In Grade 11 you learnt how a magnetic field is generated around a current carrying conductor. You also learnt how a current is generated in a conductor that moves in a magnetic field. This chapter describes how conductors moving in a magnetic field are applied in the real-world.
We have seen that when a conductor is moved in a magnetic field or when a magnet is moved near a conductor, a current flows in the conductor. The amount of current depends on the speed at which the conductor experiences a changing magnetic field, the number of turns of the conductor and the position of the plane of the conductor with respect to the magnetic field. The effect of the orientation of the conductor with respect to the magnetic field is illustrated in Figure 1.
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If the current flowing in the conductor were plotted as a function of the angle between the plane of the conductor and the magnetic field, then the current would vary as shown in Figure 2. The current alternates about zero and is known as an alternating current (abbreviated AC).
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Recall Faraday's Law which you learnt about in Grade 11:
The emf (electromotive force),
where
Faraday's Law relates induced emf (electromotive force) to the rate of change of flux, which is the product of the magnetic field and the cross-sectional area the field lines pass through. As the closed loop conductor changes orientation with respect to the magnetic field, the amount of magnetic flux through the area of the loop changes, and an emf is induced in the conducting loop.
The principle of rotating a conductor in a magnetic field is used in electrictrical generators. A generator converts mechanical energy (motion) into electrical energy.
A generator converts mechanical energy into electrical energy.
The layout of a simple AC generator is shown in Figure 3. The conductor in the shape of a coil is connected to a slip ring. The conductor is then manually rotated in the magnetic field generating an alternating emf. The slip rings are connected to the load via brushes.
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If a machine is constructed to rotate a magnetic field around a set of stationary wire coils with the turning of a shaft, AC voltage will be produced across the wire coils as that shaft is rotated, in accordance with Faraday's Law of electromagnetic induction. This is the basic operating principle of an AC generator.
In an AC generator the two ends of the coil are each attached to a slip ring that makes contact with brushes as the coil turns. The direction of the current changes with every half turn of the coil. As one side of the loop moves to the other pole of the magnetic field, the current in the loop changes direction. The two slip rings of the AC generator allow the coil to turn without breaking the connections to the load circuit. This type of current which changes direction is known as alternating current.
AC generators are also known as alternators. They are found in motor cars to charge the car battery.
A simple DC generator is constructed the same way as an AC generator except that there is one slip ring which is split into two pieces, called a commutator, so the current in the external circuit does not change direction. The layout of a DC generator is shown in Figure 4. The split-ring commutator accommodates for the change in direction of the current in the loop, thus creating direct current (DC) current going through the brushes and out to the circuit.
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The shape of the emf from a DC generator is shown in Figure 5. The emf is not steady but is the absolute value of a sine/cosine wave.
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The problems involved with making and breaking electrical contact with a moving coil are sparking and heat, especially if the generator is turning at high speed. If the atmosphere surrounding the machine contains flammable or explosive vapors, the practical problems of spark-producing brush contacts are even greater.
If the magnetic field, rather than the coil/conductor is rotated, then brushes are not needed in an AC generator (alternator), so an alternator will not have the same problems as DC generators. The same benefits of AC over DC for generator design also apply to electric motors. While DC motors need brushes to make electrical contact with moving coils of wire, AC motors do not. In fact, AC and DC motor designs are very similar to their generator counterparts. The AC motor is depends on the reversing magnetic field produced by alternating current through its stationary coils of wire to make the magnet rotate. The DC motor depends on the brush contacts making and breaking connections to reverse current through the rotating coil every 1/2 rotation (180 degrees).
The basic principles of operation for a motor are the same as that of a generator, except that a motor converts electrical energy into mechanical energy (motion).
An electric motor converts electrical energy into mechanical energy.
If one were to place a moving charged particle in a magnetic field, it would feel a force called the Lorentz force.
The Lorentz force is the force experienced by a moving charged particle in a magnetic field and can be described by:
where
Current in a conductor consists of moving charges. Therefore, a current carrying coil in a magnetic field will also feel the Lorentz force. For a straight current carrying wire which is not moving:
where
The direction of the Lorentz force is perpendicular to both the direction of the flow of current and the magnetic field and can be found using the Right Hand Rule as shown in the picture below. Use your right hand; your thumb points in the direction of the current, your first finger in the direction of the magnetic field and your third finger will then point in the direction of the force.
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Both motors and generators can be explained in terms of a coil that rotates in a magnetic field. In a generator the coil is attached to an external circuit that is turned, resulting in a changing flux that induces an emf. In a motor, a current-carrying coil in a magnetic field experiences a force on both sides of the coil, creating a twisting force (called a torque, pronounce like 'talk') which makes it turn.
