Voltage Drop: Source A to B in a Circuit?

[sameeralord]

Is voltage the potential energy difference between source A and B in a circuit? If so in absense of resistance and the presence of a 3V battery does point A have 3V to begin with and at point B there is 0 volts. Is all potential energy converted to kinetic energy when moving from A to B? A is origin and B is the terminal end of the circuit by the way. Is that voltage drop?

If what I have said is not correct and voltage doesn't drop like this does a circuit with no resistor and negligble resistance from the wires have 3V at point A and also 3V at point B?

Let's say that I have a circuit like this (made it linear for ease)

3V battery--point A----------------1ohm resistor-------------pointB

What is the voltage of the resistor? It is 3 right. Does that when current passes through the resistor it loses 3V. If it loses all the voltage how does it move to point B?

Thanks

Edit: I think I'm assuming when they say voltage drops across the 1 ohm resistor is 3, the 1 ohm resistor uses all 3V. When they say voltage drop in this case are they actually referring to voltage drop from A to B. The actual amount of energy lost due to the resistor is not really 3V. It is something less. The voltage drop across the whole thing is 3 V. Is that right?

 

[Dale]

Let's make this a little clearer:

┌─────┐
a     c
█     █
█     █
█     █
b     d
└─────┘

Points a and b are the terminals of the battery and c and d are the terminals of the resistor. Between a and c and between b and d is a very conductive wire. If the voltage of the battery is exactly 3 V then a-b = 3 V. Now, there will be some voltage drop across each of the wires, but since they are very good conductors let's say that it is 0.0001 V. Then a-c = d-b = 0.0001 V. That means that the drop across the resistor is just less than 3 V: c-d = 2.9998 V. By far, the majority of the voltage drop is across the resistor and, if your measuring device is only able to measure millivolts then your device will read no drop across the wires and 3 V across the resisitor. With a sufficiently good conductor for your wire it is sufficient to ignore a-c and b-d and treat all points in the wires as being at the same voltage.

 

[sameeralord]

Let's make this a little clearer:

┌─────┐
a     c
█     █
█     █
█     █
b     d
└─────┘

Points a and b are the terminals of the battery and c and d are the terminals of the resistor. Between a and c and between b and d is a very conductive wire. If the voltage of the battery is exactly 3 V then a-b = 3 V. Now, there will be some voltage drop across each of the wires, but since they are very good conductors let's say that it is 0.0001 V. Then a-c = d-b = 0.0001 V. That means that the drop across the resistor is just less than 3 V: c-d = 2.9998 V. By far, the majority of the voltage drop is across the resistor and, if your measuring device is only able to measure millivolts then your device will read no drop across the wires and 3 V across the resisitor. With a sufficiently good conductor for your wire it is sufficient to ignore a-c and b-d and treat all points in the wires as being at the same voltage.

Hey thanks but I still have some questions. Why should resitor voltage+wire resistor add up to 3. Is it because a-b = 3 V and b=0. If there is no resistor does all the voltage drop across the wire to make it 0. So in this case does any resistor (with any amount of resistance) have the same voltage drop?

If voltage is P.E is it converted into K.E when going from A to B. Shouldn't this mean a voltage drop as well. Thanks!

 

[fluidistic]

Voltage is not electric potential energy, but electric potential difference.
More precisely, $$\vec E = - \nabla V$$, hence $$V=-\int_a^b \vec E d \vec l$$. The units of V are volts, while energy is always measured in joules (in the SI).

 

[jtbell]

When you go completely around a circuit and return to your starting point, the total potential difference must be zero. In DaleSpam's example, let point b be the negative terminal of the battery. Start there and go clockwise. Then the potential differences are +3.0000 V (battery) - 0.0001 V (first wire) - 2.9998 V (resistor) - 0.0001 V (second wire) = 0.0000 V (total).

The total potential difference can also be considered as (potential at final point) - (potential at starting point) = (potential at point b) - (potential at point b) = 0.

 

[fluidistic]

When you go completely around a circuit and return to your starting point, the total potential difference must be zero. In DaleSpam's example, let point b be the negative terminal of the battery. Start there and go clockwise. Then the potential differences are +3.0000 V (battery) - 0.0001 V (first wire) - 2.9998 V (resistor) - 0.0001 V (second wire) = 0.0000 V (total).

