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Capacitor Circuits

Capacitor Circuits. Thunk some more …. C1=12.0 u f C2= 5.3 u f C3= 4.5 u d. C 1 C 2. (12+5.3)pf. V. C 3. So…. Sorta like (1/2)mv 2. What's Happening?. DIELECTRIC. Polar Materials (Water). Apply an Electric Field.

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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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