1. Inductance and Capacitance
Topic 4

2. Inductance and Capacitance
Inductor
Relationship between voltage, current, power and energy
Capacitor
Series-parallel combinations for inductance and capacitance

3. Inductor

4. Inductor concept An inductor consists of a coil of conducting wire.
Inductance, L is the property whereby an inductor exhibits opposition to the change of current flowing through it, measured in henrys (H).

5. Inductance Inductance, L L = inductance in henrys (H).
N = number of turns
µ = core permeability
A = cross-sectional area (m2)
ℓ = length (m)

6. Inductance and Capacitance
Inductor
Relationship between voltage, current, power and energy
Capacitor
Series-parallel combinations for inductance and capacitance

7. Relationship between voltage, current, power and energy
Inductor
symbol
Inductor
Voltage

8. Inductor
current
Power

9. Assuming that energy is zero at time t=t0, then inductor energy is:

10. Inductance and Capacitance
Inductor
Relationship between voltage, current, power and energy
Capacitor
Series-parallel combinations for inductance and capacitance

11. CAPACITOR

12. Capacitor physical concept:
A capacitor consists of two conducting plates separated by an insulator (or dielectric).
Capacitance, C is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F).

13. C = capacitance in farad (F) v = volt (V)
The amount of charge stored, represented by q, is directly proportional to the applied voltage v,
q = charge in coulomb (C)
C = capacitance in farad (F)
v = volt (V)

14. Capacitance, C: C = Capacitance in farads (F)
e = permittivity of dielectric material between the plates (C2/N∙m2)
A = surface area of each plates (m2)
d = distance between the plates (m)

15. Inductance and Capacitance
Inductor
Relationship between voltage, current, power and energy
Capacitor
Series-parallel combinations for inductance and capacitance

16. Relationship between voltage, current, power and energy
Capacitor symbol

17. Capacitor
current
Capacitor voltage

18. Power:

19. Energy stored in a capacitor from time t to t0:

20. Capacitor is not discharge at t=-∞, therefore the voltage is zero.
Energy capacitor

21. Inductance and Capacitance
Inductor
Relationship between voltage, current, power and energy
Capacitor
Series-parallel combinations for inductance and capacitance

22. Series and parallel capacitors
The equivalent capacitance, Ceq of N parallel-connected capacitors is the sum of the individual capacitances.

23. Using KCL,

24. Equivalent circuit for the parallel capacitor,

25. The equivalent capacitance, Ceq of N series-connected capacitors is the reciprocal of the sum of the reciprocals of the individual capacitances.

26. Using KCL,

27. Equivalent circuit for the series capacitor,

28. Series and parallel inductors
The equivalent inductance, Leq of N series-connected inductors is the sum of the individual inductances.

29. Using KVL,

30. Equivalent circuit for the series inductor,

31. The equivalent inductance, Leq of N parallel-connected inductors is the reciprocal of the sum of the reciprocals of the individual capacitances.

32. Using KVL,

33. Equivalent circuit for the parallel inductor,

34. Question 1
Obtain the total of capacitance.

35. Solution:
Short circuit, then:

36. Question 2
Voltage stored in a 10µF capacitor is shown in figure below. Obtain the graph for current of the capacitor.

37. Solution:
Capacitor voltage:
current:

38. Thus:

39. Question 3
Determine the voltage across a 2 µF capacitor if the current through it is
Assume that initial capacitor voltage is zero

40. Solution:
Capacitor voltage: