1. Capacitance and RC Circuits
Figure: 03-00CO
Caption:
Circuit and waveforms for Example 3.1.

2. Capacitors are constructed by separating 2 sheets of conductor, which
is usually metallic, by a thin layer of insulating material. In parallel-plate
capacitor, the sheets are flat and parallel. The insulating material
between the plates, called a dielectric, can be air, Mylar, polyester,
polypropylene, mica, etc.
Figure: 03-01
Caption:
A parallel-plate capacitor consists of two conductive plates separated by a dielectric layer.

3. Figure: 03-02ab
Caption:
A capacitor and its fluid-flow analogy.

4. Stored charge in terms of voltage
The constant of proportionality is the capacitance C, which has units
of farads (F). Farads are equivalent to coulombs per volt.
Current in terms of voltage
Note: the current reference direction points into the
positive reference polarity.

5. Voltage in terms of current Suppose that we know the current i(t)
flowing through a capacitance C and we want to compute charge
and voltage.
Figure: 03-03
Caption:
The circuit symbol for capacitance, including references for the current i(t) and voltage v(t).

6. Stored Energy
Energy stored in the capacitance is given by

7. Figure: 03-04a-dEXM
Caption:
Circuit and waveforms for Example 3.1.

8. Figure: 03-09
Caption:
Three capacitances in parallel.

9. Figure: 03-10
Caption:
Three capacitances in series.

10. Capacitance of the parallel-plate capacitor
If the distance d between the plates is much smaller than both the
width and the length of the plates, the capacitance is approximately
In which e is the dielectric constant of the material between the plates.
For vacuum, the dielectric constant is e = e0 = 8.85x10-12 F/m
Figure: 03-11
Caption:
A parallel-plate capacitor, including dimensions.

11. Figure: 03-12
Caption:
Practical capacitors can be constructed by interleaving the plates with two dielectric layers and rolling them up. By staggering the plates, connection can be made to one plate at each end of the roll.

12. Figure: 03-13
Caption:
The circuit model for a capacitor, including the parasitic elements R_s, L_s, and R_p.

13. Figure: 03-14EXM
Caption:
See Example 3.5.

14. An inductor is constructed by coiling a wire around some type of form.
Inductance
An inductor is constructed by coiling a wire around some type of form.
Current flowing through the coil creates a magnetic field or flux that links
the coil. Frequently the coil form is composed of a magnetic material
such as iron or iron oxide that increases the magnetic flux for a given
current.
Figure: 03-15a-c
Caption:
An inductor is constructed by coiling a wire around some type of form.

15. When the current changes in value, the resulting magnetic flux changes
according to Faraday’s law of electromagnetic induction,
time-varying magnetic flux linking a coil induces voltage across the coil.
For an ideal inductor, the voltage is proportional to the time rate of
change of the current. Furthermore, the polarity of the voltage is such as
to oppose the change in current. The constant of proportionality is called
inductance, L.

16. Current in terms of voltage
Figure: 03-16
Caption:
Circuit symbol and the v-i relationship for inductance.
Stored Energy

17. Figure: 03-17a-dEXM
Caption:
Waveforms for Example 3.6.

18. Figure: 03-18a-cEXM
Caption:
Circuit and waveforms for Example 3.7.

19. Figure: 03-19abEXM
Caption:
See Exercise 3.7.

20. Figure: 03-20ab
Caption:
Inductances in series and parallel are combined in the same manner as resistances.

21. Figure: 03-21abEXM
Caption:
See Exercise 3.10.

22. Figure: 03-22
Caption:
Circuit model for real inductors including several parasitic elements.

23. Figure: PA3-1
Caption:

24. Figure: PA3-2
Caption:

25. Figure: 03-23ab
Caption:
Circuit symbols and v-i relationships for mutually coupled inductances.

26. Figure: 03-24
Caption:
A linear variable differential transformer used as a position transducer.

27. Figure: P3-11ab
Caption:

28. Figure: P3-12
Caption:

29. Figure: P3-14ab
Caption:

30. Figure: P3-24ab
Caption:

31. Figure: P3-25ab
Caption:

32. Figure: P3-28
Caption:

33. Figure: P3-35
Caption:

34. Figure: P3-36
Caption:

35. Figure: P3-39
Caption:

36. Figure: P3-45
Caption:

37. Figure: P3-48
Caption:

38. Figure: P3-51
Caption:

39. Figure: P3-62ab
Caption:

40. Figure: P3-63ab
Caption:

41. Figure: P3-67
Caption:

42. Figure: P3-68
Caption:

43. Figure: P3-71
Caption:

44. Figure: P3-72
Caption:

45. Figure: P3-74
Caption:

46. Figure: P3-76
Caption: