PHY1 AQA GCE Physics A Unit 1 Revision notes

PHY1 AQA GCE Physics A Unit 1 Revision notes

Chapter 1 Base Physics! 4 Base units:! 4 Derived units:! 4 Prefixes:! 4 Chapter 2 Particles! 5 The Atom:! 5 Specific charge:! 5 Strong nuclear force:! 5 Unstable nuclei:! 5 Alpha decay:! 5 β decay:! 5 Photons particles of light:! 6 Antimatter:! 6 Annihilation:! 6 Pair production:! 7 Quarks:! 7 Hadrons:! 7 Leptons:! 7 Properties of quarks and leptons:! 7 Fundamental forces:! 8 Exchange particles:! 8 Feynman Diagrams:! 9 Weak interaction Feynman diagrams:! 9 Chapter 3 Quantum Phenomena! 11 Photoelectric effect:! 11 Einstein s photoelectric equation:! 11 Wave particle duality:! 11 The electron volt:! 12 Line spectra:! 12 Electron energy levels:! 12 page 2 of 18

Fluorescent tubes:! 13 NB:! 13 Chapter 4 Electricity! 14 Current and charge:! 14 EMF and potential difference:! 14 Circuit rules:! 14 Variation of current and potential difference:! 14 Resistivity:! 15 Resistivity of metals and superconductors:! 15 Superconductors:! 16 Resistors in series and parallel:! 16 Electrical energy and power:! 16 Internal Resistance:! 17 Potential Dividers:! 17 Potentiometer:! 17 Alternating currents:! 17 Root mean square values:! 18 The oscilloscope:! 18

Chapter 1 Base Physics Chapter 1 Base Physics Base units: International system of units (SI system) is based on 7 fundamental units: Basic Quantity Unit Symbol Mass Kilogram kg Length Metre m Time Second s Electric current Ampere A Temperature Kelvin K Amount of substance Mole mol Luminous intensity Candela cd Derived units: Some common derived units: Derived Unit Measures Derivation SI system derivation Joule (J) Energy or work N m kg m2 s-2 Watt (W) Power J/s kg m2 s-3 Coulomb (C) Electric charge A s A s Volt (V) Ampere W/A kg m2 s-3 A-1 Ohm (Ω) Electric resistance V/A kg m2 s-3 A-2 Prefixes: 10-15 " 10-12 " 10-9 " 10-6 " 10-3 " 10 0 " 10 3 " 10 6 " 10 9 " 10 12 femto" pico" nano" micro" milli" " kilo" mega" giga" terra F! p! n! μ! m!! k! M! G! T 4

Chapter 2 Particles Chapter 2 Particles The Atom: Protons and neutrons are referred to as nucleons. Particle Relative mass Relative Charge Mass / kg Charge / C Proton 1 +1 Neutron 1 0 +1.67 x 10-16 1.67 x 10-27 0 Electron 0.00005-1 9.11 x 10-31 -1.67 x 10-16 Isotopes are atoms of the same element so same no. of protons but with differing no.s of neutrons. Specific charge: Charged particles are deflected in electric or magnetic fields. Specific charge = charge / mass C kg -1 " C kg Greater the spec. charge of a particle, the greater will be its deflection in electromagnetic fields. Strong nuclear force: Reason nucleus does not break apart is because there is an attractive force between all nucleons holding them together known as the strong nuclear force. ~100 times stronger than electrostatic repulsive force but very short range less than 3fm. Also, when separation of 2 nucleons decreases to less than ~0.5fm, the strong force becomes repulsive, thus the nucleons are kept at a certain average separation. Unstable nuclei: Small stable nuclei have near enough equal numbers of protons and neutrons. However, for larger stable nuclei, there must be more neutrons to protons. This is because the strong force is very short range and only attracts nucleons which are nearest neighbours whereas the electrostatic force has a much larger range and all the protons in the nucleus repel each other. So, more neutrons are needed to hold the nucleus together. Alpha decay: An α particle is a helium nucleus 4 2He, so when an unstable nucleus decays by emitting an α particle, it loses 2 protons and 2 neutrons. E.g.: 208 84Po 4 2He + 204 82Pb β decay: The emission of an electron from an unstable nucleus there are, of course, no electrons in the nucleus of an atom. Therefore, β decay occurs when a neutron changes into a proton inside the nucleus and an electron is also formed (to conserve charge) n p + e The electron is immediately emitted from the nucleus as a β particle. 5

