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National 5 Physics Electricity and Energy Pupil Booklet Electricity and Energy Learning Outcomes Conservation of energy energy is transferred between stores. Identification and explanation of ‘loss’ of energy where energy is transferred. mass, gravitational field strength and height. problems involving kinetic energy, mass and speed. energy. Electrical charge carriers and electric fields ed per unit time. time. Potential difference (voltage) field on a charged particle. energy given to the charge carriers in a circuit. Ohm’s Law -I graph to determine resistance. onship to solve problems involving potential difference (voltage), current and resistance. resistance of a conductor. Practical electrical and electronic circuits of current, voltage and resistance, using appropriate meters in complex circuits. electronic components including cell, battery, lamp, switch, resistor, variable resistor, voltmeter, ammeter, LED, motor, microphone, loudspeaker, photovoltaic cell, fuse, diode, capacitor, thermistor, LDR, relay, transistor. -channel enhancement mode MOSFET. Explanation of their function as a switch in transistor switching circuits. resistors in series and in parallel circuits, and circuits with a combination of series and parallel resistors. Electrical power time. roblems involving power, potential difference (voltage), current and resistance in electrical circuits. appliance. Specific heat capacity ials require different quantities of heat to raise the temperature of unit mass by one degree Celsius. energy of its particles. rature and heat energy. temperature change and specific heat capacity. Gas laws and the kinetic model force and area. absolute zero of temperature. -volume, pressure-temperature and volumetemperature laws qualitatively in terms of a kinetic model. ppropriate relationships to solve problems involving the volume, pressure and kelvin temperature of a fixed mass of gas. Energy Energy cannot be destroyed, but it can be changed from one form into another. All forms of energy are measured in the same unit: the joule (J). There are eight types of energy Kinetic energy the energy of moving things Heat energy the temperature of an object is determined by the kinetic energy of its particles. Energy stored in this way is called heat energy Sound energy when atoms or molecules are made to vibrate Light energy electromagnetic radiation carries energy in photons Gravitational potential energy lifting an object in a gravitational field stores energy Chemical energy is stored in the bonds that bind atoms together Electrical the energy of moving electric charges Nuclear energy is stored in the bonds that bind a nucleus together Energy Transformations Energy can be changed from one form into another. We say energy is being transformed. An arrow is often used to indicate an energy transformation Trolley rolling down a hill Burning wood Battery connected in a circuit Loudspeaker Potential Kinetic Chemical Heat+Light Chemical Electrical Electrical Sound Energy Loss During an energy transformation, energy can be transformed into a form that is not useful. For example the energy transformation in a traditional filament bulb is electrical light and heat. The useful energy is light but some energy will be lost as it becomes heat. We say there is an energy loss (the total energy out still equals the total energy in). Kinetic energy Kinetic Energy is the energy associated with a moving object. It is measured in joules and has the symbol Ek. The kinetic energy of a moving object depends on the mass of the object and on the square of its velocity. Ek = 1 mv2 kinetic energy in joules speed in ms-1 2 mass in kg Example How much kinetic energy does a car of mass 1000 kg have when it is travelling at 20 m/s m = 1000 kg v = 20 ms-1 Ek 1mv2 2 = 1 1000 202 2 = 200000 J Kinetic energy and stopping distances The stopping distance of a vehicle consists of two parts: thinking distance and braking distance. The thinking distance increases with speed. Thinking distance = speed reaction time. To stop a vehicle, the brakes do work to transform the kinetic energy into heat. This work equals the (braking force x the braking distance). The braking distance must therefore increase as the speed and kinetic energy of the vehicle increase. Gravitational potential energy An object which is raised up to a high position is said to have gravitational potential energy. The work done against gravity to raise it equals the energy transformed