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Capacitor Circuits

This guide explores the behavior of capacitors with and without dielectrics. We examine how capacitors store charge and how inserting a dielectric material affects their capacitance and voltage. The concepts of electric fields, local ordering in polar materials, and effective charge reduction in non-polar materials are discussed. We also explain how to measure capacitance and voltage, analyze the relationships between voltage, charge, and capacitance, and summarize key results using Gauss's Law. This fundamental knowledge is crucial for understanding electrical circuits.

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Capacitor Circuits

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  1. Capacitor Circuits

  2. Thunk some more … C1=12.0 uf C2= 5.3 uf C3= 4.5 ud C1 C2 (12+5.3)pf V C3

  3. So…. Sorta like (1/2)mv2

  4. What's Happening? DIELECTRIC

  5. Polar Materials (Water)

  6. Apply an Electric Field Some LOCAL ordering Larger Scale Ordering

  7. Adding things up.. - + Net effect REDUCES the field

  8. Non-Polar Material

  9. Non-Polar Material Effective Charge is REDUCED

  10. We can measure the C of a capacitor (later) C0 = Vacuum or air Value C = With dielectric in place C=kC0 (we show this later)

  11. How to Check This Charge to V0 and then disconnect from The battery. C0 V0 Connect the two together V C0 will lose some charge to the capacitor with the dielectric. We can measure V with a voltmeter (later).

  12. V Checking the idea.. Note: When two Capacitors are the same (No dielectric), then V=V0/2.

  13. Messing with Capacitors The battery means that the potential difference across the capacitor remains constant. For this case, we insert the dielectric but hold the voltage constant, q=CV since C  kC0 qk kC0V THE EXTRA CHARGE COMES FROM THE BATTERY! + V - + - + - + V - Remember – We hold V constant with the battery.

  14. Another Case • We charge the capacitor to a voltage V0. • We disconnect the battery. • We slip a dielectric in between the two plates. • We look at the voltage across the capacitor to see what happens.

  15. No Battery q0 + - + - q0 =C0Vo When the dielectric is inserted, no charge is added so the charge must be the same. V0 V qk

  16. ++++++++++++ q V0 ------------------ -q A Closer Look at this stuff.. Consider this capacitor. No dielectric experience. Applied Voltage via a battery. C0

  17. ++++++++++++ q V0 ------------------ -q Remove the Battery The Voltage across the capacitor remains V0 q remains the same as well. The capacitor is (charged),

  18. ++++++++++++ q - - - - - - - - -q’ +q’ V0 + + + + + + ------------------ -q Slip in a DielectricAlmost, but not quite, filling the space Gaussian Surface E E’ from induced charges E0

  19. A little sheet from the past.. -q’ +q’ - - - +++ -q q 0 2xEsheet 0

  20. Some more sheet…

  21. A Few slides backNo Battery q=C0Vo When the dielectric is inserted, no charge is added so the charge must be the same. q0 + - + - V0 V qk

  22. From this last equation

  23. Original Structure Disconnect Battery Slip in Dielectric Vo + - + - + - Add Dielectric to Capacitor V0 Note: Charge on plate does not change!

  24. SUMMARY OF RESULTS

  25. APPLICATION OF GAUSS’ LAW

  26. New Gauss for Dielectrics

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