Chapter 2 Particles It is also found that the range of energies released in β decay can only be explained if another particle is emitted in addition to the electron. This particle has no charge and negligible mass (hence very hard to detect). It is called the antineutrino, ṽe. So n p + e + ṽe Following the decay, the nucleus therefore has one fewer neutron and one additional proton so the nucleon number does not change, just the proton number gains 1. Photons particles of light: Some experiments of the 20th century couldn t be explained by considering electromagnetic radiation as waves. Energy of a photon depends on the frequency of the radiation: E = hf = hc / f (h is Planks constant, = 6.63 x 10-34 ) Photons have no mass or charge but many aspects of a photon s behaviour is very similar to that of particles such as electrons. For example, photos do have momentum. Antimatter: Every particle has its equivalent antiparticle. A particle and its antiparticle have the same mass, have the same but opposite charge and spin in the opposite direction. E.g. The electron and the positron both have a rest mass of 9.11 x 10-31 kg, so both have a rest energy of 0.511 MeV. The electron has a charge -1.6 x 10-16 C and the positron +1.6 x 10-16 C. Annihilation: As soon as a particle meets its antiparticle, the 2 destroy each other. The mass of the particles is converted into energy. For example, when an electron and a positron collide, the annihilate producing 2 gamma ray photons of energy; " " e + e + 2γ 2 photons are produced since momentum (as well as charge and mass-energy) must be conserved in the interaction. When sufficient energy is available, the energy released in annihilation can be converted back into matter. This is how particles are created in accelerator experiments. 6

Chapter 2 Particles Pair production: Pair production is the opposite process to annihilation i.e. the creation of a particle and an antiparticle usually from the energy of a proton. E.g. γ e + e + This is only possible if the photon has sufficient energy to provide at least the rest mass/energies of the 2 particles i.e. in this case, the gamma ray photon must have an energy exceeding twice the rest energy of an electron, so greater than 1.022 MeV. Matter Hadrons Leptons Baryons Mesons Quarks: In the past 80 years, experiments using particle accelerators have revealed there are more than 200 subatomic particles. In 1963, Murray Gell-Mann simplified matters by suggesting that many of the new particles are made up of different combinations of smaller particles which he called quarks. Experimental evidence that quarks exist came just a few years later in 1969. There are 6 types of quark up, down, strange, (top, bottom, charm). Hadrons: Particles which are made up of quarks are called hadrons. Hadrons are subject to the strong nuclear force. There are two types of hadron: Baryons: Made up of 3 quarks q q q, (or 3 x anti-q) Protons contain 2 up quarks and 1 down u u d Neutrons contain 1 up and 2 downs u d d Mesons: Made up of a quark and an antiquark. E.g. Pions: π 0 = (u, u-) or (d, d-) π + = (u, d-) π = (u-, d) Kaons: K 0 = (d, s-) K + = (u, s-) K = (u-, s) Leptons: Leptons are fundamental particles they have no internal structure. Leptons do not feel the strong nuclear force, they are subject to the weak interaction. There are 6 types of lepton, including the electron, the muon, the electron neutrino and the muon neutrino. Properties of quarks and leptons: We know charge and mass-energy are conserved in any interaction. However, some particle interactions never occur even though these are conserved. To explain this, it is found that there are other properties which must be conserved for a particle interaction to occur. 7

