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  1. 1. <ul><li>Capacitors </li></ul>
  2. 2. Capacitors <ul><li>A capacitor is a device that stores electric charge. </li></ul><ul><li>A capacitor consists of two conductors separated by an insulator. </li></ul><ul><li>Capacitors have many applications: </li></ul><ul><ul><li>Computer RAM memory and keyboards. </li></ul></ul><ul><ul><li>Electronic flashes for cameras. </li></ul></ul><ul><ul><li>Electric power surge protectors. </li></ul></ul><ul><ul><li>Radios and electronic circuits. </li></ul></ul>
  3. 3. Types of Capacitors Parallel-Plate Capacitor Cylindrical Capacitor A cylindrical capacitor is a parallel-plate capacitor that has been rolled up with an insulating layer between the plates.
  4. 4. Capacitors and Capacitance Charge Q stored: The stored charge Q is proportional to the potential difference V between the plates. The capacitance C is the constant of proportionality, measured in Farads. Farad = Coulomb / Volt A capacitor in a simple electric circuit.
  5. 5. Parallel-Plate Capacitor <ul><li>A simple parallel-plate capacitor consists of two conducting plates of area A separated by a distance d . </li></ul><ul><li>Charge +Q is placed on one plate and –Q on the other plate. </li></ul><ul><li>An electric field E is created between the plates. </li></ul>+Q -Q +Q -Q
  6. 6. What is a capacitor? <ul><li>Electronic component </li></ul><ul><li>Two conducting surfaces separated by an insulating material </li></ul><ul><li>Stores charge </li></ul><ul><li>Uses </li></ul><ul><ul><li>Time delays </li></ul></ul><ul><ul><li>Filters </li></ul></ul><ul><ul><li>Tuned circuits </li></ul></ul>
  7. 7. Capacitor construction <ul><li>Two metal plates </li></ul><ul><li>Separated by insulating material </li></ul><ul><li>‘ Sandwich’ construction </li></ul><ul><li>‘ Swiss roll’ structure </li></ul><ul><li>Capacitance set by... </li></ul>
  8. 8. Defining capacitance <ul><li>‘ Good’ capacitors store a lot of charge… </li></ul><ul><li>… when only a small voltage is applied </li></ul><ul><li>Capacitance is charge stored per volt </li></ul><ul><li>Capacitance is measured in farads F </li></ul><ul><ul><li>Big unit so nF, mF and  F are used </li></ul></ul>
  9. 9. Graphical representation <ul><li>Equating to the equation of a straight line </li></ul>Gradient term is the capacitance of the capacitor Charge stored is directly proportional to the applied voltage Q V
  10. 10. Energy stored by a capacitor <ul><li>By general definition E=QV </li></ul><ul><ul><li>product of charge and voltage </li></ul></ul><ul><li>By graphical consideration... </li></ul>Area term is the energy stored in the capacitor Q V
  11. 11. Other expressions for energy <ul><li>By substitution of Q=CV </li></ul>
  12. 12. Charging a capacitor <ul><li>Current flow </li></ul><ul><li>Initially </li></ul><ul><ul><li>High </li></ul></ul><ul><li>Finally </li></ul><ul><ul><li>Zero </li></ul></ul><ul><li>Exponential model </li></ul><ul><li>Charging factors </li></ul><ul><ul><li>Capacitance </li></ul></ul><ul><ul><li>Resistance </li></ul></ul>I t
  13. 13. Discharging a capacitor <ul><li>Current flow </li></ul><ul><li>Initially </li></ul><ul><ul><li>High </li></ul></ul><ul><ul><li>Opposite to charging </li></ul></ul><ul><li>Finally </li></ul><ul><ul><li>Zero </li></ul></ul><ul><li>Exponential model </li></ul><ul><li>Discharging factors </li></ul><ul><ul><li>Capacitance </li></ul></ul><ul><ul><li>Resistance </li></ul></ul>I t
  14. 14. Discharging a Capacitor <ul><li>Initially, the rate of discharge is high because the potential difference across the plates is large. </li></ul><ul><li>As the potential difference falls, so too does the current flowing </li></ul><ul><li>Think pressure </li></ul>As water level falls, rate of flow decreases
