Trial version. The AC Transformer. How is a transformer designed to change the voltage from one given level to another? Teacher.

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1 The AC Transformer How is a transformer designed to change the voltage from one given level to another? The AC Transformer page: 1 of 15 Contents Initial Problem Statement 2 arrative 3-6 otes 7-9 Solutions Appendices 14-15

2 The AC Transformer Initial Problem Statement The generators used power stations to turn mechanical motion to electrical power generate high voltage AC electricity. AC electricity is used as it has the advantage over DC electricity that it can be easily transformed from high voltage, which is more efficient for long-distance transmission, to a lower voltage that is more suitable for use the home and elsewhere. To change the voltage a device called a transformer is used. How is a transformer designed to change the voltage from one given level to another? The AC Transformer page: 2 of 15

3 arrative Introduction Discussion Why do you thk high voltage AC is more efficient for long-distance transmission? A transformer makes use of an effect called mutual duction and can be schematically drawn as a soft-iron core around which two coils of wire are wrapped, see below. Figure 1. The left-hand coil is called the put coil; this is where our put voltage is applied. The applied voltage is volts and the coil has turns of wire. The right-hand coil is the called the put coil and this is where the transformed voltage is recovered for use. The ratio of the voltage levels the put and put coils is related to the number of turns the put and put coils through the expression Activity 1 = You wish to change a voltage an AC circuit from the 230 supplied by a standard domestic socket to 5 required to charge a mobile phone. (The ratio of to is therefore 230:5.) What is the ratio of to? Give your answer as a simplified fraction and also the form as x:1. Activity 2 If = 460 turns how many turns will be on the put,? The AC Transformer page: 3 of 15

4 Multimedia The resource The AC Transformer Interactive is available to demonstrate the turn and voltage ratios of a transformer. Discussion What if your mobile phone needs direct current (DC) to charge? The AC Transformer page: 4 of 15

5 2. What if the number of turns isn t an teger? Activity 3 You wish to change a voltage an AC circuit from the 230 supplied by a standard domestic socket to 5 required to charge a mobile phone. If = 520 turns how many turns will be on the put,? Discussion What does a fractional number of turns mean? Can you have a fractional turn? Activity 4 What would the error be if was rounded to the nearest whole number of turns? Would this be acceptable? Discussion Suppose the transformed voltage had to be exactly 5. How could you achieve this? The AC Transformer page: 5 of 15

6 3. UK power le transmission In the UK high voltage transmission is made at 400 k while household usage is 230. Activity 5 If the high voltage is the put voltage what is the ratio of the number of put turns to put turns to produce 230? Give your answer as x:1 with x given to the nearest teger. Discussion WARIG: The above transmission supply is 400 k, i.e. 400,000 volts! Is the ratio you have calculated sensible for a design? How could you improve the design? The AC Transformer page: 6 of 15

7 otes Why use high voltage to transmit electricity? A power cable delivers electrical power from a power station to the end-users (houses, factories, shops, etc.). Some fraction of the power generated is lost durg transmission. Generation and distribution companies seek to mimise this loss to improve efficiency. The power loss, P loss, the cable is proportional to the square of the current flowg, I, and the resistance of the cable, R: P I R loss = 2 For a given cable of fixed resistance, R, the power loss, P loss, is reduced when the current, I, is reduced. The current flowg through the cable is determed by the voltage potential of the supply,, and the total power delivered by the power station, P, such that P= I For a fixed power station supply the power delivered, P, is fixed so that the product of I and is fixed. This means that if the current of a given source is reduced the voltage must crease. Similarly if the current of a given source is creased the voltage must decrease. This is precisely what a transformer does. It changes one voltage and current level to another voltage and current level, while matag the product of the current and voltage (assumg no transformer losses). In addition to reducg losses a high voltage/low current transmission supply requires thner cables as the required cable diameter is proportional to the current carried. For domestic supply the voltage is reduced and the current creased. Each household only draws a fraction of the total power, P, so the current supplied is limited. The voltage level is chosen such that the danger of electrical arcg is reduced but still mataed at 230 to obta efficient transmission and reduced power cable diameters. Further transformation of the voltage may be required for domestic items such as televisions, games consoles, mobile phone chargers etc. Such items draw a limited power so that the current required is reasonably small. The AC Transformer page: 7 of 15