into potential energy. Imagine a mass of m kg lifted through a height of h metres: h Potential energy = mass x gravity x height gravitational potential energy gained in joules Ep = mgh mass in kg h is height gained in metres gravitational field strength (10 Nkg-1 on Earth) Example A chairlift raises a skier of mass 50 kg to a height of 250 m. How much potential energy does the skier gain? m = 50 kg g = 10 Nkg-1 h = 250 m Ep = mgh = 50 x 10 x 250 = 125000 J Principle of Conservation of energy The total amount of energy remains constant during energy transfers. Energy cannot be created or destroyed but simply transformed to one of its many forms. In the last example the skier gains 125000J of potential energy. If the skier was to ski down the hill, assuming no energy loss all of his potential energy energy would become kinetic energy at the bottom of the slope. Example A lump of ice falls from a plane flying at 350m above the ground. What is the speed of the ice as it hits the ground? Assume there is no air resistance. Solution Ek E p 1 2 mv mgh 2 1 2 v gh 2 v 2 2 gh Mass (m) on both sides can be cancelled v 2 gh v 2 9.8 350 v 82.8ms 1 Note that this question did not need to provide the mass Atoms Every substance is made up of atoms. Each element is made up of the one kind of atom, sometimes these atoms are combined together to form molecules. Inside each atom there is a central part called the nucleus. The nucleus contains two particles: protons: these have a positive charge neutrons: these have no charge. Surrounding the nucleus are negatively charged electrons. An uncharged atom will have the same number of protons and electrons. Consider the element helium, which has two neutrons and two protons in the nucleus, and two electrons surrounding the nucleus. This can be represented as: Neutron Electron Proton atom of helium CIRCUITS Electric Current Materials can be divided into two main groups, conductors and insulators. In a conductor, the electrons (sometimes referred to as charges) are free to move through the structure but in an insulator they are not. Electric current is a measure of the flow of negative charge around a circuit and depends on the amount of charge passing any point in a circuit every second. All metals are conductors and, with the occasional exception, all non-metals are insulators. I= Q t or I = electric current Q = electric charge t = time taken for charge to pass point Q=It Units Electric current is measured in Amperes, A. Electric charge is measured in Coulombs, C. Time is measured in seconds, s. Example Calculate the electric current in a circuit if 3 C of charge pass a point in a circuit in a time of 1 minute. Ensure that all quantities are stated with the correct units. I=? Q=3C t = 1 min = 60 s Q 3 I= t = 60 = 0.05 A Alternating Current (a.c.) and Direct Current (d.c.) All power supplies can be grouped into one of two categories depending on the way that they supply energy to the charges in a circuit. A d.c. supply produces a flow of charge through a circuit in one direction only. An a.c. supply produces a flow of charge that regularly reverses its direction through a circuit. The direction of the current depends on the direction of the ‘push’ from the supply, therefore power supplies can provide a direct voltage or an alternating voltage which would result in a direct current (d.c.) or an alternating current (a.c.). + - + - d.c. supplies cell battery power supply signal generator + power supply a.c. supplies Mains Supply Frequency The mains electrical supply in the U.K. is an alternating supply with a quoted voltage of 230 V and a frequency of 50 Hz, that is it completes one cycle 50 times per second. Peak Value and Quoted (Effective) Value of A.C. A d.c. supply provides a constant ‘push’ to the charges as they move around a circuit whereas the a.c. supply does not as the voltage is continually varying. The voltage for an alternating supply varies from zero to the peak value to zero to the peak value in the reverse direction and so on. V in Volts V in Volts Effective voltage Time (milliseconds) Varying a.c. supply Time (milliseconds) Steady d.c. supply The peak value of voltage for an alternating supply cannot be used as a measure of its effective voltage as the voltage is only at that peak value for a short space of time. The effective voltage of an a.c. supply is less than the peak value. For example, an alternating supply with a peak value of 10 V does not supply the same power to a circuit as a direct supply of 10 V, in