Design an experiment to predict and test the output from a simple AC generator.

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Christopher Barr                        November 2004

Design an experiment to predict and test the output from a simple AC generator

 

Design an experiment to predict and test the output from a simple AC generator.

Planning

A simple ac generator will produce an alternating emf of magnitude V0 and frequency f.

The AC generator is shown below,

 

A manufacturer of AC generators has asked you to help design a clockwork torch of peak power 1W. The bulb is powered by a hand driven AC generator that is rotated at 2Hz. It is assumed that the light bulb has a constant resistance once in use because it doesn't have time to cool down as the current alternates. The manufacturer has provided you with a horseshoe magnet of approximate field strength 50mT and gap 20cm, a selection of commercially available reels of copper wire of different diameters and the light bulb. The rest of the material necessary to build the generator is provided by the school. The coil ABCD is square.

Using classroom apparatus you must plan experiments to;

a] Determine the unknown properties of the magnet, copper wire and bulb.

b] Test the final constructed version.

You will need to find the relevant Physics to explain,

1] The factors affecting the peak emf in an ideal generator and how these can be measured.

2] The factors affecting the peak current in an ideal generator and how these can be measured.

You will need to carry out research into;

i] Commercially available bulbs and wire to give reasonable relevant values for calculations.

ii] Methods for determining magnetic field strengths.

Design

Emf is the electromotive force and is the ‘driving’ force behind electrical circuits. EMF or E for short is sometimes referred to as the voltage of the cell or the power supply. E is measured in volts (V) just as voltage however voltage is mainly regarded as a measure of how much energy each coulomb looses around the circuit. E is regarded as the energy each coulomb gains when passing through a power supply.


Emf can be induced into a wire through movement of that wire in a magnetic field.

In this example the magnetic field is out of the page. One of the fundamental properties of a magnetic field is that when a charged particle moves at right angles to the field it feels a force at right angles to the movement of itself and the magnetic field. All matter is composed of atoms which themselves contain protons electrons and neutrons. The electrons are negatively charged, protons positively charged and the neutrons have zero charge. Therefore as the wire itself is composed of atoms when it moves through the magnetic field a subatomic force is exerted on it. Using the renowned Flemings left hand rule the directions of the magnetic field (B), Current (I) and Force (F) can be found. In a conducting wire such as the wire above the particles that are free to move are the electrons. Metallic bonding is described as positively charged ions suspended in a sea of delocalised electrons

The positive ions are fixed in place and the electrons are delocalised. This means they can move from atom to atom in a random way. However if a force acts on it or a current flows the movement is no longer random and there is a ‘net movement of electrons or charge. Charge is a measurement of electrons measured in coulombs. One single electron has a charge of 1.6x10-19C so in one coulomb there are 6.25x1018 electrons.

So in the example above as the wire moves to the right so do the atoms in the wire. Conventional current flows in the opposite direction to electron flow so the current (in relation to the way the electrons in the wire move as the wire is moved) is to the left. This means using Flemings left hand rule the force the electrons feel is downward. This makes the lower end of the wire negatively charged and the upper end electron deficient, or positively charged. As the wire is in a circuit this set’s up a current and an emf is induced into the wire this current flows from the upper end of the wire to the lower end or anti-clockwise around the circuit indicated by I on the diagram.

The formula linking Emf magnetic field strength and current is not directly related to those quantities. Current is a measure of how many coulombs pass a particular point in a particular time. The amount of coulombs passing the point is going to be linked to the length of the wire in the magnetic field not to current directly. Like wise as current is the rate of coulomb flow the rate of change of distance of the length of wire in the magnetic field is also going to be linked. Speed is a measure of rate of change o distance so it is linked in the formula as well. Therefore emf can be calculated using

E=Blv

Where E is the emf, B is the magnetic field strength, l is the length of the wire in the magnetic field and v is the speed at which the wire moves through the magnetic field.

The units of emf are volts as it is a measure of energy per coulomb and the definition of a volt is 1 volt is such that when 1 joule is transferred to or from 1 coulomb.

An AC generator like what is necessary for the purpose of the torch is constructed by placing a coil of wire in a magnetic field. As the coil rotates the lengths of wire cross the magnetic field lines and an emf is induced in each wire. There are two wires that have motion perpendicular to the field direction in the diagram below, AB and CD.

         B        C

        Direction of

               Magnetic field

          A        D

The problem arises in a generator if the two emf producing lengths cancel each other because if the did then no emf would be produced. Using Flemings left hand rule the charges in AB are A is negative and B is positive. In CD the charges are C is negative and D is positive. This means the wires act as power supplies depicted below and therefore compliment each other.

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As there are two sides of the coil in the magnetic field and indeed breaking field lines then the formula can be adjusted from E=Blv to take into account the length is twice as long. Also the coil can have any number of turns. This means that another modification can be made to take into account the fact that the number of turns is a multiplier of length. Therefore for an AC generator with number of turns (N) the formula for induced emf is

E=2BlvN

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