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

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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 11 Contents Initial Problem Statement 2 Narrative 3-6 Notes 7-9 Appendices 10-11

2 The AC Transformer Initial Problem Statement The generators used in power stations to turn mechanical motion into 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 in 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 11

3 Narrative Introduction Discussion Why do you think high voltage AC is more efficient for long-distance transmission? A transformer makes use of an effect called mutual induction 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 input coil; this is where our input voltage is applied. The applied voltage is V in volts and the coil has N in turns of wire. The right-hand coil is the called the output coil and this is where the transformed voltage is recovered for use. The ratio of the voltage levels in the input and output coils is related to the number of turns in the input and output coils through the expression V V in out Activity 1 N = N in out You wish to change a voltage in an AC circuit from the 230 V supplied by a standard domestic socket to 5 V required to charge a mobile phone. (The ratio of V in to V out is therefore 230:5.) What is the ratio of N in to N out? Give your answer as a simplified fraction and also in the form as x:1. Activity 2 If N in = 460 turns how many turns will be on the output, N out? The AC Transformer page: 3 of 11

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 11

5 2. What if the number of turns isn t an integer? Activity 3 You wish to change a voltage in an AC circuit from the 230 V supplied by a standard domestic socket to 5 V required to charge a mobile phone. If N in = 520 turns how many turns will be on the output, N out? Discussion What does a fractional number of turns mean? Can you have a fractional turn? Activity 4 What would the error in V out be if N out was rounded to the nearest whole number of turns? Would this be acceptable? Discussion Suppose the transformed voltage had to be exactly 5V. How could you achieve this? The AC Transformer page: 5 of 11

230 V? Give your answer as x:1 with x given to the nearest integer.

6 3. UK power line transmission In the UK high voltage transmission is made at 400 kv while household usage is 230 V. Activity 5 If the high voltage is the input voltage what is the ratio of the number of input turns to output turns to produce 230 V? Give your answer as x:1 with x given to the nearest integer. Discussion WARNING: The above transmission supply is 400 kv, 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 11

7 Notes 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 during transmission. Generation and distribution companies seek to minimise this loss to improve efficiency. The power loss, P loss, in the cable is proportional to the square of the current flowing, 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 flowing through the cable is determined by the voltage potential of the supply, V, and the total power delivered by the power station, P, such that P= IV For a fixed power station supply the power delivered, P, is fixed so that the product of I and V is fixed. This means that if the current of a given source is reduced the voltage must increase. Similarly if the current of a given source is increased 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 maintaining the product of the current and voltage (assuming no transformer losses). In addition to reducing losses a high voltage/low current transmission supply requires thinner cables as the required cable diameter is proportional to the current carried. For domestic supply the voltage is reduced and the current increased. 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 arcing is reduced but still maintained at 230 V to obtain 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 11

8 Notes Converting 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 using diodes which only allow current to flow in 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 in the supply. This is improved with full-wave rectification in which the negative half of the AC cycle contributes to the DC: The AC Transformer page: 8 of 11 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 11

Appendix 1 using the interactives The AC Transformer Interactive This resource tests your knowledge of the relationship between the voltage and the number of turns in a transformer.

10 Appendix 1 using the interactives The AC Transformer Interactive This resource tests your knowledge of the relationship between the voltage and the number of turns in a transformer. You can choose which variable you would like to find by selecting 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 missing value. Enter your answer in the appropriate empty box. If you have chosen to find a voltage, enter your answer to 2 decimal places. If you are finding the number of coils, enter an integer value. You can check your answer by clicking on the Check button in the bottom right-hand corner. If your answer is correct, then the question will reset, providing you with another problem. If the answer you have given is wrong, then the box will clear and you will be able to try again. The AC Transformer page: 10 of 11

11 Appendix 2 mathematical coverage Use and apply mathematical modelling to solve engineering problems The engineering problem is quantified using mathematical expressions Use algebra to solve engineering problems Be able to solve problems involving 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: 11 of 11

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

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