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20.5 Generators

20.5 Generators. Alternating Current (AC) generator Converts mechanical energy to electrical energy Consists of a wire loop rotated by some external means There are a variety of sources that can supply the energy to rotate the loop

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20.5 Generators

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  1. 20.5 Generators • Alternating Current (AC) generator • Converts mechanical energy to electrical energy • Consists of a wire loop rotated by some external means • There are a variety of sources that can supply the energy to rotate the loop • For example, these may include falling water or heat by burning coal to produce steam

  2. AC Generators, cont. • Basic operation of the generator • As the loop rotates, the magnetic flux through it changes with time • This induces an emf and a current in the external circuit • The ends of the loop are connected to slip rings that rotate with the loop • Connections to the external circuit are made by stationary brushes in contact with the slip rings

  3. AC Generators, cont. Area A=ℓa The emf generated in wire BC is Bℓv where ℓ is the length of the wire and v is the velocity component perpendicular to the B field (vhas no effect on the charges in the wire ).An emf of Bℓv is also generated in the wire DA with the same sense as in BC. Because v=v sinq, the total emf is ε =2Bℓv sinθ.

  4. AC Generators, cont. Since v=rw(tangential speed=radius times angular speed), it follows v=(a/2)w and ε = 2Bℓv sinθ = 2Bℓ (a/2)wsinθ Therefore, e=Bℓawsinwt and with A=ℓa wt For a coil with N turns e=NBAw sinwt

  5. Generator equation from Faraday’s law wt e=-NDB/Dt e=-NBA[D(cosq)/Dt] Consider: d(cost)/dt=-sint e=NBAsint e=emaxsint=emaxsin2ft emax=NBAw (maximum value of the emf) 2f

  6. AC Generators, final • The emf generated by the rotating loop can be found by ε =2Bℓv=2Bℓv sinθ • If the loop rotates with a constant angular speed, ω, and N turns ε=NBAω sinωt • ε = εmax when loop is parallel to the field • ε = 0 when when the loop is perpendicular to the field

  7. Direct current (DC) Generators • Components are essentially the same as that of an ac generator • The major difference is the contacts to the rotating loop are made by a split ring, or commutator

  8. DC Generators, cont • The output voltage always has the same polarity • The current is a pulsating current • To produce a steady current, many loops and commutators around the axis of rotation are used • The multiple outputs are superimposed and the output is almost free of fluctuations

  9. Motors • Motors are devices that convert electrical energy into mechanical energy • A motor is a generator run in reverse • A motor can perform useful mechanical work when a shaft connected to its rotating coil is attached to some external device

  10. Motors and Back emf Back emf The applied voltage V supplies the current I to drive the motor. The circuit shows V along with the electrical equivalent of the motor, including the resistance R of its coil and the back emf e.

  11. Motors and Back emf • The phrase back emf is used for an emf that tends to reduce the current due to an applied voltage  current through the motor:I=V-eb/R, where V is the line voltage, eb is the back emf and R is the coil resistance • When a motor is turned on, there is no back emf initially • The current is very large because it is limited only by the resistance of the coil

  12. Motors and Back emf, cont. • As the coil begins to rotate, the induced back emf opposes the applied voltage • The current in the coil is reduced • The power (i.e., current) requirements for starting a motor and for running it under heavy loads are greater than those for running the motor under average loads

  13. Example:A motor has a 10  coil. When running at its maximum speed, the back emf is 70 V. Find the current (a) when the motor starts and (b) when the motor has reached its maximum speed. • (a)I=V/R=120 V/10  • I=12 A • (b)I=(V-eb)/R • I=(120 V-70 V)/10  • I=50 V/10 =5 A

  14. 20.6 Self-inductance • Self-inductance occurs when the changing flux through a circuit arises from the circuit itself • As the current increases, the magnetic flux through a loop due to this current also increases • The increasing flux induces an emf that opposes the current • As the magnitude of the current increases, the rate of increase lessens and hence the induced emf decreases • This opposing emf results in a gradual increase in the current

  15. Self-inductance, cont. (a) A current in the coil produces a magnetic field directed to the left. (b) If the current increases, the coil acts as a source of emf directed as shown by the dashed battery. (c) The induced emf in the coil changes its polarity if the current decreases.

  16. Self-inductance, cont. • The self-induced emf is given by Faraday’s law and must be proportional to the time rate of change of the current • Lis a proportionality constant called the inductance of the device • The negative sign indicates that a changing current induces an emf in opposition to that change

  17. Self-inductance, final • The inductance of a coil depends on geometric factors • The SI unit of self-inductance is the Henry • 1 H = 1 (Vs)/A • The equation for L

  18. 20.7 RL Circuits • Inductor has a large inductance (L) and consist of closely wrapped coil of many turns • Inductance can be interpreted as a measure of opposition to the rate of change in the current • Remember resistance R is a measure of opposition to the current • As a circuit is completed, the current begins to increase, but the inductor produces an emf that opposes the increasing current • Therefore, the current doesn’t change from 0 to its maximum instantaneously

  19. Comparison of R and L in a simple circuit e=-IR e=-L(DI/Dt) L is a measure of opposition to the rate of change in current R is a measure of opposition to the current

  20. RL Circuit • When the current reaches its maximum, the rate of change and the back emf are zero • The time constant, , for an RL circuit is the time required for the current in the circuit to reach 63.2% of its final value

  21. RL Circuit, cont • The time constant depends on R and L • The current at any time can be found by

  22. The switch in the circuit shown in the figure below is closed and the lightbulb glows steadily. The inductor is a simple air-core solenoid. An iron rod is inserted into the interior of the solenoid, which increases the magnitude of the magnetic field in the solenoid. As the rod is inserted into the solenoid, the brightness of the lightbulb (a) increases, (b) decreases, or (c) remains the same. QUICK QUIZ 20.5

  23. 20.8 Energy Stored in a Magnetic Field • The emf induced by an inductor prevents a battery from establishing an instantaneous current in a circuit • The battery has to do work to produce a current • This work can be thought of as energy stored by the inductor in its magnetic field

  24. Energy stored, final • The increment of work done by a battery to move DQ through an inductor is: DW=DQe • DW=DQ [L(DI/Dt)] • Since I=DQ/Dt, the work done is: DW=LI (DI) Energy stored by an inductor

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