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Induced Voltage ( Emf)

Induced Voltage ( Emf). Magnetic Flux ( F ) Faraday’s Law Lenz’s Law Transformers Generators AC current and voltage. Starter. A motor converts ______________energy into __________energy. Magnetic Flux. The number of arrows that pass through the loop depend on:

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Induced Voltage ( Emf)

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  1. Induced Voltage ( Emf) • Magnetic Flux ( F ) • Faraday’s Law • Lenz’s Law • Transformers • Generators • AC current and voltage

  2. Starter A motor converts ______________energy into __________energy.

  3. Magnetic Flux The number of arrows that pass through the loop depend on: 1. The density of the arrows ( B) 2. The size of the area (A) 3. The orientation of the area to the B field(q).

  4. Example A magnetic field of 3T passes through an area of 2 m2 . The B field makes an angle of 45 degrees with the area normal. What is the flux through the loop? F = ABcosq = (2)(3)cos45 = 4.24 T. m2

  5. Faraday’s Discovery If the magnetic flux through a loop of wire changes, a voltage is induced in the wire which causes a current. Induced Voltage = N ( DF/ Dt )

  6. How The Flux Can Change With Time DF/Dt • The B Field can change : DF/ Dt = NA(DB /Dt ) • The area can change: DF/ Dt = NB(DA /Dt ) • The angle can change: DF/ Dt = wNBA sinwt

  7. The area can change: V= NB(DA /Dt ) DA/ Dt = D ( Lx )/Dt = L Dx/Dt = Lv V= BLv Example: A metal bar moves to the right with a velocity of 10m/s through a magnetic field of 3T. The loop height, L, is .5m. 1. What is the induced voltage? 2. If the circuit has a resistance of 2 Ohms, what’s the current in the circuit? V = BLv = (3)(.5)( 10) = 15Volts I = V/R = 15/2= 7.5 Amps

  8. The B Field can change : V= NA(DB /Dt ) Example: A magnet is moved into a single coil with 100 turns and an area .10m2. The field in the loop changes from zero to 2T in .1 seconds. 1. What is the induced voltage? V = NA(DB /Dt ) = (100)(.1)( 2/.1) = 200Volts 2. If the coil has a resistance of 100 Ohms, what’s the current in the coil? I = V/R = 200/100= 2 Amps

  9. The angle can change: V= wNBA sinwt This is used for the generator. The maximum voltage is: Vmax = wNBA. Example: A generator turns at 100rad/sec. It has 500 turns, and a magnetic field of .5T. The loop area is.01 m2. What is the maximum voltage? Vmax = wNBA = 100(500)(.5)(.01) = 250Volts.

  10. Lenz’s Law The current induced in a loop by a changing B-field, creates a B-field that opposes the external B-field.

  11. Lenz’s Law As the magnet moves, the current in the resistor goes from…. A to B

  12. Lenz’s Law As the magnet moves, the current in the resistor goes from…. B to A

  13. Lenz’s Law As the magnet moves, the current in the resistor goes from…. B to A

  14. Lenz’s Law As the magnet moves, the current in the resistor goes from…. A to B

  15. Transformers

  16. Transformer Equations N1 = number of turns on the primary side N2 = number of turns on the secondary side V1 = AC voltage applied to the primary side V2 = AC voltage on the secondary side I1 =current in the primary windings I2 = current in the secondary windings

  17. Transformer Equations From Faraday’s Law : V2 = V1 (N2/N1) From conservation of energy: V1 I1 = V2 I2 Then: I2 = I1 (N1/N2)

  18. Step Up Transformer N2>N1 Example: A transformer has 5000 turns in the secondary and 1000 turns in the primary. The primary voltage is 100V (AC) and the primary current is 25 Amps. 1. What is the secondary voltage? 2. What is the secondary current? 3. What is the power in the primary and secondary?

  19. Solve the Problem Givens: V1 = 100 N1 = 1000 N2= 5000 I1 = 25 1. Solve for V2 : V2 = V1 (N2/N1) = 100( 5000/1000) = 500 Volts 2. Solve for I2: I2 = I1 (N1/N2) = 25( 1000/5000) = 5 Amps. 3. P1 = P2 : V1 I1 = V2 I2 = 2500 Watts

  20. Step Down Transformer N2<N1 Example: A transformer plugged into the wall ( 120V) charges a 9 volt battery. 1. What is the turn ratio (N1/N2) ? 2. What is the secondary current if the primary current is .5A? 3. What is the power in the primary and secondary?

  21. Solve the Problem Givens: V1 = 120 V2 = 9 I1 = .5 1. Solve for (N2/N1) : V2 = V1 (N2/N1) so (N2/N1) = V2 /V1 = 9/120 = .075 2. Solve for I2: I2 = I1 (N1/N2) = .5 ( 1 /.075) = 6.67Amps. 3. P1 = P2 : V1 I1 = V2 I2 = 60 Watts

  22. AC Voltage and Current

  23. Example What is the peak voltage for household voltage of 120V(rms)? V(peak) = 1.41(120) = 169 Volts

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