 Induction and Alternating Current

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Induction and Alternating Current
Alternating Current, Generators, and Motors

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 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
Since alternating current is constantly reversing, maximum current and emf values are not as useful as they are in direct current Of more importance are instantaneous and root-mean-square (rms) values Rms current – the amount of direct current that dissipates as much energy in a resistor as an instantaneous alternating current does during a complete cycle An equivalent value allowing for accurate comparisons between alternating and direct current Power can be calculated by using the appropriate rms values in the equations given previously

Generators and Alternating Current
Potential Difference Current Instantaneous values v i Maximum values Vmax Imax rms values Vrms=Vmax/√2 = 0.707*Vmax Irms = Imax/√2 = 0.707*Imax

Generators and Alternating Current
Power = rms current squared * resistance Power = one-half * maximum current squared * resistance P = (Irms)2R = ½(Imax)2R Ohm’s law still applies in ac circuits Rms potential difference = rms current * resistance Vrms = Irms*R

Generators and Alternating Current
Sample problem: A generator with a maximum output emf of 205V is connected to a 115 resistor. Calculate the rms potential difference. Find the rms current through the resistor. Find the maximum ac current in the circuit. Vmax = 205V R = 115 Vrms = ? Irms = ? Imax = ? Vrms = .707*Vmax Irms = Vrms / R Irms = .707*Imax

Generators and Alternating Current

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 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

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. 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