# Birmingham July 2012

Sunday 8th July

The first lecture of the day was really a discussion about electricity and how we use models in physics (and chemistry). Some of what I’ve written is a bit disjointed as I was trying to follow the discussion.

We started off looking at ammeters. Analogue ammeters use a moving needle attached to a moving coil to indicate the current. The movement is directly related to the force on the needle and this is equal to BIL where B is the magnetic field strength, I is the current and L is the length of wire inside the magnetic field. Digital ammeters use the Hall effect, F = qvB where F is the force on the moving charges, q is the charge value and v is the velocity of the charge.

When a current-carrying conductor is placed in a magnetic field, the conductor experiences a force which acts to push the conductor out of the field. This is the principle of operation of an analogue ammeter and voltmeter.
A light coil of wire supporting a pointer is placed between the poles of a permanent magnet. Whenever the coil rotates, the pointer sweeps across an appropriately-calibrated scale. When current flows through the coil, a torque acts to rotate the coil. However, the movement of the coil is restrained by a pair of hairsprings. When the torque due to the current is balanced by the restraining torque of the hairsprings, the coil stops rotating. Thus, the angle through which the coil rotates is proportional to the current flowing through it, and the instrument is calibrated such that the pointer directly indicates that value current on a curved scale.
Ammeters and voltmeters both work on the same principle. In the case of the voltmeter, the current which operates the coil is proportional to the voltage appearing across the instrument. The difference between the two instruments is the way in which resistors are used, within the instruments, to make one suitable for measuring current and the other suitable for measuring voltage.
Ammeters must be connected in series with the circuit under test, whereas voltmeters must be connected in parallel with the circuit under test.
Digital ammeters and voltmeters work on a completely different principle, using an electronic ‘gate’ to switch on and to switch off a series of pulses. The time for which the gate is ‘open’ is a function of the value of the current or voltage being measured -e.g. the larger the current, the longer the gate is held open. These pulses are then counted and, in simple terms, the greater the number of pulses counted, the greater the current or voltage being measured. The output is then presented, directly in amperes or volts, on a LED or LCD screen.

We then looked at internal resistance of power supplies. This isn’t in fact a resistance. It is to do with a chemical reaction. If you tried to measure it with an ohmmeter you wouldn’t get a reading. It increases as the cell ages.

When a battery is connected in a circuit negatively charged electrons are removed from the negative terminal and the current in the circuit drops. A chemical reaction starts in order to replace the electrons.

A + B <–> C + D If D are electrons and you remove them you drive the reaction forwards. The potential difference between the plates in the battery has to drop to maintain the current.

The emf of a power supply is defined as the amount of energy available to each unit of charge. Fruit and certain vegetables can be used as sources of emf http://chemistry.about.com/od/chemistryhowtoguide/a/fruitbattery.htm

The potential difference is about the difference between the spacing between the flowing charges. Work needs to be done to bring like charges together, V = kQ/r where r is the charge separation  Electricity flow is a multi electron quantum system

Electrons push producing a pressure like water. You can model the process as a tube of tennis balls. The calculated drift speed is a result of making assumptions. To keep the drift current the same the drift speed has to be a little greater near the positive plate of the battery: I = nAev and J = I/A = nev. Energy is due to spacing. Potential difference changes with spacing. Adding batteries increases the spacing. Mathematics assumes a Maxwell Boltzmann distribution in the electron gas, that the gas is in equilibrium and that they are free classical particles.

Average kinetic energy = 3kT/2 = m(c^2)/2 gives a speed of 1xE5m/s but the drift velocity is much smaller.

E = ΔV/d charges experience a force F = qE = ma therefore the acceleration a = qE/m. There is a stop-start movement and this gives an average drift velocity. Electrons must be moving as a magnetic field is detected. The quantum mechanics version does not require motion. It is a method of predicting things from measurements.

Quantum mechanical treatment of electricity is not full. Schrodinger equation is the basis but there are too many electrons. Requires adaptive maths and a quantum fiddle. You can solve it for a single electron. The wave is bounded in the wire but only certain electron waves fit. Electrons can only have set values of energies. Mathematical model explains why there are only certain states. String theory is thought to be a way of explaining it.

Quantum mechanics gives a fix to classical physics but the mass of the electron is “different” effective mass. The sketch on the left is another model. Electrons don’t move up and down a ladder.

We have an idea why there is a band gap. Electrons are fermions. You can’t have identical electrons in an energy state. You can only have one spin up and one spin down. Not a physical description of reality. Mathematical fix is used so that the theory is improved. The electron is a quantized electric charge. 