? You clearly are not conveying anything of use, just arguing. I've explained my case based on years of studying peer-reviewed texts & reference books. As far as 2 batteries connected via a resistor, the one with the higher terminal voltage & lower resistance will supply charge to the other. The sourcing battery terminal PD is an emf.

I have nothing against the phrase "voltage rise". Nothing at all. I was merely conveying the difference. A PD can be a rise or a drop. But we must remember that sometimes energy is delivered by a device vs. absorbed. It is a difference worth knowing. An emf is a voltage rise.

The OP asked & I answered. Now you bring in data not asked by the OP, then give me the 3rd degree. Good day.

Claude

 

[Delta2]

I think electromotive force is not just a voltage rise (or an increase in potential) but refers to the force that creates this voltage rise.

The point here is that inside the source the charges are flowing opposite to the direction of the E-field therefore there has to be some force opposite to the force of the E-field that is the force that gives them the energy via the work it does. (like we give potential energy to a mass when we rise it against the force of gravity)

For example inside an AC generator with moving coil this force is the lorentz force F=(Bxu)q. In a battery the potential rise is created via some chemical reactions.

 

[sophiecentaur]

This is all getting s bit futile and people are taking offense. Why not just relate it all to a simple mathematical Sign, which tells you whether charges gain or lose energy? Job done.

 

[sankalpmittal]

This is all getting s bit futile and people are taking offense. Why not just relate it all to a simple mathematical Sign, which tells you whether charges gain or lose energy? Job done.

sophiecentaur , you're correct. I don't know why people are taking offense. Let me give you my views also.
Look at my post #2. There is an unintentional mistake though. Firstly its open circuit not closed. Secondly PD is between point A and B(say) , not infinity to any point. That's what make potential difference "different" from electric potential.

Suppose you have an open circuit. The total potential difference exists between the two terminals of battery is what is electromotive force. Its sum total of all the potential differences or total P.D. For more info , look at my post #2.

There are two resistances involved in E.M.F : the internal resistance and external resistance.
Let internal resistance = r
external resistance=R
E.M.F : ε
Then
ε = I(R+r)
ε = V + Ir ( where V is Potential difference and Ir is the work done in electrolysis of battery)
ε = Total Potential difference + work done in electrolysis of battery per unit charge

However in case of parallel circuits where V is constant and in case of series circuits where V=V₁+V₂+V_n we consider only useful work done in moving charge (electrons) linearly. We neglect the friction of wire or energy manifested in overcoming resistance. This is because we want the system to behave ohmic.

Some people might say - "Potential difference is constant in parallel circuit because Work done = Force x Displacement. Displacement remains same. " This is wrong ! It has nothing to do with vector displacement as in classical mechanics.

Voltage is just defined as the difference in electric potential energies of charges at any two points in a circuit. It is a common term for electromotive force , potential difference and electric potential as well.

 

[Ravalanche]

so again, if the electric potential at a SINGLE POINT is 9 J/C, its correct to say the voltage is 9V?

 

[sophiecentaur]

so again, if the electric potential at a SINGLE POINT is 9 J/C, its correct to say the voltage is 9V?

"correct"?
Bearing in mind that a voltmeter has two leads on it, you would still have to specify where the other lead should be connected. If no one is in any doubt about it, in the particular situation, then feel free to use the word Voltage.

But, when you make a bald statement that the Potential is 9J/C, you are in the same situation. That 9J would need to refer to the energy when bringing the Coulomb in from Infinity - not very practical. You would, in practice, be referencing to a 'local' ground / frame /chassis /water pipe. To avoid confusion, you would start off with a note about where the reference 'Zero Potential' was.

If you are dealing with OP amps, for instance, you would avoid giving an 'absolute' potential in any of the circuit description because the circuit is, essential a difference amplifier and would /should be designed to be independent of how it's actually powered.

 

[Ravalanche]

why must the potential need two points to be measured? a body can possesses a certain value of kinetic energy given any particular time in motion right? I don't understand about the infinity part. Sorry if I have a hard time understanding, I'm still in high school.

 

[sophiecentaur]

why must the potential need two points to be measured? a body can possesses a certain value of kinetic energy given any particular time in motion right? I don't understand about the infinity part. Sorry if I have a hard time understanding, I'm still in high school.

OK - back to you then. How would you define potential?


Potential basically represents Work Done. Work is defined as Force times Distance, so you have to move from place to place in order to do work. Without two points, you can't have a distance - so you have to use two points. The reason that people choose to use 'infinity' as one of the points is that it is the same, wherever you happen top be. The other alternative would have to be a certain spot on the Earth - say a platinum cross hair in the middle of Trafalgar Square.
One huge advantage of using Infinity for 'the other meter connection' is that the potential emerges from integrating the force over the distance. The potential is proportional to 1/R for large distances so you would have !/R1 - 1/R2 as the work done from point 1 to point 2. Having point 1 at infinity 1/∞ is zero, so you only have one term to calculate.

Actually, your point about Kinetic Energy is not strictly valid. The KE of a moving body relates to the damage it could do when it hits something. If that something happens to be going along beside it then the KE (in that particular reference frame) would be very low. If we referred the velocity to a planet going fast in the opposite direction then the KE, in the Planet's reference frame) would be enormous. So even KE is relative but, in this case it's not a relative position but a relative velocity that counts.

 

[NascentOxygen]

What's wrong with Potential Difference?

It's fine in writing, but way too cumbersome for lab class usage, all the time having to insert the +/- sign and make it clear which point it is referenced to. The "voltage drop" term is indispensable for use in oral presentations and quickly explaining circuit operation at the lab bench.

 

[NascentOxygen]

So just what is your point?

That there is not the universal definition of EMF that some would have OP believe.

As far as 2 batteries connected via a resistor, the one with the higher terminal voltage & lower resistance will supply charge to the other. The sourcing battery terminal PD is an emf.

And the same applies to a capacitor? When it is being charged, it exhibits a PD, but when it is losing charge this is attributable to an EMF?

The OP asked & I answered.

As did I.

Let's see what wikipedia says about relying on there being a universal definition for EMF:

However, there is not complete unanimity upon this usage. As Sydney Ross says, in excusing himself for avoiding the term emf:

We have refrained from using the term 'electromotive force' or 'e.m.f.' for short; for there is no consistency between different authors in the meaning of the term. To some authors it is synonymous with 'voltage.' To others it means the open-circuit voltage of a battery. To a third group of authors it means the open-circuit voltage of any two-terminal device. This use is met most often in connection with Thevenin's theorem in circuit theory. To a fourth group it means the work accounted for by agencies other than differences of the (not measurable) Galvani potentials. Such authors equate the current–resistance product of a circuit branch to the sum of voltage plus e.m.f. A fifth group extends this use to field theory. The authors of this group equate the product of current density and resistivity to the sum of electric-field strength plus an e.m.f. gradient. A sixth group applies the term to electromagnetic induction. These authors define e.m.f. as the spatial line integral of the electric-field strength taken over a complete loop. To them the term 'counter e.m.f.' means something.

It is common in some fields, such as circuit theory, to refer to the voltage created by the emf as the emf. Some authors do not distinguish between the emf and the voltage it creates. Some use emf to refer to the open-circuit voltage and voltage to the potential difference when current is drawn. Here is a quotation describing emf as an open-circuit voltage difference:

Doesn't leave much room to argue, does it? Believe in a universal definition of EMF at your peril.

 

[sophiecentaur]

Spoken explanations may be different but one needs to be careful to make sure some ephemoral remark is not misconstrued. 'Sloppy' speech is fine in the right context, of course. We all use it.