Factors affecting drift velocity?

[LotusTK]

Homework Statement

I am having a look at drift velocity and i know essentially what it is, and i am now noting down the factors that effect the drift velocity of the charge carriers as i think its a useful thing to know.

So, so far i have that the number of charge carriers will effect the velocity. The more charge carriers you have, the less quickly they must move in order to deliver a current.

If another material is to deliver the same current, and it has less charge carriers per m^3, then those fewer charge carriers will have to move more quickly in order to deliver the charge.

I have also noted down that increasing the temperature in a conductor will increase the vibrations of the ions in the material, creating more collisions for the electrons or charge carriers. Which will increase the resistance and decrease the current flowing through that material

Also, if the temperature is increased in a semi-conductor (which will have fewer free charge carriers), the atoms in that semi conductor will be given energy, and this energy will liberate more electrons and release them into the path of flow of the current, so this will then decrease the resistance, and increase the current. (or if the current were to remain the same, the drift velocity will decrease)

I think the above statements are correct??

I do not quite know how the charge of each carrier and the cross sectional area will effect the drift velocity though.

I think i am correct in saying that an increased current will result in a higher drift velocity? But then looking at the formula I=nVQA makes me think otherwise...

Homework Equations

I=nVQA
Current = #of charge carriers x Drift Velocity x Charge per carrier x Cross sectional Area

The Attempt at a Solution

 

[mfb]

I think the above statements are correct??

Correct.

I think i am correct in saying that an increased current will result in a higher drift velocity? But then looking at the formula I=nVQA makes me think otherwise...

If you increase I, what has to happen to the velocity v if the other parameters stay constant?

If you increase the charge per charge carrier or the cross-section of the conductor, what else can you change for example if everything else stays constant?

 

[LotusTK]

Mathematically, looking at the formula, as current increases, velocity will have to decrease if all the other variables remain constant.

Then rearranging to get v = I/nAQ , could it be said that velocity is inversely proportional to number of charge carriers,cross sectional area and charge per unit carrier? Therefore an increase in any of these 3 variables means that the velocity will decrease? (So if the area decreases, velocity increases, or if the charge per unit carrier decreases, velocity increases)

Basically anything on the denominator of the equation v=i/nAQ is inversely proportional to velocity.

 

[mfb]

Yes.

To avoid ambiguity, I would write that as v = I/(nAQ)

 

[LotusTK]

Cheers.

Would it be possible for you to give me an idea or a hint as to why they change the velocity? Now that i know HOW they effect velocity, i can't quite get my head around why they change the velocity.

 

[mfb]

You rarely have a situation like "I keep current constant and increase the number of charge carriers", so I don't know how useful it is to analyze this.

Current is the charge per time that flows through the resistor. If you keep current constant but increase the density of charge carriers you need a slower velocity to get the same amount of charges per time. The same applies to the other factors.

 

[LotusTK]

In the past papers for my exam board i often see types of questions where they change something and ask how this has an implication on something else, so i find it useful to know these kind of things.

It is also really helpful for me to know as it allows me paint an image in my head of how the different concepts in physics.

Thanks for all your replies :)