1 / 24

Understanding Capacitors in Circuits and Dielectrics

Discover the concept of capacitors in circuits, the role of dielectrics, and the energy stored in capacitors through Q, V, and C relations. Learn about parallel and series capacitor circuits and the impact of adding dielectrics.

kimberlyv
Download Presentation

Understanding Capacitors in Circuits and Dielectrics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 212 Lecture 8 Today's Concept: Capacitors Capacitors in a circuits, Dielectrics, Energy in capacitors

  2. Q V +Q C Q=VC -Q Q Battery has moved charge Q from one plate to the other. Simple Capacitor Circuit V C 8

  3. Qtotal Q1 = C1V Q2 = C2V Qtotal Parallel Capacitor Circuit C2 C1 V Key point:V is the same for bothcapacitors Key Point: Qtotal = Q1 + Q2 = VC1 + VC2 = V(C1 + C2) Ctotal = C1 + C2 14

  4. Q Q=VCtotal +Q C1 -Q Q Q V1 V +Q C2 -Q Q V2 Q Q/Ctotal = Q/C1 + Q/C2 1 1 1 = + Ctotal C1 C2 Series Capacitor Circuit V Key point:Q is the same for both capacitors Key point:Q = VCtotal = V1C1 = V2C2 Also: V = V1 + V2 17

  5. Checkpoint 1 Which has lowest total capacitance: C C C C C 1/Ctotal = 1/C + 1/C = 2/C Ctotal = 2C Ctotal = C/2 Ctotal = C 18

  6. Cleft = C/2 Cright = C/2 Ctotal = C Which has lowest total capacitance ? C C C C C Ctotal = C Ctotal = Cleft + Cright 20

  7. Similar to Checkpoint 3 Q2 C2 V0 V2 C1 C3 V3 Q3 V1 Q1 Ctotal • Which of the following is NOT necessarily true: • V0 = V1 • Ctotal > C1 • V2 = V3 • Q2 = Q3 • V1 = V2 + V3 24

  8. Checkpoint 3 A circuit consists of three unequal capacitors C1, C2, and C3 which are connected to a battery of voltage V0. The capacitance of C2 is twice that of C1. The capacitance of C3 is three times that of C1. The capacitors obtain charges Q1, Q2, and Q3. Compare Q1, Q2, and Q3. A.Q1 > Q3 > Q2B.Q1 > Q2 > Q3C.Q1 > Q2 = Q3D.Q1 = Q2 = Q3E.Q1 < Q2 = Q3 X X 1. See immediately: Q2 = Q3 (capacitors in series) 2. How about Q1 vs. Q2 and Q3? Calculate C23 first. 25

  9. Charge capacitor – store a logical “1” Discharge capacitor – store a logical “0” Row select : close the switch Column select : charge or discharge C 1 Gigabyte ~ 1010 cells

  10. = 1/2CV2 Since Q = VC =1/2Q2/C Energy in a Capacitor In Prelecture 7 we calculated the work done to move charge Q from one plate to another: +Q C V U = 1/2QV -Q This is potential energy waiting to be used… 26

  11. C0 C1=kC0 V V Q0=VC0 Q1=VC1 Dielectrics By adding a dielectric you are just making a new capacitor with larger capacitance (factor ofk) 11

  12. Capacitor with dielectric Q1 = C1V1 =kCV =kQ V V1 = Q1/C1 = Q/kC= V/k If connected to a battery V stays constant. V1 = V C1 =kC k Isolated capacitor: total Q stays constant. Q1 = Q k C1 =kC

  13. Checkpoint 4a Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric. Compare the voltages of the two capacitors. A. V1 > V2B. V1 = V2C. V1 < V2 Consider first the effect on the capacitance, then, does Q or V stay constant? 33

  14. C0 V Compare using U = 1/2CV2 U1/U0 = k Potential Energy goes UP Effects of dielectric Two identical parallel plate capacitors are connected to identical batteries. Then a dielectric is inserted between the plates of capacitor C1. Compare the energy stored in the two capacitors. C1 V k=2 A) U1 < U0 B) U0 = U1 C) U1 > U0 35

  15. Checkpoint 4b Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric. Compare the potential energy stored by the two capacitors. A. U1 > U2B. U1 = U2C. U1 < U2 Consider first the effect on the capacitance, then, does Q or V stay constant? 33

  16. Checkpoint 4c V must be the same ! Q: U: Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2 has been charged and disconnected, it is filled with a dielectric. A. The charges will flow so that the charge on C1 will become equal to the charge on C2.B. The charges will flow so that the energy stored in C1 will become equal to the energy stored in C2.C. The charges will flow so that the potential difference across C1 will become the same as the potential difference across C2.D. No charges will flow. The charge on the capacitors will remain what it was before they were connected.

  17. Calculation C0 V x0 k What changes when the dielectric added? (A) Only C(B) only Q (C) only V (D) C and Q (E) V and Q C changes Adding dielectric changes the physical capacitor V does not change and C changes Q changes An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. A dielectric (k) of width x0/4 is inserted into the gap as shown. What is Qf, the final charge on the capacitor? V x0/4 38

  18. Calculation C0 V x0 k k How does potential difference change ? Vleft Vright V x0/4 (A) Vleft < Vright(B) Vleft = Vright(C) Vleft > Vright The conducting plate is an equipotential ! 40

  19. Calculation C0 V x0 k k k C2 C1 = What is C1 ? (A) C1 = C0(B) C1 = 3/4C0(C) C1 = 4/3C0(D) C1 = 1/4C0 A = 3/4A0 C1 = 3/4C0 C1 = 3/4 (e0A0/d0) d = d0 V x0/4 Consider capacitor to be two capacitances, C1 and C2, in parallel: In general. For parallel plate capacitor: C = e0A/d 43

  20. Calculation C0 V x0 k k k What is C2 ? • C2 = kC0(B) C2 = 3/4kC0(C) C2 = 4/3 kC0(D) C2 = 1/4kC0 A = 1/4A0 C2 = 1/4kC0 C = ¼(ke0A0/d0) d = d0 V x0/4 C2 C1 = C1 = 3/4C0 In general. For parallel plate capacitor filled with dielectric: C = ke0A/d 45

  21. Calculation C0 V x0 k k k What is C? • (B) (C) C = C0 (3/4 + 1/4k) V x0/4 C2 C C1 = C1 = 3/4C0 C2 = 1/4kC0 C = parallel combination of C1 and C2: C = C1 + C2 46

  22. Calculation C0 V x0 k k k C = C0 (3/4 + 1/4k) V x0/4 C2 C C1 = C1 = 3/4C0 C2 = 1/4kC0 What is Q? 50

  23. Different Problem k Q = Q0 = C0V Vf = Q/C = V/(3/4 + 1/4k) C = C0 (3/4 + 1/4k) An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V and then battery is disconnected. A dielectric (k) of width 1/4x0 is inserted into the gap as shown. What is Vf, the final voltage on the capacitor? Q0 C0 V V x0 1/4x0 Q (A) Vf < V(B) Vf = V(C) Vf > V Q stays same: no way to add or subtract We know C: (property of capacitor)

  24. An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V and then battery is disconnected. A dielectric (k) of width 1/4x0 is inserted into the gap as shown. What is Vf, the final voltage on the capacitor? Different Problem k U decreased Q0 C0 V V x0 1/4x0 Vf = Q/C = V/(3/4 + 1/4k) How did energy stored in capacitor change when dielectric inserted? • U increased(B) U stayed same(C) U decreased U = ½ Q2/C Q remained same C increased

More Related