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Capacitors!

Physics 102: Lecture 04. Capacitors!. Today’s lecture will cover Textbook Sections 17.5-6, 18.1-2, 6. A. B. Capacitance: The ability to store separated charge C = Q/V. Charge Q on plates. Charge 2Q on plates. V = V A – V B = +E 0 d. V = V A – V B =. E=. E=E 0. - - - - -. +

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Capacitors!

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  1. Physics 102:Lecture 04 Capacitors! • Today’s lecture will coverTextbook Sections17.5-6, 18.1-2, 6 Physics 102: Lecture 4, Slide 1

  2. A B Capacitance: The ability to store separated charge C=Q/V Charge Q on plates Charge 2Q on plates V = VA – VB = +E0 d V = VA – VB = E= E=E0 - - - - - + + + + + - - - - - + + + + + - - - - - + + + + + A B d d Potential difference is proportional to charge: Double Q  Double V Q = CV Physics 102: Lecture 4, Slide 2

  3. - - - - - + + + + + E d Capacitor • Any pair conductors separated by a small distance. (e.g. two metal plates) • Capacitor stores separated charge • Positive Q on one conductor, negative Q on other • Net charge is zero Q=CV • Stores Energy U =(½) Q V Physics 102: Lecture 4, Slide 3

  4. Example Capacitance Practice How much charge is on a 0.9 F capacitor which has a potential difference of 200 Volts? Q = Units? How much energy is stored in this capacitor? U = Units? Physics 102: Lecture 4, Slide 4

  5. Example Capacitance Practice How much charge is on a 0.9 F capacitor which has a potential difference of 200 Volts? Q = CV = (0.9)(200) = 180 Coulombs How much energy is stored in this capacitor? U = ½ Q V = ½ (180) (200) = 18,000 Joules! Physics 102: Lecture 4, Slide 5

  6. Capacitance of Parallel Plate Capacitor V V = Ed ANDE = Q/(e0A) (Between two large plates) So: V = Recall: CQ/V So: C = (For parallel plate capacitor) + E - A A If insert dielectric (κ>1) between plates C = κ C0 d e0=1/(4pk)=8.85x10-12 C2/Nm2 Physics 102: Lecture 4, Slide 6

  7. Capacitance of Parallel Plate Capacitor V V = Ed ANDE = Q/e0A (Between two large plates) So: V = Q d/(e0A) Recall: CQ/V So: (For parallel plate capacitor) + E - A A C = e0A/d If insert dielectric (κ>1) between plates C = κ C0 d e0=1/(4pk)=8.85x10-12 C2/Nm2 Physics 102: Lecture 4, Slide 7

  8. Parallel Plate CapacitorC = e0A/d Calculate the capacitance of a parallel plate capacitor made from two large square metal sheets 1.3 m on a side, separated by 0.1 m. Example C = A A Units? d ε0 = 8.85x10-12 C2/(Nm2) Physics 102: Lecture 4, Slide 8

  9. Parallel Plate CapacitorC = e0A/d Calculate the capacitance of a parallel plate capacitor made from two large square metal sheets 1.3 m on a side, separated by 0.1 m. Example A A d Physics 102: Lecture 4, Slide 9

  10. Dielectric constant (k > 1) Capacitance without dielectric Capacitance with dielectric Dielectric • Placing a dielectric between the plates increases the capacitance. C = k C0 Physics 102: Lecture 4, Slide 10

  11. + + + + - - - - -q +q d pull pull ACT: Parallel Plates A parallel plate capacitor is given a charge q. The plates are then pulled a small distance further apart. What happens to the charge q on each plate of the capacitor? 1) Increases 2) Constant 3) Decreases Physics 102: Lecture 4, Slide 11

  12. + + + + - - - - -q +q d pull pull ACT: Parallel Plates A parallel plate capacitor is given a charge q. The plates are then pulled a small distance further apart. What happens to the charge q on each plate of the capacitor? 1) Increases 2) Constant 3) Decreases Remember charge is real/physical. There is no place for the charges to go. Physics 102: Lecture 4, Slide 12

  13. + + + + - - - - -q +q d pull pull Preflight 4.1 A parallel plate capacitor is given a charge q. The plates are then pulled asmalldistance further apart. Which of the following apply to the situation after the plates have been moved? 1)The capacitance increases True False 2)The electric field increases True False 3)The voltage between the plates increases True False 4)The energy stored in the capacitor increases True False Physics 102: Lecture 4, Slide 13

  14. + + + + - - - - -q +q d pull pull Preflight 4.1 A parallel plate capacitor is given a charge q. The plates are then pulled a smalldistance further apart. Which of the following apply to the situation after the plates have been moved? 1)The capacitance increases True False 2)The electric field increases True False 3)The voltage between the plates increases True False 4)The energy stored in the capacitor increases True False C = e0A/d C decreases! E= Q/(e0A) Constant V= Ed U = ½QV Physics 102: Lecture 4, Slide 14

  15. Preflight 4.2 Two identical parallel plate capacitors are shown in end-view in A) of the figure. Each has a capacitance of C. B ) A ) If the two are joined as in (B) of the figure, forming a single capacitor, what is the final capacitance? 1) 2C 2) C 3) C/2 Physics 102: Lecture 4, Slide 15

  16. Preflight 4.2 Two identical parallel plate capacitors are shown in end-view in A) of the figure. Each has a capacitance of C. B ) A ) If the two are joined as in (B) of the figure, forming a single capacitor, what is the final capacitance? 1) 2C 2) C 3) C/2 Physics 102: Lecture 4, Slide 16

