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drift velocity of electrons
Hi,
I am doing my resistance and length of wire coursework for GCSE. Does anyone know how to explain why resistance increases in length without going beyond the A/A* scope of GCSE? I need to refer to the voltage as the 'push' given to electrons, the current as the 'flow of electrons' and mention something about the drift velocity of electrons. I have been looking up about this and some places say that an electron doesn't slow down when it collides with a metal ion, is this true?
Would this be a good enough explanation - i.e. is it correct?
BY doubling the length of a wire you double the amount of moving electrons and metal ions. This means that the moving electrons have twice the collisions as they travel through the wire and lose twice the amount of energy they would at the shorter length of wire. This means that their average drift velocity is divided in 2. For current to be the same in both amounts of wire the average drift velocity of the electrons needs to be the same, so we have to double the 'push' given to the electrons in the longer length of wire which doubles the drift velocity. Using ohm's law we can see that at a constant current, when voltage is doubled so is resistance, so this is why resistance is in direct prortion to length.
Thanks a lot!
I am doing my resistance and length of wire coursework for GCSE. Does anyone know how to explain why resistance increases in length without going beyond the A/A* scope of GCSE? I need to refer to the voltage as the 'push' given to electrons, the current as the 'flow of electrons' and mention something about the drift velocity of electrons. I have been looking up about this and some places say that an electron doesn't slow down when it collides with a metal ion, is this true?
Would this be a good enough explanation - i.e. is it correct?
BY doubling the length of a wire you double the amount of moving electrons and metal ions. This means that the moving electrons have twice the collisions as they travel through the wire and lose twice the amount of energy they would at the shorter length of wire. This means that their average drift velocity is divided in 2. For current to be the same in both amounts of wire the average drift velocity of the electrons needs to be the same, so we have to double the 'push' given to the electrons in the longer length of wire which doubles the drift velocity. Using ohm's law we can see that at a constant current, when voltage is doubled so is resistance, so this is why resistance is in direct prortion to length.
Thanks a lot!
As far as you need to be concerned:
Resistance is caused by electrons colliding with the ions in the metal lattice.
At each collision, the electron loses it's kinetic energy to the lattice - which eventually disperses as heat (usually).
At a given current, the pushing force of "voltage" has to balance the loss of energy due to collisions. Hence if you increase the average number of collisions, you will have to increase the voltage to keep the current the same.
If you were to double the length of wire, you're doubled the distance the electrons must travel, so on average the number of collisions will double, and so the resistance will double.
The cross-sectional area relation can be understood by considering how increasing area increases electrons passing per unit time (i.e. increases current), so to keep voltage the same, the resistance must have decreased.
Hmmm I really dont think i've done a good job of describing that, it's clear in my head but I can't find a good way to describe the dependance. Perhaps try and imagine a piece of wire with electrons flowing through it, being pushed by the voltage. If you doubled the length of the wire, you've got twice the dissipitation of energy due to double the number of collisions, so you have to "push" each electron twice as hard to keep the same flow of electrons. You've doubled the voltage to keep the current the same -> resistance doubled.
Then imagine doubling the cross sectional area. You've doubled the number of electrons going passed a point, and yet dont have to "push" each electron any harder because it's average number of collisions has been unaffected by the change. So the current has doubled, but the voltage is fixed -> resistance halved.
Resistance is caused by electrons colliding with the ions in the metal lattice.
At each collision, the electron loses it's kinetic energy to the lattice - which eventually disperses as heat (usually).
At a given current, the pushing force of "voltage" has to balance the loss of energy due to collisions. Hence if you increase the average number of collisions, you will have to increase the voltage to keep the current the same.
If you were to double the length of wire, you're doubled the distance the electrons must travel, so on average the number of collisions will double, and so the resistance will double.
The cross-sectional area relation can be understood by considering how increasing area increases electrons passing per unit time (i.e. increases current), so to keep voltage the same, the resistance must have decreased.
Hmmm I really dont think i've done a good job of describing that, it's clear in my head but I can't find a good way to describe the dependance. Perhaps try and imagine a piece of wire with electrons flowing through it, being pushed by the voltage. If you doubled the length of the wire, you've got twice the dissipitation of energy due to double the number of collisions, so you have to "push" each electron twice as hard to keep the same flow of electrons. You've doubled the voltage to keep the current the same -> resistance doubled.