8 otes Convertg AC to DC Many domestic items not only require a reduced supply voltage but also a direct current (DC). To do this the AC is rectified, typically usg diodes which only allow current to flow one direction. The simplest form of rectification is called half-wave rectification which supplies only the positive half of the AC source: Figure 2. This has obvious gaps the supply. This is improved with full-wave rectification which the negative half of the AC cycle contributes to the DC: The AC Transformer page: 8 of 15 Figure 3.

9 This DC source still shows a significant variation of voltage (although it is never negative) which would be unsuitable for most domestic DC items. To improve the design further electronic components are used to filter and smooth the supply to give: Figure 4. The AC Transformer page: 9 of 15

10 Solutions Introduction Activity 1 solution High voltage AC is more efficient as it mimises energy loss durg transmission. From the expression so that See "Why use high voltage to transmit electricity? on page 7. =, the ratio : is exactly the same as : = = = = 46 : Activity 2 solution The ratio : is 46:1. To obta this you require: Rearrangg: = = 1 1 = 1 = = = Discussion solution If your mobile phone needs direct current (DC) to charge then you need to convert the AC to DC usg a rectifier circuit. See "Convertg AC to DC" on pages 8-9. The AC Transformer page: 10 of 15

11 2. What if the number of turns isn't an teger Activity 3 solution From =, 230 = = 46 : 1 5 The ratio : must also be 46:1 Rearrangg: = = = = = = ( 2 d.p. ) Discussion solution.. The fractional part means that the wire the coil does not make a full loop. Instead it leaves the transformer, this case ab one third of the way around! This might not be convenient for manufacturg and stead the nearest whole number of turns may be made. In this case the ratio : is given by = The AC Transformer page: 11 of 15

12 Activity 4 solution To fd with this ratio you use expression 520 = = 11 =, You know that = 230 so Rearrangg = = = 520 Discussion solution = 487. ( ) ( 2d.p. ) The absolute error is 0.13 under which would probably be tolerable by most devices. If the DC voltage supply had to be controlled more tightly then a regulated transformer would be used. This would transform the mas AC to a value greater than 5 for all allowable supply variations then use a voltage regulator to limit the DC delivered to 5. ote, the value will change as the supply voltage is not exactly 230. In the UK the tolerance is %, -6%, i.e. the range to 253. This will lead to subsequent variations on the transformed value. The AC Transformer page: 12 of 15

13 3. UK power le transmission Activity 5 solution Aga, usg expression =, 400, 000 = = = 1739 : Discussion solution This ratio shows that an enormous number of coils would be required on the put coil compared with the put coil which would make an efficient transformer large. In practice the voltage on the supply grid is stepped down more gradual steps for local distribution. For example, for urban distribution the voltage is stepped down to 11 k. This gives a coil ratio of ab 48:1. The AC Transformer page: 13 of 15

14 Appendix 1 usg the teractives The AC Transformer Interactive This resource tests your knowledge of the relationship between the voltage and the number of turns a transformer. You can choose which variable you would like to fd by selectg one of the options at the bottom of the screen. If you select Random then the variable to be found will be selected at random. Figure 5. The computer supplies three known variables and you must calculate the missg value. Enter your answer the appropriate empty box. If you have chosen to fd a voltage, enter your answer to 2 decimal places. If you are fdg the number of coils, enter an teger value. You can check your answer by clickg on the Check button the bottom right-hand corner. If your answer is correct, then the question will reset, providg you with another problem. If the answer you have given is wrong, then the box will clear and you will be able to try aga. The AC Transformer page: 14 of 15

15 Appendix 2 mathematical coverage Use and apply mathematical modellg to solve engeerg problems The engeerg problem is quantified usg mathematical expressions Use algebra to solve engeerg problems Be able to solve problems volvg ratio and proportion Be able to give numerical answers to a specified number of decimal places Change the subject of a formula The AC Transformer page: 15 of 15