1. Lecture 10: Inductance & Capacitance Nilsson 6.1-6.5
ENG17 (Sec. 1): Circuits I
Summer
July 8, 2014

2. Overview Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored

3. Inductance in the Real World

4. What Does an Inductor Look Like?

5. What Does an Inductor Do?
Inductor: electrical component that opposes any change in electrical current
Associates electrical current and magnetic fields
Magnetic field generated by charge in motion (i.e., current)
If current changes wrt time, mag field changes wrt time
Varying mag field results in voltage in linked conductor

6. Add’l Note Inductors can store energy through the mag fields
Used in spark plugs
Inductors do not generate energy, so they are still passive devices

7. Inductors in Circuits Symbol: L Units: [H] for henrys = [Wb/A]
𝑣=𝐿 𝑑𝑖 𝑑𝑡

8. Determining Voltage

9. Current in Inductor
𝑖 𝑡 = 1 𝐿 𝑡 0 𝑡 𝑣 𝑑𝜏+𝑖( 𝑡 0 )

10. Power & Energy in Inductor
𝑝=𝐿𝑖 𝑑𝑖 𝑑𝑡
𝑤= 1 2 𝐿 𝑖 2

11. Overview Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored

12. Capacitance in the Real World

13. What Does a Capacitor Look Like?

14. What Does a Capacitor Do?
Capacitor: electrical component that consists of 2 conductors separated by dielectric
“Stores” electric charge (like a battery)
Associated with electric fields, due to separation of charge (voltage)
If voltage varies with time, E-field varies with time
Varying E-field generates displacement current in space occupied by field
Capacitance relates displacement current to voltage

15. Capacitors in Circuits
Symbol: C
Units: [F] for farads = [C/V]
𝑖=𝐶 𝑑𝑣 𝑑𝑡

16. Capacitor Voltage, Power, & Energy
𝑣 𝑡 = 1 𝐶 𝑡 0 𝑡 𝑖 𝑑𝜏+𝑣( 𝑡 0 )
𝑝=𝑣𝑖=𝐶𝑣 𝑑𝑣 𝑑𝑡
𝑤= 1 2 𝐶 𝑣 2

17. Example
𝑣 𝑡 = 0, 𝑡≤0 𝑠 4𝑡, 𝑠 ≤𝑡 ≤1 𝑠 4 𝑒 −(𝑡−1) , 𝑡≥1 𝑠

18. Example
Obtain the energy stored in each capacitor under DC conditions.

19. Example Under DC conditions, find i, vc, and iL.
Also, find the energy stored in the capacitor and inductor.

20. Overview Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored

21. Inductors Series-Parallel

22. Capacitors Series-Parallel

23. Example

24. Overview Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored

25. Magnetically Coupled Coils

26. Self- and Mutual-Inductance

27. Dot Convention

28. Mesh Current

29. Overview Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored

30. Self Inductance

31. Mutual Inductance i.t.o. Self Inductance

32. Overview Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored

33. Energy Stored in Magnetically-Coupled Coils

34. Recap Inductors Capacitors Series-Parallel L/C Mutual Inductance
Self Inductance
Energy Stored