6.2 Transformer and high-voltage transmission Caution! High voltage! Induction between two coils Working principle of a transformer Check-point 4 Voltage ratio Currents in a transformer Improving efficiency of transformers Check-point 5 High voltage transmission of electrical energy Power loss in transmission cable Check-point 6 1 2 3 4 5 6 7 Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Caution! High voltage! You may have seen a similar warning sign: Where can you find it? Why is there a high voltage in that place? Book 4 Section 6.2 Transformer and high-voltage transmission

1 Induction between two coils Recall: a voltage is induced across a coil if a magnet is moved towards or away from it (Lenz’s law). A changing current through a nearby coil can produce the same effect — even no movement is involved. Transformer makes use of this effect. Expt 6c Simple transformer Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Experiment 6c Simple transformer Wind 10 turns of wire round a C-core and 25 turns of wire round another C-core. Clip them together. Connect the 10-turn coil to a switch and a battery, and 25-turn coil to centre- zero galvanometer. Close the switch and then open it. Observe the effect on the galvanometer. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Experiment 6c Simple transformer Connect the 10-turn coil to an a.c. power supply and the 25-turn coil to a lamp. Connect another lamp to the a.c. supply. Switch on the supply and compare the brightness of lamps. Change the 25-turn coil to coils of other no. of turns. Observe how the brightness of lamp changes. Video 6.3 Expt 6c - Simple transformer Book 4 Section 6.2 Transformer and high-voltage transmission

1 Induction between two coils In Expt 6c, when the switch in the primary coil (10-turn coil) is closed, the pointer of the galvanometer in the secondary coil (25-turn coil) deflects momentarily to one side. when the switch is open, the pointer deflects momentarily to the other side. There is no deflection when the switch is left closed or open. Book 4 Section 6.2 Transformer and high-voltage transmission

1 Induction between two coils Changing current in one coil  produce an induced current in another coil  mutual inductance Book 4 Section 6.2 Transformer and high-voltage transmission

1 Induction between two coils When the switch is closed, a B-field builds up and ‘cuts’ through secondary coil. By Lenz’s law, a current is induced and flows as to oppose the build-up of field lines.  Pointer deflects momentarily to one side. Book 4 Section 6.2 Transformer and high-voltage transmission

1 Induction between two coils Then, the current becomes steady.  B-field stays unchanged  no voltage induced Pointer returns to 0. Book 4 Section 6.2 Transformer and high-voltage transmission

1 Induction between two coils When switch is open, B-field decays in C-cores.  Current is induced and flows as to oppose the decay of B-field  pointer deflects momentarily to other side Simulation 6.1 Mutual inductance Book 4 Section 6.2 Transformer and high-voltage transmission

2 Working principle of a transformer In Expt 6c, when the primary coil is connected to an a.c. supply, the lamp in secondary coil is lit continuously.  brighter than that in primary coil  larger voltage across the secondary coil than across the primary coil. Book 4 Section 6.2 Transformer and high-voltage transmission

2 Working principle of a transformer When an a.c. flows through the primary coil, magnetic field lines around the core change continuously.  induces alternating voltage in the secondary coil. The a.c. induced in the secondary coil has the same frequency as that in the primary coil Book 4 Section 6.2 Transformer and high-voltage transmission