Chapter 2 Particles Baryon number: All quarks have a baryon no. of +⅓ and all antiquarks of -⅓. Therefore: All baryons have baryon number +1. All anti-baryons have baryon no. -1. All mesons have baryon no. 0. All leptons have baryon no. 0. Baryon number is conserved in all interactions. Lepton number: All leptons have a lepton no. +1. All anti-leptons have lepton no. -1. All hadrons have lepton no. 0. Can be considered in generations i.e. electron lepton number, muon lepton number, and so forth. In any interaction, lepton number of any generation is conserved. Strangeness: Particles that contain strange quarks are called strange particles. Strange particles are unusually long lived. The s quark has a strangeness of -1, and the s- antiquark has a strangeness of +1. So: K 0 = (d, s-) = has strangeness +1. K + = (u, s-) = has strangeness +1. K = (u-, s) = has strangeness -1. Strangeness is conserved in interactions involving the strong nuclear force in weak interactions, strangeness can either be conserved or change by ±1 E.g. K + μ + + vμ this interaction is allowed since the Strangeness: +1 0 0 kaon decay is a weak interaction. Fundamental forces: There are 4 fundamental forces or nature: Gravitational: Weakest of the four, but acts over infinite distances and is the force which holds stars and galaxies together. Electromagnetic: Also has an infinite range and is the force which holds atoms and molecules together. It is responsible for the chemical, mechanical and electrical properties of matter. Strong nuclear: Strongest force but has a very short range and so only acts between neighbouring nucleons. It binds quarks and antiquarks to hold nucleons together. Weak nuclear: Even short range. Does not cause attraction or repulsion like the other forces, it changes particles from one type to another. It is responsible for β decay and for nuclear fusion reactions in the sun. Exchange particles: When an interaction occurs between particles, there is a change in the momentum and the energy of each particle. We know that mass and energy are interchangeable so we can explain this transfer of energy between the particles as being caused by them exchanging particles called exchange particles. For example, 2 protons repel each other by exchanging virtual photons. The photons are described as virtual because they exist for such a limited time and space that they cannot be detected. Force Acts upon Range Relative strength Exchange particle Strong nuclear Quarks 10-15 m 1 Gluons Electromagnetic Charged particles 10-2 Photons Weak nuclear Quarks and leptons 10-18 m 10-5 W bosons (and Z bosons) Gravity Anything with mass 10-38 Gravitons (not yet detected) 8

Chapter 2 Particles Feynman Diagrams: Richard Feynman devised a shorthand way of describing particle interactions called Feynman diagrams. Particles are represented by straight lines with arrows on. The precise directions of the lines are not significant and do not show the directions of the particles. Exchange particles are represented by wavy lines with no arrows. The time axis usually points upwards. Each point at which lines come together are called vertices. At each vertex, charge, baryon number and lepton number are all conserved. E.g. electromagnetic attraction between a proton and an electron: p e p γ photon e " Weak interaction Feynman diagrams: β decay: Involves the change of a neutron into a proton in the nucleus therefore involves the change in character of a quark (from d to u). p e ṽe u (uud) e ṽe n W d W (udd) " " " " β + decay: Involves the change of a proton in a neutron in the nucleus therefore the change in character of a quark (from u to d). n e + ve d (udd) e + ve " p W + " " " u (uud) W + 9

Chapter 2 Particles Electron capture: One of the innermost electrons in an atom travels very close to the nucleus and interacts with a proton by the weak force. e.g. 37 18Ar + 0-1e 37 17Cl + 0 0ve i.e. p + e n + ve The electron is effectively captured by the proton to form a neutron. n ve p W + e " " Electron proton collisions: The same electron capture interaction as above can occur when a proton and an electron collide at very high speed. If the electron has sufficiently high energy then the change can occur as a W exchange from the electron to the proton. ve n e W p " " Neutron neutrino interaction: p e n W + ve " " Proton antineutrino interaction: n e + p W + ṽe " " 10