  17. Vwire 1= 0 V Vwire 2= 5 V Vwire 3= 12 V Vwire 4= 15 V Voltage in Circuits • Elements are connected by wires. • Any connected region of wire has the same potential. • The potential difference across an element is the element’s “voltage.” Example C1 C2 C3 VC1= _____ V VC2= _____ V VC3= _____ V Physics 102: Lecture 4, Slide 17

  18. Ceq Capacitors in Parallel • Share Charge: Qeq = Q1 + Q2 • Total Cap: Ceq = (Q1 + Q2)/V = C1 + C2 • Same voltage: V1 = V2 = Veq • Both ends connected together by wire C1 C2 Physics 102: Lecture 4, Slide 18

  19. 15 V Ceq 10 V Capacitors in Parallel • Share Charge: Qeq = Q1+ Q2 • Total Cap: Ceq = (Q1+ Q2)/V = C1+ C2 • Same voltage: V1 = V2 = Veq • Both ends connected together by wire 15 V 15 V C1 C2 10 V 10 V Physics 102: Lecture 4, Slide 19

  20. Parallel Practice Example A 4 mF capacitor and 6 mF capacitor are connected in parallel and charged to 5 volts. Calculate Ceq, and the charge on each capacitor. = Ceq = C4+C6 Q4 = C4 V4 = Q6 = C6 V6 = Qeq = Ceq Veq OR Q4 + Q6 = V = 5 V 5 V 5 V 5 V C4 C6 Ceq 0 V 0 V 0 V Physics 102: Lecture 4, Slide 20

  21. Parallel Practice Example A 4 mF capacitor and 6 mF capacitor are connected in parallel and charged to 5 volts. Calculate Ceq, and the charge on each capacitor. = 4 mF+6 mF = 10 mF Ceq = C4+C6 Q4 = C4 V4 = (4 mF)(5 V) = 20 mC = (6 mF)(5 V) = 30 mC Q6 = C6 V6 = (10 mF)(5 V) = 50 mC Qeq = Ceq Veq = Q4+ Q6 V = 5 V 5 V 5 V 5 V C4 C6 Ceq 0 V 0 V 0 V Physics 102: Lecture 4, Slide 21

  22. +Q -Q + + - - Ceq +Q -Q Capacitors in Series • Connected end-to-end with NO other exits • Same Charge: Q1 = Q2 = Qeq • Share Voltage: V1+V2=Veq + + + +Q + + C1 + + - + + + + C2 -Q - + - + + + Physics 102: Lecture 4, Slide 22

  23. +Q +Q -Q + +Q -Q - -Q Series Practice Example A 4 mF capacitor and 6 mF capacitor are connected in series and charged to 5 volts. Calculate Ceq, and the charge on the 4 mF capacitor. Q = CV + C4 - Ceq + C6 - Physics 102: Lecture 4, Slide 23

  24. +Q 5 V +Q -Q + +Q -Q - 0 V -Q Series Practice Example A 4 mF capacitor and 6 mF capacitor are connected in series and charged to 5 volts. Calculate Ceq, and the charge on the 4 mF capacitor. Q = CV 5 V + C4 - Ceq + C6 - 0 V Physics 102: Lecture 4, Slide 24

  25. C1 C1 C2 C2 Comparison:Series vs. Parallel Series • Can follow a wire from one element to the other with no branches in between. Parallel • Can find a loop of wire containing both elements but no others (may have branches). Physics 102: Lecture 4, Slide 25

  26. Electromotive Force + • Battery • Maintains potential difference V • Not constant power • Not constant current • Does NOT produce or supply charges, just “pushes” them. - Physics 102: Lecture 4, Slide 26

  27. C 2 +q2 -q2 + V2 E +q1 +q3 C C V1 V3 - 1 3 -q1 -q3 Preflight 4.4 A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. • q1 = q2 • q2 = q3 • V2 = V3 • E = V1 • V1 < V2 • Ceq > C1 Physics 102: Lecture 4, Slide 27

  28. Preflight 4.4 C 2 +q2 -q2 + V2 E +q1 +q3 C C V1 V3 - 1 3 -q1 -q3 A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. 1) q1 = q2 Not necessarily C1 and C2 are NOT in series. 2) q2 = q3 Yes! C2 and C3 are in series. Physics 102: Lecture 4, Slide 28

  29. Preflight 4.4 10V 7V?? C 2 0V +q2 -q2 + V2 E +q1 +q3 C C V1 V3 - 1 3 -q1 -q3 A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. 3) V2 = V3 Not necessarily, only if C2 = C3 4) E = V1 Yes! Both ends are connected by wires Physics 102: Lecture 4, Slide 29

  30. Preflight 4.4 10V 7V?? C 2 0V +q2 -q2 + V2 E +q1 +q3 C C V1 V3 - 1 3 -q1 -q3 A circuit consists of three initially uncharged capacitors C1, C2, and C3, which are then connected to a battery of emf E. The capacitors obtain charges q1, q2,q3, and have voltages across their plates V1, V2, and V3. 5) V1 < V2 Nope, V1 > V2. (E.g. V1 = 10-0, V2 =10-7 6) Ceq > C1 Yes! C1 is in parallel with C23 (Ceq = C1 + C23) Physics 102: Lecture 4, Slide 30

  31. See you next lecture! • Read 18.4, 6, 8 Physics 102: Lecture 4, Slide 31

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