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Electricity and Magnetism 29 Alternating Currents and Power Transmission Chapter 29 Alternating Currents and Power Transmission

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Electricity and Magnetism 29 Alternating Currents and Power Transmission 29.1 Alternating current In a direct current (d.c.) circuit, electric current flows in one direction only. Alternating currents and alternating voltages

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Electricity and Magnetism 29 Alternating Currents and Power Transmission In an alternating current (a.c.) circuit, current reverses its direction periodically. In general, a.c. are produced by alternating e.m.f.s (voltages) from a.c. sources. Square waveform Sinusoidal waveform

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Electricity and Magnetism 29 Alternating Currents and Power Transmission A sinusoidal alternating voltage can be expressed as where V 0 is its peak value and is its angular frequency. The angular frequency is related to the frequency f and the period T of the voltage by V = V 0 sin t V0V0 −V0−V0

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Electricity and Magnetism 29 Alternating Currents and Power Transmission Resistive circuit In a purely resistive circuit, V and I are in phase. Example 29.1 Checkpoint (p.418) V = V 0 sin tI = I 0 sin t

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Electricity and Magnetism 29 Alternating Currents and Power Transmission However, what we really concern is the average power of an a.c. supplied to a resistive load, which is given by where the symbol denotes the time-average of the enclosed quantity. Root-mean-square (r.m.s.) values Experiment 29.1 Applying P = VI, for sinusoidal voltage and current, the instantaneous power supplied to the load is P = V 0 I 0 sin 2 t

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Electricity and Magnetism 29 Alternating Currents and Power Transmission For a sinusoidal voltage, we have The root-mean-square (r.m.s.) value of a current I is defined as Hence, for sinusoidal voltages, we have. Since, we have R.m.s. values of alternating currents of square waveform

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Electricity and Magnetism 29 Alternating Currents and Power Transmission In other words, The average power can be expressed in the following forms: For sinusoidal alternating currents and voltages, we have The root-mean-square (r.m.s.) value of an a.c. is the steady d.c. which delivers the same average power as the a.c. to a resistive load. Example 29.2 Checkpoint (p.423)

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Electricity and Magnetism 29 Alternating Currents and Power Transmission 29.2 Transformer A transformer is a device that can change the value of an alternating voltage. A transformer for notebook computers Substations contain a lot of transformers.

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Electricity and Magnetism 29 Alternating Currents and Power Transmission A change in current through a coil induces a voltage in another nearby coil due to the change in magnetic field through the latter coil. This effect is called mutual induction. Structure and working principle of a simple transformer

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Electricity and Magnetism 29 Alternating Currents and Power Transmission The primary coil of a transformer is connected to an a.c. source and the secondary coil gives the output voltage. If the magnetic flux through each turn of the coils in a transformer is the same, there is perfect flux linkage (i.e. no flux leakage) between the coils.

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Electricity and Magnetism 29 Alternating Currents and Power Transmission The voltage ratio and turns ratio of a transformer, with perfect flux linkage and negligible coil resistance, are related by Voltages and currents in transformers Experiment 29.2

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Electricity and Magnetism 29 Alternating Currents and Power Transmission Apply Faraday’s law, the alternating magnetic flux through the coils induce e.m.f.s in the coils. With the iron core, the magnetic flux through each turn of the two coils is the same.

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Electricity and Magnetism 29 Alternating Currents and Power Transmission For a step-up transformer, N s > N p, and so V s > V p. For a step-down transformer, N s < N p, and so V s < V p. The efficiency of a transformer can be expressed as Transformer

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Electricity and Magnetism 29 Alternating Currents and Power Transmission An ideal transformer has 100% efficiency. For such a transformer, we have Since, we have Hence, for an ideal transformer, whenever the voltage is stepped up (or stepped down), the current through the secondary coil decreases (or increases) by the same factor. Example 29.3 Checkpoint (p.431) Example 29.4

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Electricity and Magnetism 29 Alternating Currents and Power Transmission Transformers have very high efficiency, but are never ideal. Energy loss in transformers and practical transformer designs improvements made in practical transformers reasons for energy loss use high-quality magnetic materials to make the core continuous magnetization and demagnetization of the iron core use thick copper wires to make the coils resistance in the coils

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Electricity and Magnetism 29 Alternating Currents and Power Transmission improvements made in practical transformers reasons for energy loss use a laminated core eddy currents in the iron core Checkpoint (p.433)

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Electricity and Magnetism 29 Alternating Currents and Power Transmission 29.3 Transmission and distribution of electricity One of the problems in transmitting electricity is the power loss in the transmission lines due to the heating effect of current. Overhead transmission lines Power loss in transmission lines

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Electricity and Magnetism 29 Alternating Currents and Power Transmission If a transmission line carries a current I and has a resistance R, the power dissipated as heat is given by The lower the current, the lower the power dissipated. Using transformers, a.c. voltage can be stepped up easily and efficiently, and the current can be stepped down accordingly. Hence, alternating current is used to transmit mains electricity in order to reduce the power loss. P = I 2 R Experiment 29.3 Overhead transmission lines Example 29.5

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Electricity and Magnetism 29 Alternating Currents and Power Transmission A grid system is a transmission and distribution network of mains electricity. Grid system in Hong Kong

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Electricity and Magnetism 29 Alternating Currents and Power Transmission The voltage of the electricity generated at a power station is stepped up before transmission and stepped down successively at substations in populated areas. Checkpoint (p.441) Schematic diagram of the grid system in Hong Kong Birds on transmission lines

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