Chapter 3 Quantum Phenomena Chapter 3 Quantum Phenomena Photoelectric effect: Throughout the 19th century, it was generally accepted that light and other electromagnetic radiations travel as waves. However, 2 experiments were then investigated which could not be explained considering light as a wave motion. One of the these was the photoelectric effect. coulomb meter ultra violet radiation - - - - - - - - - - - - - - - -0.51 negatively charged zinc plate The zinc plate keeps its negative charge until UV radiation is shone onto it. It then quickly loses its negative charge, as displayed on the coulomb meter. The experiment above shows that shining light (or UV radiation) on the surface of a metal can cause electrons to be emitted from the surface. The detailed results of the experiment show that: i. Electrons are emitted instantly, no matter how weak the incident radiation. ii. The emitted electrons have various kinetic energies, ranging from zero to some maximum value. The intensity of the radiation has no effect on the kinetic energies of the emitted electrons. iii. Increasing the frequency of the incident radiation increases the energies of the emitted electrons, and in iv. particular increases the maximum kinetic energy. Emission occurs only if the frequency of the incident radiation is above that of the threshold frequency fmin. The threshold frequency depends on the particular metal being irradiated (for example, the threshold frequency for sodium is in the yellow region of the visible spectrum, that for zinc is in the UV spectrum). v. The number of electrons emitted from the metal surface per second is proportional to the intensity of the incident radiation. These results cannot be explained by using the wave theory of light, in which the energy of a wave is related to its intensity in this case, the kinetic energies of the emitted electrons would depend only on the intensity of the incident radiation and not the frequency. Einstein s photoelectric equation: In 1900, Max Planck introduced the quantum theory to explain the radiation emitted by black bodies. In 1905, Einstein extended this idea to consider light as consisting of discrete (separate) packets of energy called photons. The energy of each photon is proportional to its frequency f, i.e. E = hf The intensity of a beam of light is proportional to the number of photons per unit cross section per unit of time. Einstein proposed that when a photon collides with an electron, it must either be reflected with no reduction in energy, or it must give up all its energy to the electron. The, some of this energy is needed to release the electron from the surface of the metal, and the rest becomes the kinetic energy of the emitted electron. i.e. Energy of photon = energy needed to remove electron from metal + kinetic energy of electron More energy is needed to remove electrons from deep inside the metal than from the surface because they are involved in collisions on the way out. They therefore emerge with less kinetic energy. The minimum energy needed to remove an electron from the surface of a material is called the work function, Φ, of the metal. Then electrons emerge with maximum kinetic energy, Ek max. So," hf = Φ + Ek max and! hfmin = Φ Wave particle duality: The photoelectric effect can only be explained by considering light to consist of discrete photons (a particle model of light). Other experiments such as diffraction and interference can only be explained by considering light to consist of continuous waves (the wave model of light). 11

Similarly, electrons and proton etc. (which we normally consider as particles) under certain circumstances display behaviour which can only be explained by considering them to act as waves, e.g. electron diffraction. So, matter (like light) has a dual nature. It can be wave-like or particle-like. Which side of its nature we observe depends on the experiment we use to detect it. The wavelength of a particle is called the De Broglie wavelength, given by the formula: " λ = h! mv Electron diffraction: In 1928, diffraction patterns we obtained by passing a beam of electrons through very thin (~10-8 m) metal foils. By measuring the radii of the various rings if the diffraction pattern, it was shown that the wavelength of the electrons was in excellent agreement with that calculated by the de Broglie wavelength. The electron volt: 1 ev = 1.6 x 10-19 J From joules to electron volts, divide by conversion factor. From electron volts to joules, multiply by conversion factor. Chapter 3 Quantum Phenomena Line spectra: When light from a luminous source is dispersed (using a prism or diffraction grating), a spectrum of the different wavelengths is produced. If the source consists of isolated atoms, e.g. A gas or a vapour at low pressure, then a line spectrum is produced separate bright lines of definite wavelengths on a dark background, such as from a sodium vapour lamp. Line spectra provides direct evidence for the existence of discrete energy levels in atoms. Electron energy levels: Electrons in the atom are only allowed to exist in certain orbits of definite energies. They cannot exist between these energies. The atoms as a whole is considered as having a series of energy levels, represented as horizontal lines. The ground state is the most stable level and corresponds to every electron being in its lowest possible orbit its least energy. If the atom absorbs energy in some way (for example, in a collision or by absorbing electromagnetic radiation), an electron may move to a higher orbit and so the atom is in a higher energy level an excited state. The atom is now unstable, and after a short but random interval, the electron falls back directly or in stages to the ground state. The atoms loses this energy by radiating a photon, so if it falls, say, from energy level E2 to E1 (in joules): E2 hf E1 " " Thus, each transition between energy levels in the atom produces a definite frequency of light, i.e. only certain frequencies are possible, and this accounts for the line spectrum. Note that, since the energy levels are characteristic of the particular atom, no 2 elements have the same line spectrum and this method can be used to identify the presence of elements in, for example, stars. 12