2 Working principle of a transformer Primary + secondary coils + core  transformer When an a.c. flows through the primary coil, electrical energy is transferred continuously from the primary to the secondary circuit. Ideal transformer: 100% energy (or power) transfer Practical transformer: energy loss (or a power loss) during transfer efficiency = useful output power total input power  100% Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 4 – Q1 An alternating current is flowing in the primary coil. The current is taken as +ve if it flows from X to Y. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 4 – Q1 (a) Primary coil’s current Time duration 0–t1 t2–t3 Primary coil’s B-field direction (clockwise/anticlockwise) anticlockwise Primary coil’s B-field (increasing/decreasing) increasing Secondary coil’s B-field direction (clockwise/anticlockwise) clockwise Secondary coil’s current direction (P to Q / Q to P ) P to Q clockwise increasing anticlockwise Q to P Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 4 – Q1 (b) Is the current induced in secondary coil a direct current or an alternating current? Alternating current. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 4 – Q2 When S is closed, light bulb flashes once. What should be done to make the bulb light continuously? A More cells are required. B The cell should be replaced by a.c. source. C Solenoid P or Q should have more turns. D Use an iron core to link up the solenoids. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission 3 Voltage ratio As long as all B-field lines go through both coils, the ratio of voltages in them depends only on their number of turns. This is true for transformers of any efficiency. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission 3 Voltage ratio = Primary voltage Secondary voltage no. of turns in primary coil no. of turns in secondary coil Vp Vs Np Ns Turns ratio: primary turns to secondary turns By choosing suitable no. of turns for coils, an a.c. voltage can be stepped up or down.  a transformer can transform an a.c. voltage Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission 3 Voltage ratio A step-up transformer (Vs > Vp) has more turns in secondary coil than in primary coil (Ns > Np). It is used in a power station for stepping up voltage to 400 kV for transmission by cables to users. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission 3 Voltage ratio A step-down transformer (Vs < Vp) has fewer turns in secondary coil (Ns < Np). It is used to, for example, supply 16 V to a notebook computer from the mains. Simulation 6.2 Simple transformer Expt 6d Measuring the voltage ratio of a transformer Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Experiment 6d Measuring the voltage ratio of a transformer Make up a transformer. Apply 1-V a.c. from a low voltage power supply across the primary coil. Connect the CRO across the primary coil. Switch off the time base and measure the length of vertical trace. Repeat step 2 with the secondary coil. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Experiment 6d Measuring the voltage ratio of a transformer Note: For a dual-trace CRO, connect channel 1 across the primary coil and channel 2 the secondary coil to display their waveforms together. Or use voltage sensors and data-logger to measure the primary and secondary voltages from the scope display. Book 4 Section 6.2 Transformer and high-voltage transmission

Experiment 6d Measuring the voltage ratio of a transformer Video Video 6.4 Expt 6d - Measuring the voltage ratio of a transformer Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission 3 Voltage ratio Example 4 Turns ratio vs voltage ratio Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 4 Turns ratio vs voltage ratio The primary and secondary waveforms for Expt 6d: Scale = 0.5 V / division Calculate the voltage ratio of transformer and compare it with turns ratio. Are they the same? Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 4 Turns ratio vs voltage ratio Vp = 0.5  2 = 1 V Vs = 0.5  4 = 2 V Vp Vs = Voltage ratio = 0.5 = Np Ns Turns ratio = 10 25 = 0.4 Voltage ratio > turns ratio (∵ not all field lines from the primary coil cut the secondary coil). Book 4 Section 6.2 Transformer and high-voltage transmission

4 Currents in a transformer Without power lost, all power supplied to the primary coil is transferred to the secondary.  total input power = useful output power  VpIp = VsIs = Vp Vs Is Ip  = Ip Is Ns Np (if no power loss) = Vp Vs Np Ns By , Book 4 Section 6.2 Transformer and high-voltage transmission

4 Currents in a transformer A step-down transformer: turns ratio = 20 : 1 The voltage is reduced from 220 V to 11 V. Without power loss, Is = 10 A With power loss, Is < 10 A Example 5 Currents in the coils of transformer Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 5 Currents in the coils of transformer An ideal transformer (3300 turns in primary coil) operates a ‘12 V, 24 W’ lamp from the 220-V a.c. mains. Assume: no power loss in the transformer. (a) Number of turns in secondary coil = ? = Vp Vs Np Ns  Ns =  Np Vs Vp =  3300 12 220 = 180 The secondary coil has 180 turns. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 5 Currents in the coils of transformer (b) Current in secondary coil = ? Current taken by the lamp I = P V = 24 12 = 2 A  The current in secondary coil is 2 A. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 5 Currents in the coils of transformer (c) Current in primary coil = ? Assume: no power loss VpIp = VsIs  Ip =  Is Vs Vp =  2 12 220 = 0.109 A The primary current is 0.109 A. Book 4 Section 6.2 Transformer and high-voltage transmission

