Energy-Storage Elements Capacitance and Inductance

1. Energy-Storage ElementsCapacitance 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 308

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 308

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-plateCapacitor: ELEC 308

5. Fluid-Flow Analogy ELEC 308

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 308

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 308

8. Example 3.1 • Plot the current vs. time ELEC 308

9. Stored Energy in a Capacitor • Remember: • For an ideal capacitor: • For an ideal, uncharged capacitor (v(t0) = 0): ELEC 308

10. Example 3.3 • Plot current, power delivered and energy stored ELEC 308

11. Capacitances in Parallel ELEC 308

12. Capacitances in Series ELEC 308

13. Parallel-Plate Capacitors ELEC 308

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 εr is the relative dielectric constant • See Table 3.1 on page 135 of textbook ELEC 308

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 (become conductors) • Real capacitors have MAXIMUM VOLTAGE RATING ELEC 308

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 308

17. Inductors • Constructed by coiling a wire around some type of form ELEC 308

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 308

19. Stored Energy in an Inductor • Remember: • For an ideal inductor: • For an ideal inductor with i(t0) = 0: ELEC 308

20. Example 3.6 • Plot voltage, power, and energy ELEC 308

21. Equivalent Inductance ELEC 308

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 308

23. Electronic Photo Flash ELEC 308

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 308

25. Mutual Inductance • Flux of one coil aids the flux produced by the other coil ELEC 308

26. Ideal Transformers ELEC 308

27. Ideal Transformers ELEC 308

28. Power Transmission Losses • Power Line Losses • Large Voltages and Small Currents • Smaller Line Loss ELEC 308

29. Power Transmission • Step-Up and Step-Down Transformers • 99% Efficiency (vs. 50% with no transformers) ELEC 308

30. U.S. Power Grid ELEC 308

31. Summary • Capacitance • Voltage • Current • Power • Energy • Series • Parallel • Inductance • Voltage • Current • Power • Energy • Series • Parallel • Mutual Inductance • Transformers ELEC 308