Chapter 3 Quantum Phenomena The main justification for this model of the atom, which was proposed by Neils Bohr in 1913, is that it predicts to a high degree of accuracy the wavelengths emitted by atomic hydrogen hydrogen has only 1 electron and this normally occupies the ground state and has an energy of -13.6 ev (ground state). The spectrum of atomic hydrogen contains distinct groups of lines. The 3 most obvious are: Lyman series: Involves transitions ending in the ground state, n=1. Since these transitions involve large energy difference, and so produce high-freq. photons, Lyman series is in the UV. Balmer series: All transitions ending in the n=2 energy level. These involve smaller energy differences than the Lyman series, the photos have lower freq., so are found in the visible light region. Paschen series: All transitions ending in level n=3. Since they involve smaller energies and freq.s still, the Paschen series is found in the infra red. Fluorescent tubes: The long strip lights in classrooms and energy saving lamps used in homes are made from fluorescent tubes. The glass contains mercury vapour. Connecting a high voltage across the tube causes the movement of electrons and mercury ions in the vapour. So, mercury atoms are excited or ionised when they gain energy in collisions with each other or with electrons. As a mercury atom has a large nucleus, its energy levels are separated by larger gaps than for hydrogen, so, when the mercury atoms return to a more stable state, most energy is emitted in the UV region. The inside of the glass tube is coated with an opaque white material called phosphor. The phosphor absorbs the UV radiation and so its atoms gain energy and become excited (move to the excited states). The excited phosphor atoms then fall into lower energy states, emitting photos each time, until they are back in the ground state. As these transitions are smaller than the original jump, the photons are emitted not as UV but as visible. By a careful mixture of phosphor materials, the mixture of photons emitted can give the appearance of white light. NB: Ionisation is when an atom gains energy, for example in a collision, and an electron is completely removed from the atom. The ionisation energy of an atom is the minimum energy needed to remove an electron at ground state from the atom i.e. the positive energy of the ground state. Excitation is when an atom gains energy, for example in a collision, and an electron is moved to a higher orbit (energy level) in the atom. An atom in an excited state is unstable and so it will quickly lose energy by emitting a photon to return to its ground state. 13

Chapter 4 Electricity Chapter 4 Electricity Current and charge: Electric current is the rate of flow of charge. i.e. I = Q t So, 1 coulomb is the quantity of electric charge transported in 1 second by a steady current of 1 ampere. Note that, by convention, electric current is said to travel from the positive to the negative terminals of the supply. In metals, the opposite it true since current consists of a flow of negative electrons. Current is measured using an ammeter which is placed in series in the circuit. An ideal ammeter should have zero resistance so that is does not change the circuit it is added to. Therefore, " " Charge = current x time!!!! Q = It EMF and potential difference: Work must be done to drive a current round a circuit. This energy is provided by the electro-motive force (EMF). The EMF of a cell (in volts) is the energy (in joules) supplied by the cell to every every coulomb of charge passing through it. i.e. 1 volt = 1 joule / coulomb This energy is then transferred e.g. as heat in a resistor as charge passes round the circuit. The potential difference across a component measures the number of joules transferred per coulomb of charge passing through it (or the number of joules of work done by each coulomb of charge passing through the component). So, " " Potential difference = work done (J) "" " E = VQ!!! (V)! charge (C) Alternatively, since Power = I x V, potential difference across a component can be defined as the power transferred per ampere of current passing through it. i.e., " " Potential difference = power transferred (W) " P = IV!!! (V)!! current flowing (A) Potential difference is measured using a voltmeter which is placed in parallel across the component it s measuring. An ideal voltmeter should have infinite resistance so that it does not change the circuit it is added to. Circuit rules: Kirchoff s laws: I. The total current entering a junction must equal the total current leaving the junction. Note that this is a consequence of the conservation of charge. Since charge cannot be created or destroyed, the total charge per second (current) entering a junction equals the total charge per second (current) leaving it. II. When taken around any closed circuit, the sum of the EMFs is equal to the sum of the potential differences around the circuit. Note that this is a consequence of the conservation of energy. The energy supplied to each coulomb of charge by the EMF of the cell is transferred in the various components in the circuit. Variation of current and potential difference: If the current flowing through a given device is measured for different applied potential differences, the resulting graphs can vary widely (see graphs for ohmic conductor, filament lamp and semiconductor diode). For any device, its resistance at a particular instant is defined as the ratio of the p.d. across it to the current through it. i.e., " " Resistance = potential difference (V) " " V = IR " " (Ω)!! current (A) For some substances, notably metals, V/I is found to be constant provided physical conditions such as temperature do not alter. So, for these ohmic conductors, resistance is constant. 14

