1. Capacitors AC Circuits I

2. Capacitors and Capacitance: An Overview Capacitance – the ability of a component to store energy in the form of an electrostatic charge Capacitor – is a component designed to provide a specific measure of capacitance 2AC Circuits I - Capacitors

3. Capacitors and Capacitance: An Overview Capacitor Construction – Plates – Dielectric 3AC Circuits I - Capacitors

4. Capacitors and Capacitance: An Overview Capacitor Charge – Electrostatic Charge Develops on the Plates – Electrostatic Field Stores energy 4AC Circuits I - Capacitors

5. Capacitors and Capacitance: An Overview Capacitor Discharge 5AC Circuits I - Capacitors

6. Capacitors and Capacitance: An Overview A Practical Consideration – Before handling any capacitor in a circuit, connect a shorting tool across the capacitor terminals to short out any residual charge. 6AC Circuits I - Capacitors

7. Capacitors and Capacitance: An Overview Capacity – amount of charge that a capacitor can store per unit volt applied Capacity is directly proportional to charge and inversely proportional to voltage where C = the capacity (or capacitance) of the component, in coulombs per volt Q = the total charge stored by the component V= the voltage across the capacitor 7AC Circuits I - Capacitors

8. Capacitors and Capacitance: An Overview Capacity (Continued) 8AC Circuits I - Capacitors

9. Capacitors and Capacitance: An Overview Unit of Measure – farad (F) = 1 coulomb per volt (C/V) Capacitor Ratings – Most capacitors rated in the picofarad (pF) to microfarad (  F) range – Capacitors in the millifarad range are commonly rated in thousands of microfarads: 68 mF = 68,000  F – Capacitors in the nanofarad range are also commonly rated in microfarads: 68 nF = 0.068  F – Tolerance Usually fairly poor Variable capacitors used where exact values required 9AC Circuits I - Capacitors

10. Capacitors and Capacitance: An Overview Physical Characteristics of Capacitors where C = the capacity of the component, in farads ε 0 = the permittivity of a vacuum, in farads per meter (8.854 X 10 -12 F/m)  r = the relative permittivity of the dielectric A= the area of either plate, in square meters (m 2 ) d= the distance between the plates, in meters (m)

11. Capacitors and Capacitance: An Overview Physical Characteristics of Capacitors (Continued) – Plate Area: capacitance is directly proportional to plate area – Dielectric Thickness: capacitance is inversely proportional to dielectric thickness – Dielectric Permittivity: the ease with which lines of electrical force are established in the dielectric material – Relative Permittivity: the ratio of a material’s permittivity to that of a vacuum. See table 12.1 in text p.368 11AC Circuits I - Capacitors

12. Examples A capacitor is storing 200mC of charge when the difference of potential across its plates is 25V. Calculate the value of the component Calculate the capacitance of a device compose of two plates whose dimensions are 5m*5m and are separated by 8cm of air (  r =1). AC Circuits I - Capacitors12

13. Series and Parallel Capacitors Series Capacitors Where C T = the total series capacitance C n = the highest-numbered capacitor in the circuit

14. Series and Parallel Capacitors Connecting Capacitors in Parallel where C n = the highest-numbered capacitor in the parallel circuit

15. Examples Calculate Total Capacitance for the circuit shown 15AC Circuits I - Capacitors

16. Examples Calculate Total Capacitance for the circuit shown AC Circuits I - Capacitors16

17. Alternating Voltage and Current Characteristics AC Coupling and DC Isolation: An Overview – DC Isolation – a capacitor prevents flow of charge once it reaches its capacity 17AC Circuits I - Capacitors

18. Alternating Voltage and Current Characteristics Capacitor Current where i C = the instantaneous value of capacitor current C = the capacity of the component(s), in farads = the instantaneous rate of change in capacitor voltage 18AC Circuits I - Capacitors

19. Alternating Voltage and Current Characteristics AC Coupling and DC Isolation: An Overview – AC signal is coupled – DC offset is blocked 19AC Circuits I - Capacitors

