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Capacitance

Capacitance. PHY 2049 Chapter 25. Chapter 25 Capacitance In this chapter we will cover the following topics: -Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries.

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Capacitance

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  1. Capacitance PHY 2049 Chapter 25

  2. Chapter 25 Capacitance In this chapter we will cover the following topics: -Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries. -Methods of connecting capacitors (in series , in parallel). -Equivalent capacitance. -Energy stored in a capacitor. -Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor. -Gauss’ law in the presence of dielectrics. (25 - 1)

  3. Capacitors

  4. Capacitor • Composed of two metal plates. • Each plate is charged • one positive • one negative • Stores energy SYMBOL

  5. A simple Capacitor TWO PLATES WIRES Battery

  6. INSIDE THE DEVICE

  7. What is STORED in the capacitor? • An Electric Field • Energy • Charge • All three • None of these

  8. d Air or Vacuum E - Q +Q Symbol Area A V=Potential Difference Two Charged Plates(Neglect Fringing Fields) ADDED CHARGE

  9. Where is the charge? +++++ + - - - - - - d AREA=A s=Q/A Air or Vacuum E - Q +Q Area A V=Potential Difference

  10. One Way to Charge: • Start with two isolated uncharged plates. • Take electrons and move them from the + to the – plate through the region between. • As the charge builds up, an electric field forms between the plates. • You therefore have to do work against the field as you continue to move charge from one plate to another. The capacitor therefore stores energy!

  11. Capacitor Demo

  12. d Air or Vacuum E - Q +Q Gaussian Surface Area A V=Potential Difference More on Capacitors Same result from other plate!

  13. DEFINITION - Capacity • The Potential Difference is APPLIED by a battery or a circuit. • The charge q on the capacitor is found to be proportional to the applied voltage. • The proportionality constant is C and is referred to as the CAPACITANCE of the device.

  14. UNITS • A capacitor which acquires a charge of 1 coulomb on each plate with the application of one volt is defined to have a capacitance of 1 FARAD • One Farad is one Coulomb/Volt

  15. Continuing… • The capacitance of a parallel plate capacitor depends only on the Area and separation between the plates. • C is dependent only on the geometry of the device!

  16. After the switch is closed, how much charge passed through the capacitor? • C/V • V/C • CV • C+V V

  17. P S N (25 - 6)

  18. Units of e0 pico

  19. Simple Capacitor Circuits • Batteries • Apply potential differences • Capacitors • Wires • Wires are METALS. • Continuous strands of wire are all at the same potential. • Separate strands of wire connected to circuit elements may be at DIFFERENT potentials.

  20. NOTE • Work to move a charge from one side of a capacitor to the other is = qEd. • Work to move a charge from one side of a capacitor to the other is qV • Thus qV = qEd • E=V/d As before

  21. TWO Types of Connections SERIES PARALLEL

  22. V CEquivalent=CE Parallel Connection

  23. q -q q -q V C1 C2 Series Connection The charge on each capacitor is the same !

  24. q -q q -q V C1 C2 Series Connection Continued

  25. More General

  26. Example C1=12.0 uf C2= 5.3 uf C3= 4.5 ud C1 C2 series (12+5.3)pf (12+5.3)pf V C3

  27. E=e0A/d +dq +q -q More on the Big C • We move a charge dq from the (-) plate to the (+) one. • The (-) plate becomes more (-) • The (+) plate becomes more (+). • dW=Fd=dq x E x d

  28. So….

  29. Parallel Plate Cylindrical Spherical Not All Capacitors are Created Equal

  30. Spherical Capacitor

  31. Calculate Potential Difference V (-) sign because E and ds are in OPPOSITE directions.

  32. Continuing… Lost (-) sign due to switch of limits.

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