The total potential difference can also be considered as (potential at final point) - (potential at starting point) = (potential at point b) - (potential at point b) = 0.

I agree with this, and looking at $$V=-\int_a^b \vec E d \vec l$$, it's clear that if $$a=b$$, the $$V$$ is worth $$0$$.

 

[sameeralord]

Ok thanks for the answers guys. While I'm thinking about what you guys are saying I have another question. What is power dissipiated?

If the circuit has no resistor why is power disspiated so high and through what does the voltage drop(there is no resistor). If all energy is dissipiated as heat how can there be a current flow. What I mean is if dissipiation is turning into heat how can there be enough energy for current flow? Thanks!

 

[jtbell]

Batteries have their own resistance (look in your textbook or Google for "internal resistance"). This is usually small enough that we can often ignore it when we analyze a circuit, but when it's the largest resistance in a circuit...

Now consider $P = V^2/R$ and what happens when R is small while keeping V constant!

 

[Dale]

Hey thanks but I still have some questions. Why should resitor voltage+wire resistor add up to 3.

jtbell's answer in post 5 is good. The only thing I have to add is that this rule is called Kirchoff's Voltage Law.

If there is no resistor does all the voltage drop across the wire to make it 0. So in this case does any resistor (with any amount of resistance) have the same voltage drop?

Yes, with the additional caveat that jtbell mentioned about a real battery's internal resistance.

If voltage is P.E is it converted into K.E when going from A to B. Shouldn't this mean a voltage drop as well. Thanks!

In electric circuits there is never an appreciable amount of KE in the current. In most circuits the electron drift velocity is usually quite a bit less than 1 mm/s. With the low velocity and the low mass of the electrons the KE is negligible.

The only exception that I know of is vacuum tubes.

 

[sophiecentaur]

Current flow is not energy!
The Voltage is, effectively, the energy. That is what gets 'used up' as you go from the positive terminal 'down' to the negative terminal. The same charge flows all the way round because there are immensely strong electric forces which ensure that every electron which moves form one atom to another will displace another one, further along in the circuit, so you cannot get a build up. Even in a battery or capacitor, you still get the same number of charges leaving or entering, so the current is the same all the way round. Like a bicycle chain, carrying energy from foot to wheel.

 

[fluidistic]

The Voltage is, effectively, the energy.

Can someone confirm this? This would contradict the post #4. I'm starting to doubt.

 

[sophiecentaur]

One Volt is One Joule per Coulomb.
I am sure Wikkers will confirm that.
There's yer energy. :-)

 

[YellowTaxi]

The same charge flows all the way round because there are immensely strong electric forces which ensure that every electron which moves form one atom to another will displace another one, further along in the circuit, so you cannot get a build up. Even in a battery or capacitor, you still get the same number of charges leaving or entering, so the current is the same all the way round. Like a bicycle chain, carrying energy from foot to wheel.

If you could see what was actually happening inside the wires that would look like train carriges taking up the slack in their buffers ats they bump into each other. So you should in theory always have a flow of electricity after the power supply is turned off. Because the 'wave' can't move faster than light, it's not instantaneous. So I'd say there is always a build up, but you can't see it.

 

[YellowTaxi]

Can someone confirm this? This would contradict the post #4. I'm starting to doubt.

electricity is just the kinetic motion of electrons isn't it ?

 

[Feldoh]

http://ocw.mit.edu/NR/rdonlyres/Electrical-Engineering-and-Computer-Science/6-002Spring-2007/VideoLectures/6002_l1.pdf

See slides 6-18, it might help clear some things up.

 

[vimricu]

I accept with information: In DaleSpam's example, let point b be the negative terminal of the battery. Start there and go clockwise. Then the potential differences are +3.0000 V (battery) - 0.0001 V (first wire) - 2.9998 V (resistor) - 0.0001 V (second wire) = 0.0000 V (total).
_______________________
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[sameeralord]

Thanks guys but I'm still at square one. I don't think I expressed my question properly. I understand K.. law.

