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Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
Charging  C
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Charging C

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Transcript

  • 1. Lecture 21 - Capacitors in circuits
    • Charging a capacitor (semi-qualitative).
    • Charging a capacitor (quantitative).
    • The time constant.
    • Discharging a capacitor.
    • Energy Considerations.
    • The End
  • 2. Charging a capacitor - diagram.
  • 3. Charging a capacitor (semi-qualitative).
    • At time t=0 the switch is closed, with the capacitor initially uncharged.
    • A current will flow  =V c +V R =I 0 R , as initially V c =0. Thus the initial current is I 0 =  /R .
    • Now a charge begins to build on the capacitor, introducing a reverse voltage. The current falls, and stops when the P.D. across C is  .
    • Final charge is given by " Q=CV " => Q 0 =C  .
  • 4. Charging a capacitor (quantitative).
    • Apply Kirchoff's loop rule.
  • 5. Charging a capacitor (cont)
    • Where Q 0 = C  = the final charge on the capacitor.
  • 6. Charging a capacitor (cont).
    • To find the current, differentiate since I=dQ/dt .
    • By considering time zero, when the current is I 0 ,
  • 7.  
  • 8.  
  • 9. The time constant.
    • The time constant  =RC .
    • The units are seconds ( t/RC is dimensionless).
    • The time taken for the charge to rise to 1-(1/e) of the final value in the circuit.
    • The current to fall by 1/e of its initial value.
  • 10. Discharging capacitor - diagram.
  • 11. Discharging a capacitor.
    • Apply Kirchoff's loop rule.
  • 12. Discharging a capacitor (cont)
    • To find the current...
  • 13. Discharging a capacitor (cont)
    • To find the current...
    • Note the sign, the current flow has reversed!
    • But, when t=0, I=I 0 , so
  • 14. Energy Considerations.
    • During charging, a total charge Q=C  flows through the battery.
    • The battery does work W=Q 0  =C  2 .
    • The energy stored in the capacitor is ½ QV= ½ Q 0  = ½ C  2 .
    • Where's the other half?
  • 15. Energy considerations (cont).
    • Solve by setting x=2t/RC .
    • Which, when added to the energy stored on the capacitor, equals the work done by the battery.
  • 16. Finally…
    • E-M depends a lot on integrals, vectors etc. shows how useful they are.
    • It is one of the foundations of physics but:
      • it can be rather formal, encouraging the precise thinking that we expect of any academic training;
      • it is rather far removed from the everyday, but that develops the imagination we expect from a physicist.

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