20. Alternating Voltage and Current Characteristics Capacitor current is maximum when – reaches its maximum value when v = 0 V is maximum 20AC Circuits I - Capacitors

21. Alternating Voltage and Current Characteristics The Phase Relationship Between Capacitor Current and Voltage – Current leads voltage by 90° – Voltage lags current by 90° 21AC Circuits I - Capacitors

22. Alternating Voltage and Current Characteristics Capacitive Versus Inductive Phase Relationships – Voltage (E) in inductive (L) circuits leads current (I) by 90° (ELI) – Current (I) in capacitive (C ) circuits leads voltage (E) by 90° (ICE) – Memory Aid: ELI the ICEman 22AC Circuits I - Capacitors

23. Alternating Voltage and Current Characteristics 23AC Circuits I - Capacitors

24. Capacitive Reactance (X C ) Capacitor Resistance – Dielectric Resistance – generally assumed to be infinite – Effective Resistance – opposition to current, also called capacitive reactance ( X C ) 24AC Circuits I - Capacitors

25. Capacitive Reactance (X C ) Calculating the Value of X C 25AC Circuits I - Capacitors If Phase is required as well i.e. complex numbers

26. Capacitive Reactance (X C ) X C and Ohm’s Law – Example: Calculate the total current below 26AC Circuits I - Capacitors

27. Capacitive Reactance (X C ) Series and Parallel Values of X C 27AC Circuits I - Capacitors

28. Examples Calculate Total Capacitance and reactance for the circuit shown. Assume f = 10KHz. 28AC Circuits I - Capacitors

29. Examples Calculate Total Capacitance and reactance for the circuit shown. Assume f = 10KHz. AC Circuits I - Capacitors29

30. Ideal Capacitors Properties – Have infinite dielectric resistance – Do not Dissipate any power – Have an infinite breakdown voltage rating (due to infinite dielectric resistance) AC Circuits I - Capacitors30

31. Related Topics Breakdown Voltage Rating – indicates the voltage that will cause the dielectric of a capacitor to break down and conduct Leakage Current – Occurs because the dielectric resistance of a capacitor is not infinite 31AC Circuits I - Capacitors

32. Related Topics Capacitor Quality ( Q ) – indicates how close the capacitor comes to having the characteristics of an ideal component. Frequency dependent where X C = the reactance of the capacitor at the frequency of operation R D = the dielectric resistance of the component 32AC Circuits I - Capacitors

33. Related Topics Fixed Value Capacitors – Dielectric Absorption The tendency of a dielectric to absorb charge Limits high-frequency capabilities – Electrolytic Capacitors Extremely common in low-frequency (<1 kHz) circuits Contain an electrolyte that makes it possible to produce relatively small, high-capacity components 33AC Circuits I - Capacitors

34. Related Topics Fixed Value Capacitors (Continued) – Polarized Electrolytic Capacitors Most electrolytic capacitors are polarized Care must be taken to match the polarity of the capacitor to that of any dc voltage in the circuit 34AC Circuits I - Capacitors

35. Related Topics Variable Capacitors – Interleaved-Plate Capacitors 35AC Circuits I - Capacitors

36. Related Topics Variable Capacitors (Continued) – Variable Precision Capacitors – Trimmer Capacitors – low-value components that are used to make fine adjustments to the total capacitance in a circuit – In example below total capacitance ranges from 100.5pF-110pF 36AC Circuits I - Capacitors

37. Related Topics Capacitor Value Codes – Large (physically) capacitors usually has its value printed directly on the case – Smaller components are generally labeled using a two-digit or three-digit code Two-digit code: the number represents the value of the component in pF Example: 15 means 15 pF Three-digit code: the code is interpreted like the first three digits of a resistor code Example: 473 = 47 x 10 3 pF = 47 nF Note: The numbers 6 and 7 are not used as multiplier values The numbers 8 and 9 are decoded as follows: 8 = 0.01 and 9 = 0.1 Example: 158 = 0.15 pF 37AC Circuits I - Capacitors