Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Contents Introduction 3 Energy 4 Conservation of Energy 4 Work 5 Power 7 Power in electric circuits 9 Power rating of equipment 9 Calculating electrical power in resistive circuits 12 Other power equations 14 Resistive Loads 16 Measurement of electrical energy 17 Summary 22 Answers 23 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 1 2 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Introduction Energy is the fundamental quantity that allows changes to occur. The concept of work allows us to measure the amount of energy by mechanical definition. Power is the rate at which energy is delivered, or the rate at which work is done. In an electrical circuit, voltage can do work by moving charges around the circuit against a resistance. Electrical power in a resistive circuit is equal to voltage times current. After completing this topic, you should be able to: describe the relationships between energy, work and power calculate the power dissipated in a circuit from voltage, current and resistance values explain the meaning of power ratings of devices. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 3 Energy Without energy, nothing could happen. Whenever you see movement, sound, heat or light, there is energy. The SI unit of energy is the joule, and the unit symbol is 'J'. The joule is a very small quantity of energy, so more common units are the kilojoule (kJ) and the megajoule (MJ). Energy can exist in many forms, and we can convert energy from one form to another. Consider the following manifestations of energy: energy in sunlight allows plants to live chemical energy in food allows animals to live chemical energy in fuels powers industry electrical energy is present wherever you measure a voltage or current. Conservation of Energy The Law of Conservation of Energy says that energy is 'conserved'. This means that energy cannot be created or destroyed, but can be changed from one form to another. Technology has many examples of conversion of energy, including: 4 Solar cells convert sunlight into electrical energy. The chemical energy of coal or natural gas is converted to electrical energy at the power station. Electrical energy is converted to heat energy in a microwave. Electrical energy is converted to electromagnetic energy in a radio transmitter. Batteries convert chemical energy into electrical energy. Light emitting diodes convert electrical energy into light energy. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Notes: 1. The conservation law has had to be slightly modified in modern times, because we now know that mass can be converted into energy and vice versa. Small amounts of mass are converted to enormous amounts of energy in nuclear power stations and nuclear weapons. 2. All energy eventually ends up as heat, which is dissipated into the environment and cannot be recovered. So while energy cannot be ‘destroyed’, it cannot always be converted into a useful form for our use. In addition, our machines cannot use all the energy present in an energy source, and there will always be some wastage or loss. Work The concept of work gives us a very straightforward definition to determine an amount of energy. Work is done when a force moves a body through a distance. The work done is given by: work force distance or in symbols: W Fd where: W = work (joule) F = force in (newton) d = distance (metre) Work has the same units as energy, and we can say that energy is the capacity to ‘do work’. Work is signified by the letter 'W'. Note that 'work' is a scientific term with a very specific meaning — it does not mean people doing work in the everyday sense of the term. However, when doing physical work, people are also doing some amount of work in this technical sense. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 5 Example 6 A force of 600 N is required to move a body against frictional forces. The body is moved 2 m. Determine the work done. F d W W 600 N 2m ? Fd 600 2 1200 J The work done in moving the body is 1200 J. 6 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Power Power is the rate of doing work, or equivalently, the rate of producing or expending energy. The symbol for power is P, and the unit is the watt (W). When energy is consumed at the rate of one joule per second, the power is one watt. Power can be illustrated by the fact that it may take several hours to dig a trench with hand tools, but an engine-driven backhoe could do the same job in a few minutes. We say the machine is more powerful, because it delivers much more energy in the same period of time. As power is the rate of doing work we can say that power is work per unit time, or in symbols: P W t where: P = power (watt) W = work (joule) t = time (second) Don’t confuse the ‘W’ used here for watt with the ‘W’ used for ‘work’. When dealing with small or large quantities we make use of the milliwatt, the kilowatt, and the megawatt: megawatt (MW) = 1 000 000 W kilowatt (kW) = 1000 W milliwatt (mW) = 0.0001 W Example 7 If the energy required to raise a certain mass to the top of a building is 5000 J, determine the output power rating of an electric motor required to do the work in: (a) 30 s (b) 15 s. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 7 Solution W = 5000 J (a) t P 30 s ? W P T 5000 30 166.7 W (b) t 15 s P ? W P T 5000 15 333.3 W The power required to do the work in 30 s is 166.7 W and the power required to do the work in 15 s is 333.3 W. If you have Hampson, read the ‘Power, work and energy’ section on page 5 through to page 12, taking note how the equations are used. If you have Jenneson, refer to Section 2.9, ‘Electrical power and on page 35 for brief summary of key issues. 8 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Power in electric circuits When electric current flows through a resistor, electrical energy is converted to heat and leaves the circuit (it is ‘expended’ use ‘used’). For example, current flowing through a lamp causes it to emit light and heat energy. The energy required to light the bulb is provided by the flow of charges through the lamp. The rate at which energy is delivered to a circuit is the power. Another example is the electric motor. The energy delivered to an electric motor is converted to useful mechanical work. A motor that is efficiently converting energy to work behaves like a resistor. The power of an appliance is one of the most important parameters to specify. For example, to boil a litre of water using a 750 W electric jug might take three minutes. To boil the same amount of water using a 1500 W electric jug would take about half that time. Likewise, an air conditioner with insufficient power may fail to maintain a room at a comfortable temperature. Power rating of equipment The power rating of an electrical appliance is important because it determines: the capability of doing the required work, the size of cable required for the current the appliance will draw, the running cost of the appliance. Information relating to the electrical characteristics of an appliance is stamped on a manufacturer’s nameplate which is attached to the appliance. The information always includes the: voltage to which the equipment can be safely connected, both the type (ac/dc) and the value. maximum power the appliance will consume. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 9 Figure 1: A typical electrical nameplate The nameplate in Figure 1 belongs to an electrical stapling machine. The information on it shows that: it is suitable for operation on 200–240 V alternating current with a frequency of 50–60 hertz, its maximum power consumption is 500 W. Electric light globes are a common example. A globe rated at 240 V, 100 W is brighter and costs more to operate than a 240 V, 40 W lamp. Input and output power Lamp wattages refer to the input power. However, this is not always the case. The power rating of electrical equipment may specify either: the input power drawn from the supply, or the output power. The input power of an appliance is usually quoted when it is not practical to quote the output power. Common examples of such equipment are a bread toaster, a hot-water service, a welding machine or a lamp. In these examples electrical energy is being converted to heat, and this represents the ‘final’ state of the energy – the energy will not be converted to another form. It therefore makes sense to simply quote the power used by the device. For industrial equipment such as transformers or motors, the output power is quoted, because this figure is required to make use of the device For example, it is important to know that mechanical output power that is provided by a motor in order to select a motor for a particular job. Note that where the output power is quoted, the electrical power that is actually used will be greater, because of the losses within the device. 10 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Activity 1 1 What is the unit of electric power? _____________________________________________________________________ 2 What can we learn from the power rating of an electrical appliance? _____________________________________________________________________ _____________________________________________________________________ 3 What information is usually given on an appliance nameplate? _____________________________________________________________________ _____________________________________________________________________ 4 If work of 100 J is used to move a body a certain distance in 0.25 s, what power would be required? _____________________________________________________________________ _____________________________________________________________________ 5 What is the relationship between a watt and a milliwatt? _____________________________________________________________________ 6 Define power. _____________________________________________________________________ _____________________________________________________________________ 7 What work is done if a force of 20 N moves a body a distance of 5 m? _____________________________________________________________________ _____________________________________________________________________ Check your answers with those given at the end of the section. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 11 Calculating electrical power in resistive circuits In a resistive circuit, electrical power is determined from the equation: P VI where: V = voltage (volt) I = current (ampere) P = power (watt) To make sense of this equation, we can compare the electrical situation to a water pump that is lifting water uphill. The height through which the water is lifted is similar to the circuit voltage. The flow rate of water is similar to the current. But the power expended depends upon both the amount of liquid pumped, and the height. Example 1 An electric circuit comprises a voltage source of 20 V and a resistance of 5 . Determine the power dissipated by the resistor. First find I: V R 20 5 4A I Draw the complete diagram with all the relevant information. Now: P VI 20 4 80 W 12 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Example 2 If, in the circuit of Example 1, the voltage is doubled determine the power. Again first find I: V R 40 5 8A I P VI 40 8 320 W Note that this answer is four times that of Example 1. That is, when the applied voltage is doubled, the power is increased four times (power is proportional to the voltage squared). Example 3 Determine the power in the circuit of Example 1 if the supply voltage of remains at 20 V but we increase the resistance from to 10 . Again first find I: V R 20 10 2A I P VI 20 2 40 W EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 13 Note that when compared to Example 1, the power is halved. Therefore, we can say when the resistance is doubled the power is halved. In other words, power is inversely proportional to resistance. Other power equations We know from Ohm’s law that: V R and V IR I If we substitute for I or V in the power equation: P VI V V R V2 R P VI IR I I 2R We now have three options when calculating power in resistive circuits. We can use: P VI V2 R P I 2R P If we are given: voltage and current we use equation (a). current and resistance we use equation (b). voltage and resistance we use equation (c). All of the equations will give exactly the same results. It is purely a matter of available information which determines the one you use. 14 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Example 4 Using the original values from Example 1, determine power using all three equations. Given: V = 20 V R=5 I=4A (a) P VI 20 4 80 W (b) P = = (c) P = = = I2R 42 5 80 W V2 R 20 20 5 80 W Example 5 A 300 resistor takes a current of 2 A. Determine the power dissipated by the resistor. P I 2R 22 300 1200 W 1.2 kW EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 15 Example 6 Consider example 5 but with the current increased to 4 A. What power will be dissipated in the resistor? P I 2R 42 300 4800 W 4.8 kW Note: Doubling the current through the same resistance increases the power four times. Example 7 A 3 resistor is connected to a 12 V DC power supply as shown below. Determine the power dissipated by the resistor. V2 R 122 3 48 W P Resistive Loads The above equations can be used to determine the power consumed in a resistive circuit. So for example, it can be used for incandescent lamps, electric radiators or water heaters, which all use resistive elements. Note however that the circuit elements need not be resistors to behave like resistive loads! Any device that simply removes energy from the circuit will look like a resistor to the circuit. For example, electric motors when working a maximum efficiency behave almost like a resistive load. 16 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Measurement of electrical energy The utility that sells you electrical energy must bill you for the amount of energy used. Electrical energy is measured by adding up the power usage over time. Since power is equal to energy used per unit time, it follows that energy is equal to power multiplied by time: energy T energy P T P Thus one joule of energy is expended when a device with a power of one watt operates for one second. (We could also call this amount of energy one 'watt-second'.) In practice, electrical energy is measured by a device called a watt-hour meter or electrodynamometer. The watt-hour meter in your home's main switchboard measures your energy usage by measuring the total power at every instant, and continuously accumulating this over time. Domestic electrical energy usage is therefore quoted as kilowatt-hours (kWh). Kilowatt-hours are the so-called 'units' on your electricity bill. The kilowatt-hour is not an SI unit, so we need to be able to convert to joules for comparison purposes. As there are 3600 seconds in one hour, we have: 1 kilowatt-hour = 3600 kilowatt-second = 3600 kilojoule = 3.6 megajoule. If you have Hampson, read the ‘Electrical power, work and energy’ section on pages 10-12, checking to see how the equations are used. If you have Jenneson, refer to Section 2.9, ‘Electrical power and energy’ on page 35 for brief summary of key issues. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 17 Activity 2 1 When a 50 resistor is connected to a 10 V supply, 200 mA of current flows. Determine the power consumed using each of the three power equations. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 2 What current is taken by a 100 W incandescent lamp when connected to a 240 V supply? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3 What is the resistance of a toaster element if it consumes 900 W from a 240 V supply? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 4 A 240 V electric jug takes 8 A from the supply. What is its power rating? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 5 Across what voltage must a 3.3 k resistor be placed for it to consume 5 W of power? _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Check your answers with those given at the end of the section. 