physics capacitors

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ghoran
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292491
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physics capacitors
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2015-01-07 12:33:26
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  1. capacitor
    device that stores electrical charge and therefor electrical energy
  2. capacitor consists of
    two conductors placed near each other but not touching
  3. parallel plate capacitors are separated by
    an electrically charged insulating material called a dielectric
  4. one capacitor plate is
    positively charged the other is negatively charged
  5. electric potential of positive plate exceeds that of the negative plate by an amount
    V
  6. when the magnitude of the charge on each plate is doubled the electric potential is
    • doubled 
    • Q is proportional to V
    • Q=CV where c is capacitance and is a constant
  7. units of capacitance
    • CV-1 
    • F
  8. 1uF =
    1*10-6F
  9. 1nF
    • 1*10-9F
  10. 1pF
    1*10-12F
  11. capacitance
    the charge stored per unit potential difference across a capacitor
  12. initially the flow of charge , current , to an uncharged capacitor is
    high as time passes the rate reduces as the charge from the cell must overcome the build of of charge on the plate
  13. on charging electrons flow from
    negative terminal of cell to one end of plate (which becomes negative) and then from the other end of the plate (which becomes positive) to positive terminal of cell
  14. it isn't possible to store more and more charge by applying an ever increasing pd across the capacitor
    eventually the pd becomes too large for the insulating material between the plates . electrical breakdown then occurs and conduction takes place across the gap
  15. various dielectrics are used to
    increase the capacitance , the material used and its thickness determine the max working pd of the capacitor
  16. for a Q VS pd graph the gradient is
    C
  17. .... must be done to charge up a capacitor therefor
    • work
    • electrical potential energy is stored as a result
  18. the amount of energy stored depends on
    charge stored by the capacitor and the pd across it
  19. when a capacitor is being charged
    charge flows on to the capacitor
  20. the battery has to
    transfer energy to do work against the repulsive force from the charge already on the capacitor
  21. work done in moving charge through a pd is
    W=QV
  22. ... across a capacitor isn't constant
    pd
  23. average pd is
    0.5pd (pd increases from 0 to max pd when capacitor is fully charged)
  24. work done in charging a capacitor is therefor
    0.5QV
  25. energy stored by the capacitor is therefor
    0.5QV
  26. Q=CV so energy stored also =
    0.5CV2 or 0.5Q2/V
  27. draw a Q vs V graph
  28. draw a V vs Q graph
    what's the gradient
    what does the area under the graph represent
    • 1/C 
    • work done in charging a capacitor , energy stored by a capacitor 0.5QV 
  29. capacitor discharge circuit
  30. charging through a fixed resistor 
    when an uncharged capacitor is placed in a circuit to be charged the initial current I0 depends on the
    • emf of the battery and the resistance of the circuit 
    • I0 = V0/R
  31. as charge accumulates on the capacitor the
    pd across it increases .
  32. the pd opposes that of the battery and it becomes
    increasingly difficult to push charge on to the capacitor and the charging current drops
  33. eventually the pd across the capacitor is
    equal but opposite to that of the battery and the charging current drops to zero
  34. as the capacitor charges the pd across the resistor
    gets smaller because the pd across the capacitor gets bigger and so the current drops
  35. Q ∞ V sp Q vs t graph is the same as V vs T graph 
    draw these graphs for charging through a fixed resistor
  36. the rate at which the current drops depends on
    resistance and on the capacitance of the circuit
  37. the larger the resistance
    the lower the current the capacitor therefor takes longer to charge
  38. a large value of capacitance
    also increases the charging time since it takes more charge to fill the capacitor
  39. the product RC is known as
    the time constant for the circuit
  40. draw an I vs T graph for charging through a fixed resistor
  41. time constant is the time
    it takes for current to drop to 1/e of its original value
  42. draw a V vs T graph for charging across a fixed resistor showing curves for pd across capacitor and pd across resistor


    • where :
    • A = across capacitor and
    • B = across resistor
    • Vc + Vr = EMF
  43. exponential decay curves
    have the property that they always take the same time to decrease by a given fraction
  44. to discharge a capacitor
    take out the battery and reconnect the circuit
  45. when a charged capacitor is connected across a resistor the pd
    drives a current through the circuit
  46. the current flows in the
    opposite direction from the charging current
  47. the capacitor is fully discharged when
    the pd across the plates and the current in the circuit are both zero
  48. draw the three  vs T graph for discharging through a fixed resistor
  49. the I vs T graph is the same as the one for charging
    the current starts off relatively high and gradually decreases to zero . this is because  initially when a charged capacitor is connected across a resistor the pd drives a current through the circuit but the pd across the resistor decreases as the charge on the capacitor decreases
  50. Q =
    Q0e-t/RC 
  51. I =
    I0e-t/RC
  52. V =
    V0e-t/RC
  53. time constant is the
    • time taken for charge/voltage/current on a discharging capacitor to fall to 0.37Q0/V0/I0
    • its's also the time taken for voltage/charge on a charging capacitor to rise to 0.63V0/Q0
    • it's also the time taken for current on a charging capacitor to fall to 0.37I0
  54. Q =
    It
  55. capacitors discharge energy quickly so they can be used in
    applications where a lot of energy is required rapidly , a taser is an example . Filters also use capacitors to smooth electrical signals
  56. if we have two capacitors in parallel the voltage of each capacitor has to be the same because
    the capacitors are in parallel
  57. if we have two capacitors in parallel the final charge in each capcitor is
    • capacitor A
    • ------------         x total charge 
    • total capacitance

    • and the same goes for B 
    • total charge is Q=CV for capacitor that is being charged 
    • voltage can be worked out in the same way but you will find the voltage is the same for both capacitors as discussed in previous question
  58. if we have two capacitors in parallel the final energy stored in each capacitors is
    E = 0.5CV2 where v is the final pd across the capacitor
  59. why is there a loss of energy stored
    because battery has to transfer energy to do work against the repulsive force from the charge already on the capacitor so energy is wasted and hence less is stored
  60. battery has more energy because
    pd in battery is constant so E=QV

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