Lesson 13 Applications of Time-varying Circuits

1. Lesson 13Applications of Time-varying Circuits

2. Class 38 • Today we will: • find out how transformers work • learn about how electrical power is generated and delivered to our homes.

3. Be able to draw the impedance diagram and find the magnitude and phase angle of the impedance The Series LRC Circuit

4. The Series LRC Circuit

5. Resonance is where the inductive and capacitive reactances are equal. • The resonant frequency is: • The impedance is minimum and the current is maximum. Resonance

6. Transformers

7. Iron Core Inductors Adding an iron core to an inductor accomplishes two things: It increases the magnetic field It tends to keep the magnetic field confined in the core.

8. Note how an iron core modifies the magnetic field lines of a wire coil. Iron Core Inductors

9. Iron Core Inductors We can even make an iron core that forms a closed loop.

10. Iron Core Inductors We can use Ampere’s Law around one field line to find the magnetic field. Assuming B is uniform:

11. Iron Core Inductors We can use Faraday’s Law to find the impedance:

12. Mutual Inductance We can also put two coils on the same core or yoke.

13. Mutual Inductance We attach a power supply to one coil. This is the “primary.”

14. Mutual Inductance Since the magnetic flux in the upper coil changes in time, an EMF is induced.

15. Transformers This is called a transformer.

16. Transformers We attach a load to the other coil. This coil is the “secondary.”

17. Transformers The magnetic flux through one coil of either winding is the same, as the number of filed lines is the same.

18. Transformers Since the flux is the same through both coils, the change in flux is also the same:

19. Transformers If there are 10 times as many windings in the secondary as the primary, there is 10 times the voltage in the secondary. This is called a “step-up” transformer. If there are 10 times fewer windings in the secondary as the primary, there is 10 times less voltage in the secondary. This is called a “step-down” transformer.

20. Power in AC Circuits Recall that the power provided by a power supply is If the load is resistive, the phase angle is zero and The power dissipated in a resistor is

21. Power and Transformers Transformers have very little power loss to heating, etc. The power provided by the primary is used in the secondary. If the power factors are approximately equal to 1:

22. Power and Transformers This means that step-down transformers can have high currents, but step-up transformers have smaller currents.

23. Power Transmission

24. Load resistance Line resistance Transmission Lines We can model a transmission line as a simple circuit.

25. Load resistance Line resistance Transmission Lines

26. Transmission Lines Let’s compare two cases with a 250 W load and a 10Ω transmission line:

27. Transmission Lines Conclusion: Transmission lines are more efficient when they have very high voltages. Major lines have voltages of several hundred kV. Substations lower the voltage of local lines to 4-8 kV.

28. Transmission

29. Lines into a Home If the primary voltage is 2400 V, then the local transformer has a 10:1 ratio of turns. The middle of the secondary coil is attached by a wire to ground. A ground wire and wires from the two ends of the secondary come into your home.

30. Lines into a Home The ground wire is at 0 V, and the other two wires at 120 V (rms). The 120 V wires are out of phase with respect to each other.

31. Lines into a Home

32. The Service Panel and Circuit Breakers

33. The Service Panel The service panel is where outside power comes in and wires are then distributed through different circuits throughout your house. Either 120 V or 240 V circuits can be taken from the service panel. The service panel is often called the “circuit breaker box.”

34. from transformer to circuit to circuit to circuit 120 V 0 V 120 V ground The Service Panel

35. Circuit Breakers Circuit breakers provide two functions: They serve as switches to shut off power to parts of your house. They automatically shut of power if too much current flows into the circuit. Large currents cause wires to heat and start fires.

36. Circuit Breakers A resistor in the circuit breaker heats as current flows though. This heats a bimetallic strip that is part of a switch. The switch opens, turning off power in the circuit.

37. Circuit Breakers A circuit breaker also contains a solenoid that controls a second switch. When the current rises above a given level, the solenoid opens the circuit in a fraction of a second. The circuit breaker switch flips to a middle position between on and off and can be reset by turning the switch back to on.

38. Class 39 • Today we will: • learn about wires used in homes • learn how switches and outlets are wired • learn how to wire a 3-way switch • find out about safety devices: grounds, GFCI’s, and AFCI’s

39. Home Wiring

40. Wires ground hot Wires are bundled into cables of three or four wires. neutral ground hot hot neutral

41. Wires Conductors are either copper or aluminum. Copper is a better conductor, more flexible, and corrodes less. Aluminum is cheaper. Special components are made for aluminum wires.

42. Wires and Heat – E&M The source of heat is resistance in the wire. A length of wire generates heat at the rate:

43. Wires and Heat – E&M The source of heat is resistance in the wire. A length of wire generates heat at the rate: The more current in a circuit, the larger the wire must be to keep the wire from overheating.

44. Wires • Rough rule of thumb: • Cu can take 4 A/mm2 • Al can take 2.3 A/mm2

45. Copper Wires

46. Wiring Switches and Outlets

47. Switches

48. Switches Switches are placed along the hot wire.

49. Switches

50. Switches