# Homework Help: Drift Velocity & Current

1. Apr 3, 2015

### BoanviaFx

1. The problem statement, all variables and given/known data

Can someone confirm if I answered correctly? Thanks

Ai) Define the term drift velocity with reference to a current in a circuit.
ii) Derive an expression to describe the current passing through a metallic conductor of cross-sectional area A having n charge carriers per unit volume.

Bi) Two cylindrical conductors of the same material are connected together as shown in figure( )
Current passes through the first conductor which has a cross-sectional radius r1 and an associated drift velocity of v1. The second conductor has a cross-sectional radius of r2. Express the drift velocity, v2, of the electrons in second material in terms of the other quantities.

ii) The conductors are made of iron which has 1028 charge per unit volume. The conductors carry a current of 1A. Given that the radii of the first and second cylinders are given by 0.5mm and 3.0mm respectively, determine the drift velocity within each conductor.

2. Relevant equations

3. The attempt at a solution

Ai) The drift velocity is the velocity of the electrons moving across a conductor, and colliding with nearby particles. This is when a p.d is applied and the electrons move from a lower potential to a higher potential thus creating an electric current.

ii) Solution:

I=Q/t Formula for Current.
Q=nAle Formula for Charge.

v = l/t Formula for drift velocity.
t = l/v

Substituting:
I = (nAle)/(l/v)

I = nAve New Expression

Bi) Since Current is the same in both conductors:

I1=I2
n1A1v1e1=n2A2v2e2

so A1v1=A2v2

Therefore v2 = A1v1/A2

Area would be substituted with πr2

ii)
A1 = 7.85x10-7
A2 = 2.82x10-5
e = 1.6x10-19

Conductor 1 Drift velocity
v = I/nAe
v = 1/(1028*7.85x10-7*1.6x10-19)
v = 7.96x10-4

Conductor 2 Drift velocity
v = I/nAe
v = 1/(1028*2.82x10-5*1.6x10-19)
v = 2.21x10-5

2. Apr 3, 2015

### Staff: Mentor

There are units missing in (Bii).

Is it really the velocity of the electrons?
There is a difference between the velocity and the drift velocity.

3. Apr 3, 2015

### BoanviaFx

Sorry Bi) Area: m2 Current: A Drift velocity: m/s Electronic Charge: C
As for Ai) Since the electrons move in a zig zag fashion they will have change in directions & velocity. The drift velocity would be the resultant of these motions.
I hope I have a good understanding of drift velocity, I'm assuming the rest is correct.

4. Apr 3, 2015

Right.