1. Inductance and Capacitance Lecture 4

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

3. Inductor

4. Inductor concept An inductor consist 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 Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

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

8. Inductor current Power

9. Assuming that energy is zero at time t=t 0, then inductor energy is:

10. Inductance and Capacitance Inductor Relationship between voltage, current, power and energy Capacitor Relationship between voltage, current, power and energy 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. The amount of charge stored, represented by q, is directly proportional to the applied voltage v, q = charge in coulomb (C) C = charge in farad (F) v = voltage in 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 (m 2) d = distance between the plates (m)

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

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

17. Capacitor’scurrentCapacitor’scurrent Capacitor’s voltage

18. Power:

19. Energy stored in a capacitor from time t to t 0 :

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 Relationship between voltage, current, power and energy Series-parallel combinations for inductance and capacitance

22. Series and parallel capacitors The equivalent capacitance, C eq 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, C eq 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, L eq 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, L eq 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 capacitance.

35. Answer 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. Answer Capacitor voltage: current: t tttv µsecond 50 50 105 )( 6      tA dt tdv Cti µsecond 5020 105 )( )( 6 6            

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. Answer Capacitor voltage: