1. Induction and Alternating Current
Alternating Current, Generators, and Motors

2. 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

3. 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

4. Generators and Alternating Current

5. Generators and Alternating Current

6. 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

7. Generators and Alternating Current

8. 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

9. 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

10. 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

11. 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

12. 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

13. Generators and Alternating Current

14. 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

15. Generators and Alternating Current

16. Generators and Alternating Current

17. Generators and Alternating Current

18. 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

19. Motors