<ul><li>Capacitors  </li></ul><ul><li>revision </li></ul>
What is a capacitor? <ul><li>Electronic component </li></ul><ul><li>Two conducting surfaces separated by an insulating mat...
Capacitor construction <ul><li>Two metal plates </li></ul><ul><li>Separated by insulating material </li></ul><ul><li>‘ San...
Defining capacitance <ul><li>‘ Good’ capacitors store a lot of charge… </li></ul><ul><li>… when only a small voltage is ap...
Graphical representation <ul><li>As the capacitor is charged to higher and higher P.d.  …….. </li></ul>Gradient term is th...
Energy stored by a capacitor <ul><li>By general definition E=QV </li></ul><ul><ul><li>product of charge and voltage </li><...
Other expressions for energy <ul><li>By substitution of Q=CV </li></ul>
Charging a capacitor <ul><li>Current  flow </li></ul><ul><li>Initially  </li></ul><ul><ul><li>High </li></ul></ul><ul><li>...
Discharging a capacitor <ul><li>Current  flow </li></ul><ul><li>Initially  </li></ul><ul><ul><li>High </li></ul></ul><ul><...
Voltage and charge characteristics <ul><li>Charging Discharging </li></ul>V or Q t V or Q t
<ul><li>Product of </li></ul><ul><ul><li>Capacitance of the capacitor being charged </li></ul></ul><ul><ul><li>Resistance ...
When t equals tau during discharge <ul><li>Discharging:  At t = tau the capacitor has fallen to 37% of its original value....
Graphical determination of tau <ul><li>V at 37% </li></ul><ul><li>Q at 37% </li></ul><ul><li>Compared to initial maximum d...
Logarithmic discharge analysis <ul><li>Mathematical consideration of discharge </li></ul><ul><li>Exponential relationship ...
Logarithmic discharge graph Gradient term is the -1/Tau lnV t
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Capacitors

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  • Construction and charging and discharging
  • Capacitors

    1. 1. <ul><li>Capacitors </li></ul><ul><li>revision </li></ul>
    2. 2. 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>
    3. 3. 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>
    4. 4. 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>
    5. 5. Graphical representation <ul><li>As the capacitor is charged to higher and higher P.d. …….. </li></ul>Gradient term is the capacitance of the capacitor Charge stored is directly proportional to the applied voltage Q V
    6. 6. 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
    7. 7. Other expressions for energy <ul><li>By substitution of Q=CV </li></ul>
    8. 8. 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><ul><li>Because rate of charge flow depends on ‘how much charge is on plate' </li></ul></ul><ul><li>Charging factors </li></ul><ul><ul><li>Capacitance </li></ul></ul><ul><ul><li>Resistance in outer circuit </li></ul></ul>I t
    9. 9. 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><ul><li>Because rate of charge flow depends on how much charge is on plate </li></ul></ul><ul><li>Discharging factors </li></ul><ul><ul><li>Capacitance </li></ul></ul><ul><ul><li>Resistance in outer circuit </li></ul></ul>I t
    10. 10. Voltage and charge characteristics <ul><li>Charging Discharging </li></ul>V or Q t V or Q t
    11. 11. <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><ul><ul><ul><li>To show units of tau are seconds, use Ohm’s Law to substitute for R and Capacitance definition to substitute for C </li></ul></ul></ul>Time constant
    12. 12. When t equals tau during discharge <ul><li>Discharging: At t = tau the capacitor has fallen to 37% of its original value. </li></ul><ul><li>Charging :By a similar analysis tau can be considered to be the time taken for the capacitor to reach 63% of full charge. </li></ul>
    13. 13. 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
    14. 14. Logarithmic discharge analysis <ul><li>Mathematical consideration of discharge </li></ul><ul><li>Exponential relationship </li></ul><ul><li>Taking natural logs produces expression of form ‘y=mx+c’ </li></ul><ul><li>Gradient is -1/Tau </li></ul>
    15. 15. Logarithmic discharge graph Gradient term is the -1/Tau lnV t
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