4 Currents in a transformer Example 6 Why is a transformer preferred Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 6 Why is a transformer preferred A ‘12 V, 24 W’ lamp is connected in series with a resistor to the 220-V a.c. mains. The resistor enables the lamp to be operated at 12 V. (a) Current drawn from the mains = ? = P V = 24 12 Current I = 2 A The current drawn from the mains is 2 A. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 6 Why is a transformer preferred (b) Resistance of resistor = ? The resistor has to take up 208 V, leaving 12 V for the lamp. R = V I = 208 2 = 104  (c) Power supplied by the mains = ? Power supplied by the mains = total input power = VI = 220  2 = 440 W Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 6 Why is a transformer preferred (d) Efficiency in supplying power to the lamp = ? Power to lamp = useful power output = 24 W Efficiency = useful output power total input power  100% = 24 440  100% = 5.45% (e) Why is a transformer preferred to a resistor in ‘stepping down’ a voltage? The power loss can be greatly reduced. Book 4 Section 6.2 Transformer and high-voltage transmission

5 Improving efficiency of transformers In practical transformers, some energy supplied to the primary coil is lost as heat. Reasons for energy loss: 1. Resistance of coils ∵ coils have resistance ∴ heated when currents flow through Solution: Use thick wires for the coil Book 4 Section 6.2 Transformer and high-voltage transmission

5 Improving efficiency of transformers 2. Magnetization and demagnetization of core ∵ Magnetization & demagnetization need energy ∴ Heat is given out Solution: Use soft iron to make the core (∵ easily magnetized and demagnetized) Book 4 Section 6.2 Transformer and high-voltage transmission

5 Improving efficiency of transformers Induced currents in the core ∵ the core lies in a changing B-field ∴ eddy currents induced  heating effect Solution: Use a laminated core (made from electrically insulated thin sheets of soft iron  high resistance) Book 4 Section 6.2 Transformer and high-voltage transmission

5 Improving efficiency of transformers The transformer is a very efficient device. Well-designed transformers can have efficiency > 90%. The low voltage power supply in the school laboratory contains a special transformer. The secondary coil can be tapped at different points to give different voltages. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 5 – Q1 The transformer of a mobile phone: Turns ratio and the efficiency of the transformer = ? Turns ratio = no. of turns in primary coil no. of turns in secondary coil primary voltage secondary voltage = = 230 4.8 = 47.9 Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 5 – Q1 Efficiency = useful output power total input power  100% = 4.8  0.35 230  0.05  100% = 14.6% Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 5 – Q2 An ideal transformer is used to operate a lamp rated at ‘8 V, 12 W’: What is the current in the secondary coil? Is = P V = 12 8 = 1.5 A Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 5 – Q3 An ideal transformer is used to operate a lamp rated at ‘8 V, 12 W’: What is the current in the primary coil? = Ip Is Ns Np  Ip =  Is Ns Np =  1.5 100 2500 = 0.06 A Book 4 Section 6.2 Transformer and high-voltage transmission

6 High voltage transmission of electrical energy Electrical energy generated at a power station is transmitted over great distances. Transmission cables are made of copper (very good conductor). However, the resistance of a long cable is still large. How to reduce power loss (I 2R)? Expt 6e The model power line Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Experiment 6e The model power line Set up the model power line. Switch on the 12 V d.c. power supply and compare the brightness of the two lamps. Repeat by using a 12 V a.c. power supply. Note any difference in brightness between the two lamps. Book 4 Section 6.2 Transformer and high-voltage transmission