Why do different resistances get different portions of the voltage. For example in 1--4 do have a voltage you need to have more electrons at 4 than 1. If the current (rate) flowing through each resistor is the same how can there be different electron differences. Basically why do different resistances have different voltage drops?

 

[Integral]

Voltage is not about the number of electrons. It is about the energy available to move electrons. Outside of the battery electrons are not stored, gained, or lost anywhere in the circuit so the number of electrons passing any point in a time interval must be constant. In other words current is constant in a series circuit.

Now do you know Ohms Law?

E=IR

This gives the voltage measured across a resistor given the current through it.

In a series circuit the current is constant and the sum of the voltage drops is equal to the source voltage.

 

[sophiecentaur]

If you could see what was actually happening inside the wires that would look like train carriges taking up the slack in their buffers ats they bump into each other. So you should in theory always have a flow of electricity after the power supply is turned off. Because the 'wave' can't move faster than light, it's not instantaneous. So I'd say there is always a build up, but you can't see it.

There may an initial build up of charge in some parts of a circuit - as when a capacitor charges up - but this cannot continue. We were discussing 'current' electricity - in which a steady state has been reached in the flow through resistance only when there is no reactive component to store energy.
If you want to show why there can't be a constant build up of charge then go and calculate the force involved when a charge of one Coulomb (that could be just 1/10Amp for 10 seconds)is brought 1m away from another 1 Coulomb. The analogy to a bicycle chain is still there; the chain stretches, initially, when you start pedalling and takes up the slack. This is equivalent to a small amount of polarisation in parts of the circuit.

And NO: 'Electricity' is not the Kinetic Motion of Electrons. They only drift through wires at a few mm per second! 'Electricity' is not really a Scientifically defined term - it just covers the general subject of Electrical Energy, Forces, Current etc.

 

[sophiecentaur]

Thanks guys but I'm still at square one. I don't think I expressed my question properly. I understand K.. law.


Why do different resistances get different portions of the voltage. For example in 1--4 do have a voltage you need to have more electrons at 4 than 1. If the current (rate) flowing through each resistor is the same how can there be different electron differences. Basically why do different resistances have different voltage drops?

They get different shares of the Voltage because they need different amounts of energy to shift charge through them. Once the situation has settled down (after 1ns or so) the KII situation will apply. The battery supplies just enough power to drive current through them all and each one dissipates just enough to balance the situation. If you short one of the resistors out, then the PD is shared out amongst the rest, after another ns and KII rules again.

 

[sophiecentaur]

I know the water analogy can be full of pitfalls but consider a a length of pipe with sections of different thicknesses and stuffed with various different fillings carrying a fast flow of water. You would get different pressure drops across the thin and fat sections and the overall pressure drop would be the sum of these pressure drops. The pressure of water coming out of the end would be the input pressure minus the sum of the pressure drops. Moreover, if you open the nozzle wider and increase the flow, the output pressure would drop more and, if you shut off the nozzle, the pressure would go up to the value of the supply.

 

[sameeralord]

When electrons go through a resistor they lose energy right. When they lose energy they would stop moving right? So how does same amount of electrons travel through each resistor if there are 3 resistors in a circuit?

Ok this is my final understanding. Tell me if this is write.

Wait is this what happens. When there are 3 resistors in a circuit. The electrons flowing for a second is the same but to maintain this they would lose different amount of energies depending on the resistance of the resistor. So example.

res 1-100 ohm
res 2- 200 ohm
res 3-300 ohm

After a minute as sophie said the electrons would come up with a constant flow rate that would allow electrons to flow throughout the circuit(let's say it is 3 electrons/s). Since resistor 1 has less resistance it loses only a little amount of energy compared to other 3 to maintain this flow(3 electrons per second).

About the kinetic energy. Since electrons are moving very slowly all the potential energy can not be converted into kinetic. So voltage is disspiated as heat instea.

Is this right!