Any coil carrying current can feel a force in a magnetic field. The force is the Lorentz force on the moving charges in the conductor. The force on opposite sides of the coil will be in opposite directions because the charges are moving in opposite directions. This means the coil will rotate, see the picture below:
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Instead of rotating the loops through a magnetic field to create electricity, a current is sent through the wires, creating electromagnets. The outer magnets will then repel the electromagnets and rotate the shaft as an electric motor. If the current is AC, the two slip rings are required to create an AC motor. An AC motor is shown in Figure 8
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If the current is DC, split-ring commutators are required to create a DC motor. This is shown in Figure 9.
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A car contains an alternator that charges its battery and powers the car's electric system when its engine is running. Alternators have the great advantage over direct-current generators of not using a commutator, which makes them simpler, lighter, less costly, and more rugged than a DC generator.
Try to find out the different ampere values produced by alternators for different types of machines. Compare these to understand what numbers make sense in the real world. You will find different numbers for cars, trucks, buses, boats etc. Try to find out what other machines might have alternators.
A car also contains a DC electric motor, the starter motor, to turn over the engine to start it. A starter motor consists of the very powerful DC electric motor and starter solenoid that is attached to the motor. A starter motor requires a very high current to crank the engine, that's why it's connected to the battery with large cables.
AC generators are mainly used in the real-world to generate electricity.
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Most students learning about electricity begin with what is known as direct current (DC), which is electricity flowing in a constant direction. DC is the kind of electricity made by a battery, with definite positive and negative terminals.
However, we have seen that the electricity produced by some generators alternates and is therefore known as alternating current (AC). The main advantage to AC is that the voltage can be changed using transformers. That means that the voltage can be stepped up at power stations to a very high voltage so that electrical energy can be transmitted along power lines at low current and therefore experience low energy loss due to heating. The voltage can then be stepped down for use in buildings and street lights.
In South Africa alternating current is generated at a frequency of 50 Hz.
The circuit symbol for alternating current is:
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Graphs of voltage against time and current against time for an AC circuit are shown in Figure 13
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In an ideal DC circuit the current and voltage are constant. In an AC circuit the current and voltage vary with time. The value of the current or voltage at any specific time is called the instantaneous current or voltage and is calculated as follows:
The average value we use for AC is known as the root mean square (rms) average. This is defined as:
Since AC varies sinusoidally, with as much positive as negative, doing a straight average would get you zero for the average voltage. The rms value by-passes this problem.
Capacitors and inductors are found in many circuits. Capacitors store an electric field, and are used as temporary power sources as well as to minimize power fluctuations in major circuits. Inductors work in conjunction with capacitors for electrical signal processing. Here we explain the physics and applications of both.
You have learnt about capacitance and capacitors in Grade 11.
In this section you will learn about capacitance in an AC circuit. A capacitor in an AC circuit has reactance. Reactance in an AC circuit plays a similar role to resistance in a DC circuit. The reactance of a capacitor
where
If we examine the equation for the reactance of a capacitor, we see that the frequency is in the denominator. Therefore, when the frequency is low, the capacitive reactance is very high. This is why a capacitor blocks the flow of DC and low frequency AC because its reactance increases with decreasing frequency.
When the frequency is high, the capacitive reactance is low. This is why a capacitor allows the flow of high frequency AC because its reactance decreases with increasing frequency.
Inductance (measured in henries, symbol H) is a measure of the generated emf for a unit change in current. For example, an inductor with an inductance of 1 H produces an emf of 1 V when the current through the inductor changes at the rate of 1 A
An inductor is a passive electrical device used in electrical circuits for its property of inductance. An inductor is usually made as a coil (or solenoid) of conducting material, typically copper wire, wrapped around a core either of air or of ferromagnetic material.
Electrical current through the conductor creates a magnetic flux proportional to the current. A change in this current creates a change in magnetic flux that, in turn, generates an emf that acts to oppose this change in current.
The inductance of an inductor is determined by several factors:
The inductance of a solenoid is defined by:
where
Permeability is the property of a material which describes the magnetisation developed in that material when excited by a source.
The permeability of free space is
Determine the inductance of a coil with a core material of air. A cross-sectional area of
Calculate the inductance of a 5 cm long solenoid with a diameter of 4 mm and 2000 turns.
An inductor in an AC circuit also has a reactance,
where
If we examine the equation for the reactance of an inductor, we see that inductive reactance increases with increasing frequency. Therefore, when the frequency is low, the inductive reactance is very low. This is why an inductor allows the flow of DC and low frequency AC because its reactance decreases with decreasing frequency.
When the frequency is high, the inductive reactance is high. This is why an inductor blocks the flow of high frequency AC because its reactance increases with increasing frequency.
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This work is licensed by Rory Adams, Free High School Science Texts Project, and Heather Williams under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.
Last edited by Free High School Science Texts Project on Jul 6, 2011 3:20 am -0500.