18 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Check your progress 1 A generator is to be lifted vertically to a position nine metres above the ground by means of a crane. If the work done by the crane is 45 kJ, determine the force required. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 2 An electric motor of mass 500 kg is lifted through a height of 10 m. Determine the work done on the motor. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 3 Neatly draw a circuit diagram that shows a 100 resistor connected to a 9 V battery. Include the following in the circuit: (a) a switch controlling current to the resistor (b) an ammeter measuring the current through the resistor (c) a voltmeter measuring the load voltage (d) calculate the current. 4 Using Ohm’s law, fill in the blanks in the table below. Voltage (V) volts Current (I) amperes 30 V 12 V 3 k 40 mA 600 4.8 mA 2.2 330 A 20 V 10 V 12 M 10 A EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Resistance (R) Ohm 19 5 Calculate the resistance of the lamp in the following circuit. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 6 A 24 heating element requires a current of 10 A to produce its specified heat output. Calculate the required supply voltage for this heater. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 7 Calculate the resistance of a resistor that takes 100 mA when connected to a 10 V battery. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 8 Calculate the voltage across a 4.7 k resistor that has 3.5 A passing through it. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 20 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 9 Calculate the power consumed by an electrical appliance that is drawing 5 A from a 240 V supply. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 10 A motor consumes 12 kW when connected to 240 V. Calculate the motor current. _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ 11 A resistance of 30 is connected to an 80 V DC power supply. Determine the: (a) circuit current __________________________________________________________________ __________________________________________________________________ (b) power dissipated by the resistor. __________________________________________________________________ __________________________________________________________________ 12 An electric toaster element has a voltage rating of 240 V and a power rating of 550 W. Determine the: (a) circuit current when the rated voltage is applied to the element __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ (b) resistance of the element. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Check your answers with those given at the end of the section. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 21 Summary Energy is a fundamental quantity that drives change of any kind. Energy comes in many forms, and one form can often be converted to another. Work is done when a force moves its point of application. The unit of work is the joule. Work and energy use the same unit, which is the joule. Power is the rate of doing work. If work is to be done more quickly, more power is required. The unit of power is the watt. Power rating determines work capacity, cable size requirements and running costs. Nameplates usually nominate voltage and power ratings. Power rating can indicate input or output depending on the type of equipment. The SI derived unit of power is the watt. Commonly used multiple and sub-multiple units used for nominating power are: 1 MW = 1 000 000 W = 106 W 1 kW = 1000 W = 103 W 1 mW = 0.001 W = 10-3 W Power may be calculated from any of the following equations. Use the most convenient. P VI P I 2R P 22 V2 R Power is proportional to the current squared. For example twice the current gives four times the power, if the resistance is the same. Power is inversely proportional to the resistance. For example, half the resistance gives twice the power, if the voltage is the same. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 Answers Activity 1 1 The unit of electric power is the watt. 2 Power rating gives us an indication of: 3 capability to do a required amount of work size of cables necessary to wire device cost of running device. Nameplate particulars always include: voltage rating type of voltage: ‘AC’ or ‘DC’ power rating. 4 W 100 J t 0.25 s P ? P W t 100 0.25 400 W The power required to move the body in 0.25 s is 400 W. 5 There are 1000 milliwatt in a watt, or conversely a milliwatt is one thousandth of a watt. 6 Power is the rate of doing work. EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 23 7 F d W W 20 N 5m ? Fd 20 5 100 J So the work done in moving the body is 100 J. Activity 2 1 P VI 10 0.2 2W P I 2R 0.2 2 50 2W V2 R 10 2 50 2W P 2 P VI P I V 100 240 0.417 A 24 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 3 V2 R V2 R P 240 250 900 64 P 4 P VI 240 8 1920 W 5 P PR V2 R V2 V PR V 5 3300 V 16 500 V 128.5 V Check your progress 1 5000 N 2 49 000 J 3 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659 25 P VI 10 0.2 2W P I 2R 4 0.2 2 50 2W Voltage (V) volts Current (I) amperes Resistance (R) Ohm 30 V 0.01 A 3 k 24 V 40 mA 600 0.0106 V 4.8 mA 2.2 12 V 330 A 36 364 20 V 1.67× 10–6.A 12 M 10 V 10 A 1 2 V R 10 2 50 2W P 5 1200 6 240 V 7 100 8 16 450 V 9 1200 W 10 50 A 11 (a) 2.67 A (b) 21.3 W 12 (a) 2.3 A (b) 105 26 EEE042A: 5 Calculate electrical power NSW DET 2017 2006/060/04/2017 LRR 3659