How much do you remember? Mini-white boards – no notes! Definition for current Definition of a coulomb Define the coulomb in base SI units Who completed the oil drop experiment? What did he/she discover the fundamental charge to be? Name the charge carriers in silver nitrate Name the charge carriers in a copper wire How fast do the charge carriers in a copper wire move?

Is there a difference between the velocity at which an electron travels through a wire and the velocity an ion travels through an electrolyte? e-

Mean Drift Velocity 15/06/2018 LO: Practice calculations of cross sectional area and volumes in cylinders. Explain the density of charge carriers in insulators, semi-conductors and conductors. Derive and use the drift velocity formula.

Experiment – Use potassium permanganate to attempt to measure the velocity charge carrier move in a circuit. Potassium permanganate crystals placed at the negative end Ammonium Hydroxide + pipette Power pack at 20V 2 needles Ruler Stop clock

The mean drift velocity, v, is the average velocity of an electron as it travels through a wire due to a potential difference (p.d). So why do electric devices work instantaneously when a switch is turned on?

Calculating Areas and Volumes Formula for calculating the cross-sectional area of a cylinder (2D slice) A = π x r2 Formula for calculating the volume of a cylinder V = A x l A l

Calculating Areas and Volumes A = π x r2 V = A x l Copper wire with a radius of 0.2mm and a length of 2.4m. Constantan wire with a diameter of 10.5μm and a length of 2.5m Steel cable with a circumference of 22cm and a length of 426.25 meters. A l

Calculating Areas and Volumes A = π x r2 V = A x l Copper wire with a radius of 2mm and a length of 2.4m. A = 3.14 x (2X10-3)2 V = 1.26 X10-5 x 2.4 V = 3.02 x 10-5 A l

Deriving an expression for drift velocity Now let’s consider a piece of conductor of cross-sectional area, A, and length, l, which contains n free electrons per unit volume, each carrying a charge, e. v A l n is known as the number density (and is the number of free electrons per unit volume)

Deriving an expression for drift velocity The volume of the wire is: V= The total number of free electrons N is: N= So total charge of free electrons Q =

Deriving an expression for drift velocity The volume of the wire is: V= A x L The total number of free electrons N is: N= n x A x L So total charge of free electrons Q = n x A x L x e-

If a p.d is applied to either end of the conductor, a current, I will flow: Substituting in for Q gives us: Notice that L/t is the equivalent of velocity, so: Where v is the mean drift velocity of the electrons

If a p.d is applied to either end of the conductor, a current, I will flow: I = Q / t Substituting in for Q gives us: I = nALe / t Notice that l/t is the equivalent of velocity, so: I = nAve Where v is the mean drift velocity of the electrons

Drift Velocity Equation I = nAve v = I / nAe I = Current (A) n = Current carrier density A = Cross-sectional area of wire v = Mean drift velocity e = Fundamental charge / Charge on 1 e- So… the drift velocity equals the current divided by the total charge of electrons in a set area.

Think about it… v = I / nAe So… the drift velocity equals the current divided by the total charge of electrons in a set area. What will the effect on drift velocity be if… The current is increased The density of charge carriers is reduced The cross sectional area of the wire is increased The wire increases in length.

Think about it… v = I / nAe So… the drift velocity equals the current divided by the total charge of electrons in a known area. What will the effect on drift velocity be if… The current is increased The density of charge carriers is reduced The cross sectional area of the wire is increased The wire increases in length (INCREASE) (DECREASE) (DECREASE) (NOTHING)

Think about it… What will the effect on drift velocity be if… The current is increased (INCREASE) Faster rate of flow of charge therefore must be quicker moving e- The density of charge carriers is reduced (DECREASE) Each charge carrier less likely to collide with another preventing the e- from slowing down

Think about it… What will the effect on drift velocity be if… The cross sectional area of the wire is increased (DECREASE) Double the area and it would be the same as putting 2 wires in parallel, you are halving the current down each (see no. 1) The wire increases in length (NOTHING) Independent of drift speed in any one section.

Complete the sheet on Drift Velocities

Draw two copper wires showing the crystal lattice like seen below Draw two copper wires showing the crystal lattice like seen below... Add one conduction electron per atom. Now show; The electron drift path of an electron under a direct current The electron drift path of an electron under no current.

Is there a difference between the velocity at which an electron travels through a wire and the velocity an ion travels through an electrolyte? e-

“Depends on” …Cross sectional area of the electrolyte – this tends to be ___________ than that of a lead / wire. …The density of charge carriers – this tends to be ________ than that of a lead / wire. …What is being electroylsed – ions with a +2 or -2 charge will be accelerated ________ by the same current.

Altering Drift Velocity Electrical devices do not require the same drift velocity at all points within the circuit. Think of a river flowing down stream, some points are faster than others. Electrical devices do however require that electrons entering a component must be equal to the electrons exiting the device – charge carriers are conserved.

Altering Drift Velocity Tungsten light bulb: Faster in thin tungsten filament Slower in the remainder of the circuit. Toaster: ___________ in the filament ____________ in the remainder of the circuit National grid Pylons ________________ in the pylon leads ________________ in the remainder of the circuit (your home)

Drift Velocity in different materials Drift velocity is partly a function of the charge carrier density. This means if we control all other factors, such as cross sectional area, we can see that the lower the density of charge carriers the faster the drift velocity. Conductors have a huge abundance of charge carriers so drift velocity is low.

Drift Velocity in different materials Drift velocity is partly a function of the charge carrier density. This means if we control all other factors, such as cross sectional area, we can see that the lower the density of charge carriers the faster the drift velocity. Conductors have a huge abundance of charge carriers so drift velocity is low.

Explaining Conductance Conductor Semi-conductor Insulator Example of material n (density of current carriers) Range depending on material – Around 2X1028 1x106 – 1x1010 fewer than a conductor In some circumstances 0. Drift Velocity Order of cm/hour Considerably faster than in conductor N/A if perfect

Doping a semi-conductor Semi-conductors Vital to modern circuitry! Have properties which are intermediate between a conductor and an insulator. Have roughly 1 million times fewer free charge carriers than a copper wire so drift velocity is high. Number of charge carriers can be changed via doping. Doping a semi-conductor

A semiconductor has far fewer free electrons than copper A semiconductor has far fewer free electrons than copper. If a copper wire and semiconductor of equal cross sectional area have a current of 0.5A, which material has the highest drift velocity? Semiconductors – fewer electrons – much few collisions – higher drift velocity

What if I’m asked to work out number density? You will need to work out how many atoms there are per m3 of the conductor. Chemistry  The molar mass tells you the mass of 6.02x1023 (NA) atoms The density tells you the mass of 1m3 of the conductor Density/Molar mass tells you the number of moles in 1m3 of the conductor Multiplying by NA tells you how many atoms per m3

The density of copper is 8900 kgm-3 In copper, there is one free electron for every atom. Determine the drift velocity if a current of 5A flows through a copper wire of cross-sectional area 3x10-6 m2. The density of copper is 8900 kgm-3 The molar mass of copper is 0.064kgmol-1 n = (density / molar mass) x NA n = 8.37 x 1028 I = nAve 5 = 8.37 x 1028 x 3 x 10-6 x 1.6 x 10-19 v v = 1.24 x 10-4 ms-1

Now try… Qu 1-3 pg 87 in textbook