 

[sophiecentaur]

That seems to be along the right lines.
The KE thing.
Just think of the vanishingly small mass that the conduction electrons constitute and then think about a mean speed of a few mm/s. (Their RMS speed due to thermal energy is much, much faster than that.) That represents a really really small amount of KE - so don't include it in any of your reasoning any more than you would include the mass of the chain when discussing the power transfer from a motorbike engine to the wheels.

The resistor heats up as a result of the 'forces' pushing the electrons through. They interact with the resistor material and transfer energy to it. If you replace a resistor with a motor, the same sort of interaction produces movement energy.

 

[jtbell]

When electrons go through a resistor they lose energy right. When they lose energy they would stop moving right?

No, because they lose potential energy, not kinetic energy (on the average).

Think of a block sliding down an inclined plane, whose surface produces just the right amount of friction so that the block slides at constant speed. Its kinetic energy remains constant, but it's losing gravitational potential energy as it slides downhill. That energy appears as thermal energy in the block and incline: they become warmer.

Similarly, as current flows through a resistor, the electrons move at constant speed (on the average) but lose electric potential energy. That energy appears as thermal energy in the resistor and its surroundings: they become warmer.

 

[YellowTaxi]

No, because they lose potential energy, not kinetic energy (on the average).

Think of a block sliding down an inclined plane, whose surface produces just the right amount of friction so that the block slides at constant speed. Its kinetic energy remains constant, but it's losing gravitational potential energy as it slides downhill. That energy appears as thermal energy in the block and incline: they become warmer.

Similarly, as current flows through a resistor, the electrons move at constant speed (on the average) but lose electric potential energy. That energy appears as thermal energy in the resistor and its surroundings: they become warmer.

so that's the explicit reason why the voltage drops as you go round the circuit with a voltmeter, but if you put an ammeter in there it measures the same value all the way around ? Voltmeter measures potential (the 'height' above ground). The ammeter is measuring the kinetic of the electron flow? or have i got that wrong ?

 

[Astronuc]

so that's the explicit reason why the voltage drops as you go round the circuit with a voltmeter, but if you put an ammeter in there it measures the same value all the way around ? Voltmeter measures potential (the 'height' above ground). The ammeter is measuring the kinetic of the electron flow? or have i got that wrong ?

An ammeter measures current, or flow of charge. That has to be continuous, otherwise charge would decrease or increase locally.

The rate of flow depends on the potential difference and the resistance.

It's a bit like measuring the flow of water (e.g. down a sluice or incline) or flow of heat.

 

[YellowTaxi]

'Electricity' is not the Kinetic Motion of Electrons. They only drift through wires at a few mm per second! 'Electricity' is not really a Scientifically defined term - it just covers the general subject of Electrical Energy, Forces, Current etc.

the speed may be very slow , but generally there's a lot of them to make say one Amp.

 

[YellowTaxi]

An ammeter measures current, or flow of charge. That has to be continuous, otherwise charge would decrease or increase locally.

The rate of flow depends on the potential difference and the resistance.

It's a bit like measuring the flow of water (e.g. down a sluice or incline) or flow of heat.

yes exactly, so current is just a measure of the kinetic energy of the electrons (?)

 

[Dale]

yes exactly, so current is just a measure of the kinetic energy of the electrons (?)

NO. Current is NOT a measure of the kinetic energy of the electrons. I mentioned this explicitly in post 9. The kinetic energy of the electrons is completely negligible for most circuits.

 

[Naty1]

Bell's post #24 is a nice analogy.

Current (i) is a measure of the flow of electrons past a measurement point; it measures the rate of flow of charge. i = dq/dt. Voltage (difference) measures the potential pushing the electrons along.

The flow of charge (movement of electrons) through a conductor is often compared with the flow of water thru a pipe; water flows thru a pipe because of a difference in presssure while electric charge flows through a conductor to to a difference in electrical pressure, an old name for voltage (electric potential)difference. With an increase in water pressure more water flows; with an increase in electric pressure(potential) more electrons flow. You can think of the rate of flow of water molecules as analogous to the rate of flow of electrons.

With water, the more resistance, the less the flow of water, say due to a smaller pipe; with electricity, the more the resistance the less the flow of electrons, perhaps due to a smaller conductor, perhaps due to a material with higher resistance (fewer free electrons to move).