Chapter 4 Electricity Ohm s law: I. Provided temperature remains constant, the current through an ohmic conductor is proportional to the potential difference across it. Resistivity: The resistance of a piece of wire depends of three factors: i. its length, ii. its thickness, i.e. cross-sectional area, iii. and the material it s made of. So, " " R = ρ L " " where:!! A R = resistance of the wire (in ohms) L = length of the wire (in metres) A = cross-sectional area of the wire (in m 2 ) ρ is a constant which depends only on the material the wire is made of. It is called the resistivity of the material the units are ohm metres. Resistivity of metals and superconductors: Metals: Each atom of a metal has, on average, one outer electron which is not required for bonding and so is free to move throughout the structure. When no potential is applied, the free electrons move randomly, but a p.d. causes them to drift towards the point of higher potential. i.e. the p.d. superimposes a small drift velocity (~ mm/s) onto the random motion of the free electrons. There is now a net flow of charge an electric current. As the electrons move through the metal, they collide with the positive ions of the lattice and so transfer some kinetic energy to the ions. This increases the vibrational energy of the lattice and so increases the temperature of the metal joule heating. Similarly, if for any reason the temperature of the metal is made to increase, the ions vibrate more and so present a larger collision cross section to the electrons. As a result, the electrons collide more frequently and so the resistivity of the metal increases with temperature. Insulators: All electrons used for bonding, so there are no charge carriers. Semiconductors: (e.g. silicon, germanium, gallium arsenide, etc.) At absolute zero, all electrons are used for bonding, so there are no conduction electrons and hence, semiconductors are insulators at absolute zero. However, at temperatures above absolute zero, some electrons have sufficient thermal energy to break free and so can travel through the material when a p.d. is applied. The higher the temperature, the greater the number of free electrons, so the resistivity of a semiconductor decreases as temperature rises. A negative temperature coefficient (NTC) thermistor is made of a semiconductor whose resistance decreases markedly with temperature. It can therefore be used as a temperature sensor. A light dependent resistor (LDR) is made of a semiconductor, often cadmium sulphide, whose resistance decreases markedly as the light intensity falling on increases. R R " Temp. Light intensity " " " An increase in temperature of a semiconductor therefore causes a decrease in resistance which in turn can lead to an increase in current and so a further increase in temperature and so on. Breakdown can easily occur in semiconductors. 15

