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Capacitance

(C/V=F). Capacitance. Two conductors with equal but opposite charges. Potential Difference Between the Charges. Electric Field. Now turn the problem around …. Given a potential difference (a voltage) between two conductors, what is the charge on them?. Announcements .

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Capacitance

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  1. (C/V=F) Capacitance Two conductors with equal but opposite charges Potential Difference Between the Charges Electric Field Now turn the problem around … Given a potential difference (a voltage) between two conductors, what is the charge on them?

  2. Announcements • Cell phones on silent.

  3. Purpose of capacitors • Mainly as a reservoir of charge. • About 2%: timing or frequency control.

  4. Calculating Capacitance Assume a charge q on the plates Calculate the e-field using Gauss’ Law Calculate the potential Find the capacitance

  5. Parallel Plate Capacitor Find electric field for the above using Gauss’s Law.

  6. Parallel Plate Capacitor Increased area results in increased charge storage for a constant voltage. Capacitance is proportional to area

  7. +Q + + +Q E E V V -Q - - -Q Parallel Plate Capacitor The potential difference between the battery terminals and the plates will create a field and charges will flow from the battery to the plates until the potential difference is zeroed. Capacitance is inversely proportional to the distance between the plates.

  8. Parallel Plate Capacitor Surface charge density on the plates: The field (assuming d<<A1/2): The potential difference: The capacitance:

  9. Cylindrical Capacitor

  10. Spherical Capacitor

  11. Announcements • Cell phones on “silent.” • Test September 18. • Covers chapters 23 – 26. • Multiple choice concept tests + problems. • Cut up answer sheets and bring to all classes.

  12. C,Q + DV Circuits with Capacitors • A battery drives charges to accumulate on the capacitor plates. • A switch controls the flow of charge. Derive series, parallel formulae on board.

  13. Parallel Combination For parallel capacitors

  14. Parallel Connections All are parallel connections This is not

  15. Series Combination For series capacitors

  16. Series and Parallel • Consider circuit on board. • 1. Name all pairs of capacitors in series. • 2. Name all pairs of capacitors in series. • Key ideas: • For capacitors in series, the charges are all the same. • For capacitors in parallel, the potential differences are all the same.

  17. Mixed Combination of Capacitors

  18. Find the capacitance

  19. Energy Stored in a Capacitor • Since capacitors can carry charge after a battery is disconnected, they can store energy. • To calculate this energy, consider the work done to move a small amount of charge from one plate of the capacitor to the other. • As more and more charges are moved, the work required increases.

  20. Concept Question Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and are separated by a distance d. Suppose the plates are pulled apart until they are separated by a distance D > d. The electrostatic energy stored in the capacitor is 1. greater than 2. the same as 3. smaller than before the plates were pulled apart.

  21. Energy Density • Defined as stored energy per unit volume. • Consider the parallel plate capacitor.

  22. Rewiring Two Charged Capacitors

  23. Dielectrics • Dielectrics are insulators like glass, rubber or wood. • They are used to increase the charge storage capacity and maximum voltage in capacitors while providing mechanical support. • They are characterized by a dielectric constant, k, and are limited by the dielectric strength.

  24. Capacitors With Dielectrics

  25. An Atomic View • As we apply a voltage to the plates, the dielectric in between is polarized. • This creates a field in the opposite direction to the applied field and therefore reduces the effective voltage.

  26. Concept Question A parallel-plate capacitor is attached to a battery that maintains a constant potential difference V between the plates. While the battery is still connected, a glass slab is inserted so as to just fill the space between the plates. The stored energy 1. increases. 2. decreases. 3. remains the same.

  27. Metallic Slab Inside a Capacitor

  28. Summary • Capacitors are geometries that can hold charges. • Use Gauss’ Law symmetries to calculate capacitance. • Series and parallel connections. • Dielectrics increase capacitance.

  29. For Next Class • Reading Assignment • Chapter 27 – Current and Resistance • WebAssign: Assignment 4

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