Batteries, conductors and resistors

Transcription

1 Batteries, conductors and resistors Lecture 3 1 How do we generate electric fields where does the energy come from? The e.m.f. generator uses some physical principle to create an excess of electrons at one terminal and a deficit at the other. This requires energy Electrical conductors transfer the potential difference to the device (more later!) + terminal (electron deficit) e.m.f. generator energy - terminal (electron excess) + - conductor electric field potential difference When electrons move in the device electrons flow from the negative terminal to the positive terminal. Energy has been transferred from the e.m.f. generator to the K.E. of electrons Lecture 3 2 1

2 How can we generate e.m.f.? : 1 Dynamo, generator Rotary energy from a petrol engine, turbine etc. moves a conductor in a magnetic field Mains power we can use a POWER SUPPLY to create the e.m.f. we need Solar cells Ultraviolet photons from the sun create electrons directly in silicon Thermo-electric generator Temperature difference between junctions of different metals generates electron excess Lecture 3 3 How can we generate e.m.f.? : 2 Fuel cell Recombining H 2 and O 2 to make water releases extra electrons (energy is needed to separate H 2 and O 2 in the first place) Chemical battery Chemical reactions transfer electrons Lecture 3 4 2

3 Batteries Store a fixed amount of charge (in the form of chemical energy) So they run down Cannot supply an unlimited current (more later) battery with a stored charge Q can supply a current for how long? Lecture 3 5 The ideal battery: 1 oltage source We will see that (for physicists!) it does not matter exactly how the e.m.f. is generated We will represent our e.m.f. generator as an ideal battery E.m.f. is constant independent of the current supplied Capable of supplying any current indefinitely Circuit symbol Lecture 3 6 3

4 The ideal battery: 2 Current source device which provides a constant current NDEPENDENT OF THE OLTGE REQURED TO DO THS Circuit symbol Lecture 3 7 Things you can t do with ideal sources Connect voltage sources in PRLLEL Connect current sources in SERES Lecture 3 8 4

5 Electrons in conductors:1 Two states of the outer electrons 1. alence electrons These are responsible for holding the metal together very tightly bound to the atoms 2. Conduction electrons Left over from chemical bonds Loosely bound to atoms and can drift through the lattice Lecture 3 9 Electrons in metals:2 Drifting electrons have many collisions. Electrons do not accelerate but reach a constant average drift velocity proportional to the applied field v = μe Electron velocity Free electron Electron in metal verage velocity where μ is the electron mobility in the metal (units m 2-1 s -1 ) Mobility depends on the chemical and physical form of the material and on temperature time Lecture

6 Resistance Now we can calculate the current that passes through a block of material if you apply a potential difference across it E l v rea Electrons / second: dn dt n = n μ E e dn n e μ n = dt l Charge / sec (= current) i = neμe l This is OHM S LW: Current is proportional to applied voltage Lecture 3 11 Georg Simon Ohm ( ) Discovered Ohm s law in 1829 (experimentally) at the University of Cologne. The Prussian Minister of Science thundered that any professor who preaches such heresy is unworthy to teach science!. Ohm resigned his professorship, went into exile and eventually settled in Bavaria Lecture

7 Resistance and Resistivity i = ne μ e l i = where R ρ l R = and 1 ρ = neμ e R is a property of the conductor called RESSTNCE [Symbol in equations r, R. Units OHMS, symbol Ω] Resistance depends on the shape of the conductor (cross section area,, length, l) and the properties of the material, ρ ρ is the RESSTTY of the material [units OHM.METRE, Ω m] Ohms law again: volts = amps x ohms Lecture 3 13 R Calculating resistance Material Silver Copper luminium ron Platinum Nichrome* Carbon (graphite) Glass Rubber Quartz Resistivity (ohm.m) 1.59 x x x x x x x x x *Nichrome an alloy of Ni, Fe and Cr used for making resistor wire 7.5 x R = ρl Example: resistance of 1 m. of 1mm diameter Pt wire: = πr = π( ) = m 8 ρl R = = = Ω Lecture 3 14 l 7

8 Resistors Components designed to have a well defined value of resistance are called RESSTORS These can be made of carbon, metal film or metal wire R R Circuit symbols The values of small resistors are often indicated by coloured rings (the colour code). has a nice graphical calculator Lecture 3 15 Connectors, wires We will assume that all the components we use are connected together by ideal conductors of ZERO resistance (so we can ignore them not always true in real life!) Real connectors are usually copper wire (low resistivity, comparatively cheap) or copper foil printed in a pattern onto an insulating sheet (printed circuit board, PCB) Lecture

9 Energy in resistors Each time an electron in a conductor collides with another electron in the material, it loses kinetic energy. This energy is eventually transferred to the lattice HET! The power dissipated in a resistor is equal to the energy drawn from the power source: W = watts watts = volts x amps Conservation of energy: n any circuit the power dissipated in the resistors is LWYS equal to the power drawn from the batteries Lecture 3 17 Summary of formulae so far Q= t (for constant current) = R; = / R; R= / (Ohm's law) P= (Power in a resistor) P= = 2 R 2 P R / Lecture

10 Measuring devices n MMETER is inserted into a circuit to measure current. deal ammeter has ZERO RESSTNCE (introduces no voltage drop) OLTMETER is used to measure the potential difference across a component. n ideal voltmeter has NFNTE RESSTNCE (draws no current) Lecture curves X We can learn a lot about a component by plotting its - curve ideal resistor (low R) REL resistor: R increases when resistor gets hot ideal resistor (high R) - curve is LNER (only two points required) NON-linear - curve several points required Lecture

11 - curves - active and passive 2 < 0 > 0 1 n quadrants 1 and 3: > 0 Current flowing in the same direction as applied voltage Energy is dissipated in the component Passive (e.g. resistor) > 0 < n quadrants 2 and 4: < 0 Current flowing against the applied voltage Energy is supplied by the component ctive (e.g. battery or current source) Lecture curves - Sources oltage source (battery) oltage is constant independent of current When current has the same sign as voltage, battery is absorbing energy Current source Current is constant independent of voltage When voltage has the same sign as current, source is absorbing energy Lecture