fact it is less, approximately 7 V. The effective value of current and voltage in an a.c. circuit is measured using a.c. meters in the circuit. The peak value of voltage in an a.c. circuit can be measured using an oscilloscope. Voltage and Potential Difference (p.d.) The voltage or potential difference (often referred to as the p.d.) of the supply is a measure of the energy given to the charges in a circuit. Units Voltage (p.d.) has the symbol V and is measured in volts, V. Force Fields In Physics, a field means a region where an object experiences a force without being touched. For example, there is a gravitational field around the Earth. This attracts masses towards the earth’s centre. Magnets cause magnetic fields and electric charges have electric fields around them. Electric Fields In an electric field, a charged particle will experience a force. We use lines of force to show the strength and direction of the force. The closer the field lines the stronger the force. Field lines are continuous - they start on positive and finish on negative charge. The direction is taken as the same as the force on a positive “test” charge placed in the field. Electric Field Patterns Positive point charge Negative point charge + test charge has a force ‘outwards’ + test charge has a force ‘inwards’ These are called radial fields. The lines are like the radii of a circle. The strength of the field decreases as we move away from the charge. Electric Field Pattern Positive and negative point charges Circuit Symbols Circuit symbols are used in electrical circuits to represent circuit components or devices to make them easier to draw and understand. Some of the circuit symbols that you will need to know are shown below. A V ammeter voltmeter resistor cell variable resistor battery (of cells) fuse lamp switch Series and Parallel Circuits Components in a circuit can be connected in series or parallel. A series arrangement of components is where they are in-line with each other, that is connected endto-end. Series A parallel arrangement of components is where they are connected across each other where the current has more than one path through that part of the circuit. Parallel Measuring Current and Potential Difference or Voltage Electric current is measured using an ammeter which is connected in series with the component. Potential difference (p.d.), or voltage, is measured using a voltmeter which is connected in parallel with the component. Measuring the current through the lamp A Measuring the voltage (p.d.) across the lamp V Current and Potential Difference or Voltage in Series Circuits The current is the same at all points in a series circuit. The sum of the potential differences across the components in a series circuit is equal to the voltage of the supply. VS I IA C I B IA = IB = IC V1 V2 VS = V1 + V2 Current and Potential Difference or Voltage in Parallel Circuits The potential difference across components in parallel is the same for all components. The sum of the currents in parallel branches is equal to the current drawn from the supply. IS V1 A IA I V2 V1 = V2 IS = IA + I B B Electrical Resistance Resistance is a measure of the opposition of a circuit component to the flow of charge or current through that component. The greater the resistance of a component, the less will be the current through that component. All normal circuit components have resistance and the resistance of a component is measured using the relationship R= V or R = resistance V = potential difference (voltage) V=IR I I = current Resistance is measured in ohms, Ω. Potential difference (or voltage) is measured in volts, V. Current is measured in amperes, A. This relationship is known as Ohm’s Law, named after a German physicist, Georg Ohm. For components called resistors, the resistance remains approximately constant for different values of current therefore the ratio V/I (= R) remains constant for different values of current. A V Example Calculate the resistance of the resistor in the diagram opposite. Ensure that all quantities are stated in the correct units. R=? V=5V I = 200 mA = 0.2 A R= V = 5 = 25 Ω I 0.2 Ohmmeter Another way of measuring resistance is to use an Ohmmeter. The symbol for an ohmmeter is Ω To connect an ohmmeter only the meter and the measured device are used. There is no need for a power supply. E.g. To measure the resistance of a resistor Ω Resistors in Series When more than one component is connected in series, the total resistance of all the components is equivalent to one