Chapter 4 Electricity Superconductors: In 1911 it was discovered that when mercury is cooled to -269ºC (4.15K), its resistance is zero. A superconductor is a material that will conduct electricity with zero resistivity below a certain critical temperature, Tc. Resistivity Tc Temp. " " The critical temperature depends on the material some materials have already been developed with critical temperatures above 150K (-123ºC). Scientists are trying to make materials that are superconductors at room temperature. When a current passes through a superconductor, there is no p.d. across it since its resistance is zero. So no energy is transferred to the superconductor i.e. the current has no heating effect. Thus very large currents can be passed down a superconductor wire without overheating. Applications: Very strong electromagnets can be produced as in maglev trains and magnetic resonance scanners (MR). Power cables made from superconducting material can transfer electrical energy with no energy wasted as heat in the cables. All this can only be achieved if the superconductor is maintained below its critical temperature. Resistors in series and parallel: I. Series: V I R1 R2 R3 V1 V2 V3 II. The same current, I, passes through each resistor. The potential difference across R1, V1 = I R1; The potential difference across R2, V2 = I R2; etc. Total resistance of the circuit, Rtot = R1 + R2 + R3 + Parallel: The potential difference across each resistor is V. By Kirchoff s 1 st law, I = I1 + I2 + I3. So, 1 = 1 + 1 + 1! Rt R1 R2 R3 Note: For series resistors, the total resistance is large than the total resistance is larger than the largest individual resistor value. For parallel resistors, the total resistance is less than the smallest individual resistor value. I I1 I2 I3 R1 R2 R3 V Electrical energy and power: Consider a device which has a potential difference V across it. This means that V joules of energy are transferred for every coulomb of charge passing through it. So id a charge Q coulomb is passed, the total energy transferred is VQ joules. If the charge consists of a flow of current I for a time t, then Q=It. So energy transferred = V I t. Power is the rate at which a device transfers energy (measured in joules/second, or watts). Power = energy/time = VIt/t, so P=VI. can also be written as P=I 2 R=V 2 /R. 16

Chapter 4 Electricity Internal Resistance: A cell must not only provide energy to drive a current through the external circuit, it must also do work to drive the current itself. We say that cell has an internal resistance r. The cell may be considered to be a source of constant EMF E in series with a resistance r the cell s internal resistance. " " V = E Ir!! V = I (R + r) E r Note: The only occasion when the full EMF of the cell is available at its terminals is when no current is drawn from the cell (so that Ir=0, and then V=E [equation above]). i.e. the EMF can only be measured accurately by a device which takes no current e.g. a very high resistance voltmeter. For the starter motor of a car to turn, the engine requires a large amount of power, and since the EMF of a car battery is only 12V, a very large current is needed (P=IV). For the battery to produce this large current (~100A), it must have a very small internal resistance (~0.01Ω). Potential Dividers: A potential divider is a device which can be used to supply a variable p.d.. In its simplest form, it consists of 2 resistors connected in series to a voltage supply as below. I Supply p.d., V R2 " R1 V1 "" " V1 = VR1 (R1 + R2) Applications: A thermistor or a LDR can be used in a potential divider circuit to produce a simple light or temperature sensor. The example does not give the full range of output voltages i.e. it cannot product all voltages in the range 0V to (e.g.) 12V. To achieve this, a potentiometer circuit is used. Potentiometer: By moving the slider along the resistor, output voltage can be varied continuously from 0V to the supply voltage V. When drawing a voltage-current graph, the potentiometer circuit shown gives a full range of applied voltages. Alternating currents: An alternating current or EMF is one whose direction varies periodically with time. The simplest AC is one which varies sinusoidally with time. Frequency = 1/t. Supply p.d., V Vout 17

Chapter 4 Electricity Root mean square values: The average value of a sinusoidal AC is, of course, zero. The effective value of an AC is called the root mean square value Irms. It s deduced by considering the heating effect of a current. A 4A r.m.s. AC must have exactly the same effect in a given resistor as a steady DC current of 4A. i.e. The root mean square value of an alternating current is that value of a steady current which would dissipate heat at the same rate in a given resistor. For sinusoidal ACs: Irms = I0! 2 Vrms = V0! 2 The oscilloscope: The cathode ray oscilloscope (CRO) is an important instrument for measuring DC and AC voltages, measuring time intervals and frequencies, and displaying AC waveforms. No input, time-base off DC input, time-base off DC input, time-base on No input, time-base on AC input, time-base off AC input, time-base on 18