Induction and Alternating Current

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


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 = 2f




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 = ?

= 2f emfmax = NAB I=emf / R



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


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


Potential Difference

Current

Instantaneous values v iMaximum values Vmax Imax

rms values Vrms=Vmax/√2 = 0.707*Vmax

Irms = Imax/√2 = 0.707*Imax


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


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



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




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

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Induction and Alternating Current