single resistor, RT, calculated using the relationship RT = R1 + R2 + R3 For the following circuit with three components in series, is equivalent to R1 R2 R3 RT The above relationship is true for two or more components connected in series. Resistors in Parallel When more than one component is connected in parallel, the total resistance of all the components is equivalent to one single resistor, RT, calculated using the relationship 1 1 RT = R1 1 1 + R2 + R3 Example 1 Components in series Calculate the total resistance of the circuit opposite. R1 = 10 Ω R2 = 50 Ω RT = R1 + R2 + R3 R3 = 25 Ω RT = 10 + 50 + 25 = 85 Ω 10 Ω 50 Ω 25 Ω Example 2 Components in parallel Calculate the total resistance of the components above when connected in parallel. R1 = 10 Ω R2 = 50 Ω R3 = 25 Ω 1 R T 1 R 1 + 1 R 2 + 1 R = 3 = 1 RT Note: = 1 10 5 50 RT 8 50 = 50 therefore = 8 1 + + 1 50 1 50 + + 1 25 2 50 = 8 50 RT = 6.5 Ω For components in series, RT is always greater than the largest resistance. For components in parallel, RT is always less than the smallest resistance. Temperature and Resistance As the temperature of a conductor increases, its resistance increases. When a conductor is heated, the atoms vibrate with greater amplitude. This makes it more difficult for electrons to move through the material so resistance increases. Electrical Components Name Photovoltaic cell Symbol Fuse Function Also known as a solar cell, converts light energy to electrical energy Thin piece of wire designed to melt (and break the circuit) when a certain current passes through it. Used as a safety device Current can only flow through a diode in one direction Can store charge, used in timing circuits Diode Capacitor Thermistor Temperature dependant resistor. Temperature increases, resistance decreases Temperature decreases, resistance increases (Note that this is different from most conductors as stated above) Light Dependant resistor Light level increases, resistance decreases Light level decreases, resistance increases LDR The Light Emitting Diode (LED) LEDs operate at much lower voltages and currents then conventional bulbs and will therefore require a protective resistor in series to limit the current. The LED is a diode and therefore will only allow current to flow in one direction. To operate it must be connected as shown below. +ve -ve Voltage Dividers A voltage divider does exactly as its name suggests - it divides a supply voltage across two resistors which are connected in series. The two resistors may have fixed values or one may be a LDR, a thermistor or other input device. The supply voltage is divided in the ratio of the resistances in the voltage divider For the voltage divider shown: ELECTRICAL ENERGY In the earlier section on potential difference, it was stated that the potential difference of the supply is a measure of the energy given to the charges in the circuit. The energy carried by these charges around the circuit is then converted to other forms of energy by the components in the circuit. Electrical components are devices that change or transform the electrical energy from the supply to the circuit into other forms of energy. If energy is supplied to the charges in the circuit, then an electric current exists and there is an energy transformation in each of the components in the circuit. Examples An electric lamp is designed to emit light energy. This happens because the electric current passing through the filament causes it to get hot; hot enough to glow and emit light. A lamp therefore transforms electrical energy to heat and light energy. An electric bar fire works in a similar way. The bar of the fire is made from a length of resistance wire similar to the filament of a lamp. The resistance wire is designed to get hot when a current passes through it. It also glows when it is hot, but not as much as the filament of the lamp. Energy Units Electrical energy, like all forms of energy, has the symbol E and is measured in joules, J. Power and Energy To compare different components, it is often useful to compare the rate at which energy is transformed, that is the energy transformed each second. This electrical energy transformed each second is known as the power. E P= t or E=Pt P = power E = energy t = time Units Power is measured in watts, W. Energy is measured in joules, J. Time is measured in seconds, s. 1 watt is equivalent to the transfer of 1 joule per second. Example If an electric fire uses 1.8 MJ of energy in a time of 10 minutes, calculate the power output of the fire. Ensure that all quantities are stated with the correct units. P=? 