Experiment 6e The model power line 3. Step up the 12 V a.c. at the ‘station’ end and step it down at the ‘consumer’ end by transformers. Compare the brightness of the lamps. Video 6.5 Expt 6e - The model power line Book 4 Section 6.2 Transformer and high-voltage transmission

7 Power loss in transmission cable Expt 6e: For the first two cases, the lamp at ‘station’ is brightly lit, but that at ‘consumer’ end is dimly lit due to the power loss in ‘cables’. However, by using transformer, the ‘consumer’ lamp is almost as bright as the ‘station’ lamp. Stepping up V  Stepping down I ∴ Power loss (I 2R ) in the cables is reduced. Book 4 Section 6.2 Transformer and high-voltage transmission

7 Power loss in transmission cable Power loss in transmission can be reduced if the electricity is transmitted at a high voltage. A.c. is used to transmit electrical power. ∵ Voltage of a.c. can be stepped up and stepped down easily Example 7 Power loss in cables Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 7 Power loss in cables 4 kW of power is transmitted through cables of total resistance 5 . Calculate the power loss in the cables if it is transmitted at (a) 200 V, (b) 4000 V. What can you conclude from the results? Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 7 Power loss in cables (a) Power transmitted at 200 V: = P V Current through cables = 4000 200 = 20 A  power loss in cables = I 2R = 202  5 = 2000 W Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 7 Power loss in cables (b) Power transmitted at 4000 V: = P V = 4000 Current through cables = 1 A  power loss in cables = I 2R = 12  5 = 5 W The power loss in the cables is much reduced by transmitting the power at a high voltage. Book 4 Section 6.2 Transformer and high-voltage transmission

7 Power loss in transmission cable Example 8 Electric supply to MTR Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 8 Electric supply to MTR CLP Power supplies power to MTR at 33 kV a.c. Transformer substations are built every 4 to 5 km along the railway line to step down the voltage to 1.5 kV a.c. The 1.5 kV a.c. is then converted to d.c. and passed through the overhead cables to drive the traction motors on the MTR trains. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 8 Electric supply to MTR (a) Why are so many transformer substations built on the railway line? If only one substation were built to supply power to the entire railway line, there would be considerable power loss in the cables. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 8 Electric supply to MTR (b) What turns ratio for the transformers is needed for converting 33 kV to 1.5 kV? = Np Ns Vp Vs = 33 1.5 = 22  The turns ratio = 22 : 1 Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 8 Electric supply to MTR (c) The peak value of 33 kV a.c. is 25.7 A. Assume: no power loss in conversion of a.c. to d.c. and transformer is 100% efficient. (i) Equivalent d.c. flowing in the primary coil of transformer = ? Equivalent d.c. = r.m.s. value of a.c. = I0 2 = 25.7 2 = 18.2 A Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Example 8 Electric supply to MTR (c) (ii) Current in the overhead cable = ? Current Np Ns =  Ip = 22  18.2 = 400 A (iii) Power supplied by the secondary coil of the transformer = ? Power supplied = VI = 1500  400 = 600 kW Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 6 – Q1 What is the function of a district substation in the transmission network? A To generate electricity B To step down voltage C To step down current Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 6 – Q2 The power loss in transmission can be reduced if the electricity is transmitted at a ( low / high ) voltage. Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission Check-point 6 – Q3 3420 MW of electrical power is transmitted at 275 kV. If resistance of cable = 5 , power loss in cable = ? Current flowing along the cable = P V = 3420  106 275  103 = 12 436 A Power loss in the cable = I 2R = 12 4362  5 = 773 MW Book 4 Section 6.2 Transformer and high-voltage transmission

Book 4 Section 6.2 Transformer and high-voltage transmission The End Book 4 Section 6.2 Transformer and high-voltage transmission