  15. 15. <ul><li>At some time t, with charge Q on the capacitor, the current that flows in an interval  t is: </li></ul><ul><li>I =  Q/  t </li></ul><ul><li>And I = V/R </li></ul><ul><li>But since V=Q/C, we can say that </li></ul><ul><li>I = Q/RC </li></ul><ul><li>So the discharge current is proportional to the charge still on the plates. </li></ul>
  16. 16. <ul><li>For a changing current, the drop in charge,  Q is given by: </li></ul><ul><li> Q = -I  t (minus because charge Iarge at t = 0 and falls as t increases) </li></ul><ul><li>So  Q = -Q  t/RC (because I = Q/RC) </li></ul><ul><li>Or -  Q/Q =  t/RC </li></ul>
  17. 17. Voltage and charge characteristics <ul><li>Charging Discharging </li></ul>V or Q t V or Q t
  18. 18. Dielectrics <ul><li>A dielectric is an insulating material (e.g. paper, plastic, glass) . </li></ul><ul><li>A dielectric placed between the conductors of a capacitor increases its capacitance by a factor κ , called the dielectric constant . </li></ul><ul><li> C= κC o ( C o =capacitance without dielectric) </li></ul><ul><li>For a parallel-plate capacitor: </li></ul>ε = κε o = permittivity of the material.
  19. 19. Properties of Dielectric Materials <ul><li>Dielectric strength is the maximum electric field that a dielectric can withstand without becoming a conductor. </li></ul><ul><li>Dielectric materials </li></ul><ul><ul><li>increase capacitance. </li></ul></ul><ul><ul><li>increase electric breakdown potential of capacitors. </li></ul></ul><ul><ul><li>provide mechanical support. </li></ul></ul>Dielectric Strength (V/m) Dielectric Constant κ Material 3 x 10 6 1.0006 air 8 x 10 6 300 strontium titanate 150 x 10 6 7 mica 15 x 10 6 3.7 paper
  20. 20. Practice Quiz <ul><li>A charge Q is initially placed on a parallel-plate capacitor with an air gap between the electrodes, then the capacitor is electrically isolated. </li></ul><ul><li>A sheet of paper is then inserted between the capacitor plates. </li></ul><ul><li>What happens to: </li></ul><ul><ul><li>the capacitance? </li></ul></ul><ul><ul><li>the charge on the capacitor? </li></ul></ul><ul><ul><li>the potential difference between the plates? </li></ul></ul><ul><ul><li>the energy stored in the capacitor? </li></ul></ul>
  21. 21. Capacitors in Parallel Capacitors in Parallel:
  22. 22. Capacitors in Series For n capacitors in series:
  23. 23. Circuit with Capacitors in Series and Parallel a b 15 μF 3 μF 6 μF What is the effective capacitance C ab between points a and b? 20 μF C 1 C 2 C 3 C 4 C ab ?
  24. 24. <ul><li>Product of </li></ul><ul><ul><li>Capacitance of the capacitor being charged </li></ul></ul><ul><ul><li>Resistance of the charging circuit </li></ul></ul><ul><ul><li>CR </li></ul></ul><ul><li>Symbol  ‘Tau’ </li></ul><ul><li>Unit seconds </li></ul>Time constant
  25. 25. When t equals tau during discharge <ul><li>At t = tau the capacitor has fallen to 37% of its original value. </li></ul><ul><li>By a similar analysis tau can be considered to be the time taken for the capacitor to reach 63% of full charge. </li></ul>
  26. 26. Graphical determination of tau <ul><li>V at 37% </li></ul><ul><li>Q at 37% </li></ul><ul><li>Compared to initial maximum discharge </li></ul>V or Q t
  27. 27. Logarithmic discharge analysis <ul><li>Mathematical consideration of discharge </li></ul><ul><li>Exponential relationship </li></ul><ul><li>Taking natural logs equates expression to ‘y=mx+c’ </li></ul><ul><li>Gradient is -1/Tau </li></ul>
  28. 28. Logarithmic discharge graph Gradient term is the -1/Tau lnV t
  29. 29. for... <ul><li>Capacitors </li></ul>