6 E = 1.8 MJ = 1.8 x10 J P= t = 10 min = 600 s E t = 1.8 x 10 600 6 = 3000 W Power Current and Voltage Electrical power is also dependent on the potential difference across the component and the current through it. If 1 volt across a component pushes a current of 1 ampere, then the power will be 1 watt. P = power in watts V = voltage or potential difference in volts I = current in amperes P=IV Example A 230 V toaster draws a current of 4 A from the mains supply. Calculate the power output of this toaster. P=? V = 230 V P = V I = 230 4 = 920 W I =4A More Power Equations Using the equation P = I V and Ohm’s Law equation V = I R, we are able to obtain - V IR P I ( IR ) P I 2R V I R V P V R V2 P R Example A component data book states that a 1 kΩ resistor can safely handle a power output of 0.4 W. a) What is the maximum current it can safely handle? b) What potential difference would exist across the resistor at this current? a)I = ? P = 0.4 W R = 1 kΩ = 1000 Ω b)V = ? P = 0.4 W R = 1000 Ω I = 0.02 A P 2 I =R = 0.4 4 1000 = 4x10- I = 0.02 A 2 V =PR = 0.4 x 1000 = 400 or V =IR = 0.02 x 1000 V = 20 V V = 20 V HEAT Heat is a measure of the average kinetic energy of the particles in a substance. Temperature is a measure of the quantity of heat energy in a substance. Can be measured in C or Kelvin. Specific Heat Capacity The specific heat capacity of a substance is the amount of heat energy required to change the temperature of 1 kg of a substance by 1 C. Specific heat capacity is calculated using the formula: heat transferred Eh = cm t change in temperature mass of material specific heat capacity Units The unit for specific heat capacity is the joule per kilogram degree celsius (J/kg C). The specific heat capacity shows that the same mass of different materials requires different quantites of energy to raise their temperature of unit mass by one degree Celsius. Example When a kettle containing 2 kg of water (specific heat capacity 4200 J/kg C) cools from 40 C to 20 C, calculate the heat given out by the water. m = 2 kg T 2 = 40 C Eh = ? c = 4200 J/kg C T = 20 C Eh = cm T = 4200 x 2 x (40 – 20) = 168000 J or 168 kJ 1 GAS LAWS Pressure Pressure on a surface is defined as the force acting normal (perpendicular) to the surface. p = pressure in pascals, Pa F p= F = normal force in newtons, N A A = area in square metres, m2 1 pascal is equivalent to 1 newton per square metre; ie 1 Pa = 1 N m-2. Example Calculate the pressure exerted on the ground by a truck of mass 1600 kg if each wheel has an area of 0.02 m2 in contact with the ground. Total area A = 4 × 0.02 = 0.08 m2 Normal force F = weight of truck = mg = 1600 × 9.8 = 15680 N p=? F = 15680 N A = 0.08 m2 p= F A = 15680 0.08 = 196,000 Pa or 196 kPa Kinetic Theory of Gases The kinetic theory tries to explain the behaviour of gases using a model. The model considers a gas to be composed of a large number of very small particles which are far apart and which move randomly at high speeds, colliding elastically with everything they meet. Volume The volume of a gas is taken as the volume of the container. The volume occupied by the gas particles themselves is considered so small as to be negligible. Temperature The temperature of a gas depends on the kinetic energy of the gas particles. The faster the particles move, the greater their kinetic energy and the higher the temperature. Pressure The pressure of a gas is caused by the particles colliding with the walls of the container. The more frequent these collisions or the more violent these collisions, the greater will be the pressure. Relationship Between Pressure and Volume of a Gas For a fixed mass of gas at a constant temperature, the pressure of a gas is inversely proportional to its volume. pα1 V p × V = constant p1 V1 = p2 V2 Graph 0 0 Example The pressure of a gas enclosed in a cylinder by a piston changes from 80 kPa to 200 kPa. If there is no change in temperature and the initial volume was 25 litres, calculate the new volume. p1 = 80 kPa p1 V1 = p2 V2 V1 = 25 litres 80 × 25 = 200 × V2 p2 = 200 kPa V2 = 10 litres V2 = ? Relationship Between Pressure and Temperature of a Gas If a graph is drawn of pressure against temperature in degrees celsius for a fixed mass of gas at a constant volume, the graph is a straight line which does not pass through the origin. When the graph is extended until the pressure reaches zero, it crosses the temperature axis at -273 oC. This is true for all gases. Kelvin Temperature Scale -273oC is called absolute zero and is the zero on the kelvin temperature scale. At a temperature of absolute zero, 0 K, all particle motion stops and this is therefore the lowest possible temperature. One division on the kelvin temperature scale is the same size as one division on the celsius temperature scale, i.e. temperature differences are the same in kelvin as in degrees celsius, e.g. a temperature increase of 10°C is the same as a temperature increase of 10 K. Note the unit of the kelvin scale is the kelvin, K, not degrees kelvin, °K! Converting Temperatures Between °C and K Converting °C to K add 273 Converting K to °C subtract 273 If the graph of pressure against temperature is drawn using the kelvin temperature scale, zero on the graph is the zero on the kelvin temperature scale and the graph now goes through the origin. For a fixed mass of gas at a constant volume, the pressure of a gas is directly proportional to its temperature measured in kelvin (K). pT p = constant T p1 p = 2 T1 T2 Example Hydrogen in a sealed container at 27 °C has a pressure of 1.8 × 105 Pa. If it is heated to a temperature of 77 °C, what will be its new pressure? p1 = 1.8 × 105 Pa T1 = 27 °C = 300 K p2 = ? T2 = 77 °C = 350 K p2 = 2.1 × 105 Pa Relationship Between Volume and Temperature of a Gas If a graph is drawn of volume against temperature, in degrees celsius, for a fixed mass of gas at a constant pressure, the graph is a straight line which does not pass through the origin. When the graph is extended until the volume reaches zero, again it crosses the temperature axis at -273 °C. This is true for all gases. If the graph of volume against temperature is drawn using the kelvin temperature scale, the graph now goes through the origin. For a fixed mass of gas at a constant pressure, the volume of a gas is directly proportional to its temperature measured in kelvin (K). V T V = constant T V1 V = 2 T1 T2 Example 400 cm3 of air is at a temperature of 20 °C. At what temperature will the volume be 500 cm3 if the air pressure does not change? V1 = 400 cm3 T1 = 20 °C = 293 K V2 = 500 cm3 T2 = ? V1 V = 2 T1 T2 400 500 = 293 T2 T2 = 366 K = 93 °C (convert back to temperature scale in the question) Combined Gas Equation By combining the above three relationships, the following relationship for the pressure, volume and temperature of a fixed mass of gas is true for all gases. pV = constant T p 1 V1 p 2 V2 = T1 T2 Example A balloon contains 1.5 m3 of helium at a pressure of 100 kPa and at a temperature of 27 °C. If the pressure is increased to 250 kPa at a temperature of 127 °C, calculate the new volume of the balloon. p1 = 100 kPa V1 = 1.5 m3 100 1.5 200 V2 = T1 = 27 °C = 300 K 300 400 p2 = 250 kPa V2 = ? V2 = 0.8 m3 T2 = 127 °C = 400 K Gas Laws and the Kinetic Theory of Gases Pressure - Volume (constant mass and temperature) Consider a volume V of gas at a pressure p. If the volume of the container is reduced without a change in temperature, the particles of the gas will hit the walls of the container more often (but not any harder as their average kinetic energy has not changed). This will produce a larger force on the container walls. The area of the container walls will also reduce with reduced volume. As volume decreases, then the force increases and area decreases resulting in, from the definition of pressure, an increase in pressure, i.e. volume decreases hence pressure increases and vice versa. Pressure - Temperature (constant mass and volume) Consider a gas at a pressure p and temperature T. If the temperature of the gas is increased, the kinetic energy and hence speed of the particles of the gas increases. The particles collide with the container walls more violently and more often. This will produce a larger force on the container walls. As temperature increases, then the force increases resulting in, from the definition of pressure, an increase in pressure, i.e. temperature increases hence pressure increases and vice versa. Volume - Temperature (constant mass and pressure) Consider a volume V of gas at a temperature T. If the temperature of the gas is increased, the kinetic energy and hence speed of the particles of the gas increases. If the volume was to remain constant, an increase in pressure would result as explained above. If the pressure is to remain constant, then the volume of the gas must increase to increase the area of the container walls that the increased force is acting on, i.e. volume decreases hence pressure increases and vice versa.