Then imagine doubling the cross sectional area. You've doubled the number of electrons going passed a point, and yet dont have to "push" each electron any harder because it's average number of collisions has been unaffected by the change. So the current has doubled, but the voltage is fixed -> resistance halved.
yes the current is affected by the average drift velocity. If you double the length of the wire, you have twice the number of collisions, so electrons take twice the time to get out. However, they are also travelling twice the distance....so I dont think their drift velocity is affected. I can't see why it would be. It's merely that they have to travel further. I think of it as doubling the voltage required for that current: you have to give each electron twice the amount of energy since they will have twice the number of collisions.. But then if you had a fixed voltage and doubled the length, then yes I guess the current would decrease.
I dont know, someone else have a go!
I dont know, someone else have a go!
becky789
Hi,
I am doing my resistance and length of wire coursework for GCSE. Does anyone know how to explain why resistance increases in length without going beyond the A/A* scope of GCSE? I need to refer to the voltage as the 'push' given to electrons, the current as the 'flow of electrons' and mention something about the drift velocity of electrons. I have been looking up about this and some places say that an electron doesn't slow down when it collides with a metal ion, is this true?
Would this be a good enough explanation - i.e. is it correct?
BY doubling the length of a wire you double the amount of moving electrons and metal ions. This means that the moving electrons have twice the collisions as they travel through the wire and lose twice the amount of energy they would at the shorter length of wire. This means that their average drift velocity is divided in 2. For current to be the same in both amounts of wire the average drift velocity of the electrons needs to be the same, so we have to double the 'push' given to the electrons in the longer length of wire which doubles the drift velocity. Using ohm's law we can see that at a constant current, when voltage is doubled so is resistance, so this is why resistance is in direct prortion to length.
Thanks a lot!
I am doing my resistance and length of wire coursework for GCSE. Does anyone know how to explain why resistance increases in length without going beyond the A/A* scope of GCSE? I need to refer to the voltage as the 'push' given to electrons, the current as the 'flow of electrons' and mention something about the drift velocity of electrons. I have been looking up about this and some places say that an electron doesn't slow down when it collides with a metal ion, is this true?
Would this be a good enough explanation - i.e. is it correct?
BY doubling the length of a wire you double the amount of moving electrons and metal ions. This means that the moving electrons have twice the collisions as they travel through the wire and lose twice the amount of energy they would at the shorter length of wire. This means that their average drift velocity is divided in 2. For current to be the same in both amounts of wire the average drift velocity of the electrons needs to be the same, so we have to double the 'push' given to the electrons in the longer length of wire which doubles the drift velocity. Using ohm's law we can see that at a constant current, when voltage is doubled so is resistance, so this is why resistance is in direct prortion to length.
Thanks a lot!
It is a good way to think of voltage as being a push on electrons. But it isn't very useful. A better way of looking at it is this.
Your wire is a queue, for example to Air at Alton Towers. Its the end of the day and everyone is really tired so they don't want to do much moving. the wire has a certain thickness, everywhere. Now the velocity of the people moving thru the queue is roughly equal at all points (we can't have ppl moving too fast and too slow in different places as there would be alot of bumping of ppl). Okay lets say that Air is running really fast an the limit is how fast we can get ppl on to the ride (ppl are really really lazy today). But there is a problem, the people in the queue are so lazy they don't want to move. However the engineers at Alton Towers saw it coming, so they engineered the queue to push the ppl towards the front of the queue, by changing the height (voltage) from the start of the queue to the end so they roll down hill.
The drift velocity is pretty much constant for a wire of constant thickness.
So is this more like it?
By doubling the length of the wire you double the amount of fixed atoms. This means that the electrons which flow through the wire will have twice the number of collisions as at the original legnth because they have to travel further. This means that they lose double the amount of energy and that the flow of electrons, that is the current, is halved. For the current to remain constant we therefore have to double the voltage, which is the push given to the electrons.
By doubling the length of the wire you double the amount of fixed atoms. This means that the electrons which flow through the wire will have twice the number of collisions as at the original legnth because they have to travel further. This means that they lose double the amount of energy and that the flow of electrons, that is the current, is halved. For the current to remain constant we therefore have to double the voltage, which is the push given to the electrons.
becky789
So is this more like it?
By doubling the length of the wire you double the amount of fixed atoms. This means that the electrons which flow through the wire will have twice the number of collisions as at the original legnth because they have to travel further. This means that they lose double the amount of energy and that the flow of electrons, that is the current, is halved. For the current to remain constant we therefore have to double the voltage, which is the push given to the electrons.
By doubling the length of the wire you double the amount of fixed atoms. This means that the electrons which flow through the wire will have twice the number of collisions as at the original legnth because they have to travel further. This means that they lose double the amount of energy and that the flow of electrons, that is the current, is halved. For the current to remain constant we therefore have to double the voltage, which is the push given to the electrons.
That about right for GCSE level...
Come to think of it you can probabily get away with that in ALevel.
I certainly didn't understand it any better in ALevel...
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