1. Energy-Storage Elements Capacitance and Inductance ELEC 308 Elements of Electrical Engineering Dr. Ron Hayne Images Courtesy of Allan Hambley and Prentice-Hall

2. Energy-Storage Elements  Remember Resistors convert electrical energy into heat Cannot store energy!  Inductors and Capacitors can store energy and later return it to the circuit Do NOT generate energy! Passive elements, like resistors  Capacitance is a circuit property that accounts for energy STORED in ELECTRIC fields  Inductance is a circuit property that accounts for energy STORED in MAGNETIC fields ELEC 3082

3. Inductance and Capacitance Uses  Microphones Capacitance changes with sound pressure  Linear variable differential transformer Position of moving iron core converted into voltage  Conversion from DC-AC, AC-DC, AC-AC  Electrical signal filters Combinations of inductances and capacitances in special circuits ELEC 3083

4. Capacitors  Constructed by separating two sheets of CONDUCTOR (usually metallic) by a thin layer of INSULATING material Insulating material called a DIELECTRIC Can be air, Mylar®, polyester, polypropylene, mica, etc.  Parallel-plate Capacitor: ELEC 3084

5. Fluid-Flow Analogy ELEC 3085

6. Stored Charge in Terms of Voltage  In an IDEAL capacitor Stored charge, q, is proportional to the voltage between the plates: Constant of proportionality is the capacitance, C Units are farads (F) Units equivalent to Coulombs per volt Farad is a VERY LARGE amount of capacitance  Usually deal with capacitances from 1 pF to 0.01 F  Occasionally, use femtofarads (in computer chips) ELEC 3086

7. Current in Terms of Voltage  Remember that current is the time rate of flow of charge  In an IDEAL capacitor The relationship between current and voltage is ELEC 3087

8. Example 3.1  Plot the current vs. time ELEC 3088

9. Stored Energy in a Capacitor  Remember:  For an ideal capacitor:  For an ideal, uncharged capacitor (v(t 0 ) = 0): ELEC 3089

10. Example 3.3  Plot current, power delivered and energy stored ELEC 30810

11. Capacitances in Parallel ELEC 30811

12. Capacitances in Series ELEC 30812

13. Parallel-Plate Capacitors ELEC 30813

14. Parallel-Plate Capacitors  If d<<W and d<<L, the capacitance is approx. where ε is the dielectric constant of the material BETWEEN the plates  For vacuum, the dielectric constant is  For other materials, where ε r is the relative dielectric constant  See Table 3.1 on page 135 of textbook ELEC 30814

15. Practical Capacitors  Dimensions of 1μF parallel-plate capacitors are TOO LARGE for portable electronic devices  Plates are rolled into smaller area  Small-volume capacitors require very thin dielectrics (with HIGH dielectric constant) Dielectric materials break down when electric field intensity is TOO HIGH (b ecome conductors) Real capacitors have MAXIMUM VOLTAGE RATING ELEC 30815

16. Electrolytic Capacitors  One plate is metallic aluminum or tantalum  Dielectric is OXIDE layer on surface of the metal  Other “plate” is ELECTROLYTIC SOLUTION  Metal plate is immersed in the electrolytic solution  Gives high capacitance per unit volume Requires that ONLY ONE polarity of voltage can be applied ELEC 30816

17. Inductors  Constructed by coiling a wire around some type of form ELEC 30817

18. Voltage in Terms of Current  In an IDEAL inductor Voltage across the coil is proportional to the time rate of change of the current Constant of proportionality is the inductance, L Units are henries (H) Units equivalent to volt-seconds per amperes Usually deal with inductances from 0.001μH to 100 H ELEC 30818

19. Stored Energy in an Inductor  Remember:  For an ideal inductor:  For an ideal inductor with i(t 0 ) = 0: ELEC 30819

20. Example 3.6  Plot voltage, power, and energy ELEC 30820

21. Equivalent Inductance ELEC 30821

22. Practical Inductors  Cores (metallic iron forms) are made of thin sheets called laminations  Voltages are induced in the core by the changing magnetic fields Cause eddy currents to flow in the core Dissipate energy Results in UNDESIRABLE core loss Can reduce eddy-current core loss Laminations Ferrite (iron oxide) cores Powdered iron with insulating binder ELEC 30822

23. Electronic Photo Flash ELEC 30823

24. Mutual Inductance  Several coils wound on the same form Magnetic flux produced by one coil links the others Time-varying current flowing through one coil induces voltages on the other coils ELEC 30824

25. Mutual Inductance  Flux of one coil aids the flux produced by the other coil ELEC 30825

26. Ideal Transformers ELEC 30826

27. Ideal Transformers ELEC 30827

28. Power Transmission Losses  Power Line Losses Large Voltages and Small Currents Smaller Line Loss ELEC 30828

29. Power Transmission  Step-Up and Step-Down Transformers 99% Efficiency (vs. 50% with no transformers) ELEC 30829

30. U.S. Power Grid ELEC 30830

31. Summary  Capacitance Voltage Current Power Energy Series Parallel  Inductance Voltage Current Power Energy Series Parallel Mutual Inductance Transformers ELEC 30831