Electromagnetic induction Generators, Motors, and Mutual Inductance

Generators and Alternating Current Generator – a device that uses induction to convert mechanical energy to electrical energy Commonly uses rotational energy by having steam or running water turn a turbine Steam may be generated by a coal or natural gas fire or from geothermal heat sources The rotation of the turbine causes a wire loop to rotate in a magnetic field

Generators and Alternating Current When a loop is parallel to a magnetic field, the charges are perpendicular to the magnetic field Current is maximized, induced emf is maximized When a loop is perpendicular to a magnetic field, the charges are parallel to the magnetic field Current is zero, induced emf is zero Induced emf versus time graphs as a sine curve emf for a generator = number of loops * cross sectional area of the loops * magnetic field strength * angular frequency of rotation of loops * time emf = NABt

Generators and Alternating Current When the loop and the magnetic field are parallel, we may calculate the maximum emf Maximum emf for a generator = number of loops * cross sectional area of the loops * magnetic field strength * angular frequency of rotation of loops emfmax = NAB Angular frequency = 2*pi*frequency  = 2f

Generators and Alternating Current

Generators and Alternating Current

Generators and Alternating Current Sample Problem: A generator consists of exactly eight turns of wire, each with an area A = 0.095m2 and a total resistance of 12. The loop rotates in a magnetic field of 0.55T at a constant frequency of 60.0Hz. Find the maximum induced emf and maximum current in the loop. f = 60.0Hz A = 0.095m2 R = 12 B = 0.55T = 0.55V*s/m2 N = 8 emfmax = ? Imax = ?  = 2f emfmax = NAB I=emf / R

Generators and Alternating Current

Generators and Alternating Current Alternating current (ac) – an electric current that changes direction at regular intervals Typically produced in generators Is reflected in the sinusoidal nature of the graph In the US, Canada, and Central America the current reverses itself at a frequency of 60Hz or 60 reversals/second In Europe and most of Asia and Africa, the frequency is 50Hz

Generators and Alternating Current Alternating current can be converted in to direct current The conducting loop in an ac generator must be free to rotate while remaining part of the circuit at all times The ends of the conducting loop are connected to conducting rings called slip rings that rotate with the loop Connections to the external circuit are made by stationary graphite strips called brushes that stay in contact with the slip rings

Generators and Alternating Current Both the loop current and the output current are continuously changing direction By replacing the two slip rings with a single split slip ring called a commutator, the generator can produce direct current The brushes change halves of the commutator at the same instant the current reverses so there is a double reversal which cancels out leaving the current flowing in a single direction By using multiple loops and commutators, the fluctuations from the individual loops are canceled out resulting in an almost constant output current

Generators and Alternating Current

Generators and Alternating Current

Motors Motors – convert electrical energy into mechanical energy Reverse of a generator Looks much like a dc generator The coil of wire is mounted on a rotating shaft and is positioned between the poles of a magnet. Brushes make contact with a commutator, which alternates the current in the coil. The alternation of current causes the magnetic field produced by the current to regularly reverse and thus always be repelled by the fixed magnetic field.

Motors The coil and shaft are therefore kept in continuous rotational motion Back emf – the emf induced in a motor’s coil that tends to reduce the current powering the motor The induced emf If this did not occur, Lenz’s law would be violated The faster the coil rotates, the greater the back emf The potential difference available to supply current to the motor equals the difference between the applied potential difference and the back emf

Motors

Mutual Inductance Faraday used a two coil system to demonstrate electromagnetic induction Primary circuit is a simple dc circuit with a switch and a wire coil (the primary coil) wrapped around an iron ring Secondary circuit is a wire coil (secondary coil) wrapped around another part of the same iron ring connected to a galvanometer By opening and closing the switch in the primary circuit, an emf is induced in the secondary circuit A steady current will not produce an emf in this manner, only a variable current Faraday’s law can be rewritten for a changing primary current

Mutual Inductance emf = - N * ΔΦM / Δt = -M * ΔI / Δt M is a constant called mutual inductance The ability of one circuit to induce an emf in a nearby circuit in the presence of a changing current The secondary circuit can also induce an emf in the primary circuit Induction of Current by a Fluctuating Current Changing the number of turns in the coil is the basis of the transformer