Generators and Alternating Current If one end of a magnet is moved in and out of a coil of wire, the induced voltage alternates in direction. The greater the frequency with which the magnet moves in and out, the greater the induced voltage. The frequency of the induced alternating voltage equals the frequency with which the magnet is moved in and out. Rather than moving the magnet, it is more practical to move the coil. This is best accomplished by rotating the coil in a stationary magnetic field. This arrangement is called a generator. As the loop rotates, the number of magnetic field lines passing through the loop changes (thus changing the magnetic field strength inside the loop). For exactly half of one rotation, the number of field lines passing through the loop will be increasing. This will generate a voltage in one direction. For the remaining half of the rotation, the number of field lines passing through the loop will be decreasing, producing a voltage in the opposite direction. The voltage induced by the generator alternates, and the current produced is alternating current (AC). The current changes magnitude and direction periodically (60 times per second in North America).
Plotting voltage versus time for a typical AC generator will result in a sinusoidal graph, such as the one shown below. The amount of voltage produced by an AC generator can be changed by: 1. Rotating the coil at a different speed. rotating faster will produce a larger voltage 2. Changing the number of loops in the coil. more loops will result in a larger voltage (twice as many loops will result in twice as much voltage) 3. Changing the area of the loops in the coil. a larger coil will produce a larger voltage It is important to emphasize that an energy source of some kind is needed to turn the coil of wire. In Manitoba, for example, we use turbines (propellers) spun by water to rotate the coils of wire. The mechanical energy of the water gets converted into electrical energy.
Transformers One of the most important applications of electromagnetic induction takes place in a transformer. A transformer is a device that increases or decreases an AC voltage. For example, when cordless appliances are plugged into a wall receptacle to recharge the batteries, a transformer reduces the 120 V AC voltage to a much smaller value (typically 3 V to 9 V ) needed to recharge the batteries. The diagram below shows a simple transformer. The transformer consists of an iron core on which two coils are wound: a primary coil with turns, and a secondary coil with N s turns. The primary coil is connected to an AC generator. The secondary coil is connected to an external circuit. The alternating current in the primary coil establishes a changing magnetic field in the iron core. Because iron is easily magnetized, it greatly enhances the magnetic field and guides the field lines to the secondary coil. In a well designed core, nearly all of the magnetic field lines that pass through the primary coil also pass through the secondary coil. Since the field is changing, the field passing through the two coils is also changing, and consequently a voltage is induced in both coils. Voltages may be stepped up or stepped down with a transformer. If the secondary coil has more turns than the primary coil, the voltage will increase (step up). If the secondary coil has less turns than the primary coil, the voltage will decrease (step down). The exact relationship between primary and secondary voltages with respect to the number of turns in each coil is primary voltage number of primary turns = secondary voltage number of secondary turns
This is more commonly written as V s V p = N s This is called the transformer equation. The ratio N s the transformer. is referred to as the turns ratio of There is also a similar equation relating the current in the secondary and the current in the primary, as shown below. I p I s = N s Notice that a transformer that steps up the voltage simultaneously steps down the current, and a transformer that steps down the voltage steps up the current. Example 1 A step-down transformer inside a stereo receiver has 330 turns in the primary coil and 25 turns in the secondary coil. The plug connects the primary coil to a 120 V wall socket, and there is a current of 0.83 A in the primary coil while the receiver is turned on. Connected to the secondary coil are the transistor circuits of the receiver. Find (a) the voltage across the secondary coil, (b) the current in the secondary coil, and (c) the average electrical power delivered to the transistor circuits.
Induction Worksheet 1. The batteries in a portable CD player are recharged by a unit that plugs into a wall socket. Inside the unit is a step-down transformer with a turns ratio of 1 13. The wall socket provides 120 V. What voltage does the secondary coil of the transformer provide? ( 9.2 V ) 2. In some places, insect zappers, with their blue lights, are a familiar sight on a summer night. These devices use a high voltage to electrocute insects. One such device uses an AC voltage of 4320 V, which is obtained from a standard 120 V outlet by means of a transformer. If the primary coil has 21 turns, how many turns are in the secondary coil? (756) 3. Electric doorbells found in many homes require 10 V to operate. To obtain this voltage from the standard 120 V supply, a transformer is used. Is a step-up or step-down transformer needed, and what is the turns ratio N s? (step-down, 1 12 ) 4. A step-down transformer (turns ratio = 1 8 ) is used with an electric train to reduce the voltage from the wall receptacle ( 120 V ) to a value needed to operate the train. When the train is running, the current in the secondary coil is 3.4 A. What is the current in the primary coil? ( 0.425 A) 5. The secondary coil of a step-up transformer provides the voltage that operates an electrostatic air filter. The turns ratio of the transformer is 43 1. The primary coil is plugged into a standard 120 V outlet. The current in the secondary coil is 1.5 10 3 A. Find the power consumed by the air filter. ( 7.7 W ) 6. In a television set the power needed to operate the picture tube is 95 W and is derived from the secondary coil of a transformer. There is a current of 5.3 ma in the secondary coil. The primary coil is connected to a 120 V receptacle. Find the turns ratio N s of the transformer. (149 1)