1. Physics 102: Lecture 4, Slide 1 Capacitors! Physics 102: Lecture 04 Today’s lecture will cover Textbook Sections 17.5-6, 18.1-2, 6

2. Physics 102: Lecture 4, Slide 2 Capacitance: The ability to store separated charge C=Q/V A B E=E 0 d V = V A – V B = +E 0 d ++++++++++ ---------- A B d ++++++++++ ---------- ++++++++++ ---------- E= V = V A – V B = Potential difference is proportional to charge: Double Q  Double V Q = CV Charge Q on platesCharge 2Q on plates

3. Physics 102: Lecture 4, Slide 3 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 E d ++++++++++ ---------- Q=CV U =(½) Q V Stores Energy

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

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

6. Physics 102: Lecture 4, Slide 6 Capacitance of Parallel Plate Capacitor V = Ed AND E = Q/(  0 A) (Between two large plates) So: V = Recall: C  Q/V So: C = (For parallel plate capacitor) A d A E+ - V  0 =1  k)=8.85x10 -12 C 2 /Nm 2 If insert dielectric (κ>1) between plates C = κ C 0

7. Physics 102: Lecture 4, Slide 7 Capacitance of Parallel Plate Capacitor V = Ed AND E = Q/  0 A (Between two large plates) So: V = Q d/(  0 A) Recall: C  Q/V So: (For parallel plate capacitor) A d A E+ - V  0 =1  k)=8.85x10 -12 C 2 /Nm 2 C =  0 A/d If insert dielectric (κ>1) between plates C = κ C 0

8. Physics 102: Lecture 4, Slide 8 Parallel Plate Capacitor C =  0 A/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. A d A C = Units? ε 0 = 8.85x10 -12 C 2 /(Nm 2 )

9. Physics 102: Lecture 4, Slide 9 Parallel Plate Capacitor C =  0 A/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. A d A

10. Physics 102: Lecture 4, Slide 10 Dielectric Placing a dielectric between the plates increases the capacitance. C =  C 0 Capacitance with dielectric Dielectric constant (  > 1) Capacitance without dielectric

11. Physics 102: Lecture 4, Slide 11 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? ACT: Parallel Plates 1) Increases2) Constant3) Decreases +q-q ++++++++ -------- d pull

12. Physics 102: Lecture 4, Slide 12 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? ACT: Parallel Plates 1) Increases2) Constant3) Decreases Remember charge is real/physical. There is no place for the charges to go. +q-q ++++++++ -------- d pull

13. Physics 102: Lecture 4, Slide 13 A parallel plate capacitor is given a charge q. The plates are then pulled a small distance 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 Preflight 4.1 +q-q ++++++++ -------- d pull

14. Physics 102: Lecture 4, Slide 14 A parallel plate capacitor is given a charge q. The plates are then pulled a small distance 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 Preflight 4.1 +q-q ++++++++ -------- d pull C =  0 A/dC decreases! E= Q/(  0 A)Constant V= Ed U = ½ QV

15. Physics 102: Lecture 4, Slide 15 Two identical parallel plate capacitors are shown in end- view in A) of the figure. Each has a capacitance of C. A) B) 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 Preflight 4.2

16. Physics 102: Lecture 4, Slide 16 Two identical parallel plate capacitors are shown in end- view in A) of the figure. Each has a capacitance of C. A) B) 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 Preflight 4.2

17. Physics 102: Lecture 4, Slide 17 Voltage in Circuits Elements are connected by wires. Any connected region of wire has the same potential. V wire 1 = 0 VV wire 2 = 5 VV wire 3 = 12 VV wire 4 = 15 V V C 1 = _____ VV C 3 = _____ VV C 2 = _____ V C1C1 C2C2 C3C3 The potential difference across an element is the element’s “voltage.”

18. Physics 102: Lecture 4, Slide 18 Capacitors in Parallel Both ends connected together by wire C1C1 C2C2 C eq Share Charge: Q eq = Q 1 + Q 2 Total Cap: C eq = (Q 1 + Q 2 )/V = C 1 + C 2 = V eq Same voltage: V 1 = V 2

19. Physics 102: Lecture 4, Slide 19 Capacitors in Parallel Both ends connected together by wire C1C1 C2C2 C eq 15 V 10 V 15 V 10 V 15 V 10 V Share Charge: Q eq = Q 1 + Q 2 Total Cap: C eq = (Q 1 + Q 2 )/V = C 1 + C 2 = V eq Same voltage: V 1 = V 2

20. Physics 102: Lecture 4, Slide 20 Parallel Practice A 4  F capacitor and 6  F capacitor are connected in parallel and charged to 5 volts. Calculate C eq, and the charge on each capacitor. C4C4 C6C6 C eq 5 V 0 V 5 V 0 V 5 V 0 V C eq = C 4 +C 6 Q 4 = C 4 V 4 Q 6 = C 6 V 6 Q eq = C eq V eq = = = OR Q 4 + Q 6 = V = 5 V

21. Physics 102: Lecture 4, Slide 21 Parallel Practice A 4  F capacitor and 6  F capacitor are connected in parallel and charged to 5 volts. Calculate C eq, and the charge on each capacitor. C4C4 C6C6 C eq 5 V 0 V 5 V 0 V 5 V 0 V C eq = C 4 +C 6 Q 4 = C 4 V 4 Q 6 = C 6 V 6 Q eq = C eq V eq = 4  F+6  F = 10  F = (4  F)(5 V) = 20  C = (6  F)(5 V) = 30  C = (10  F)(5 V) = 50  C = Q 4 + Q 6 V = 5 V

22. Physics 102: Lecture 4, Slide 22 Capacitors in Series Connected end-to-end with NO other exits Same Charge: Q 1 = Q 2 = Q eq C eq C1C1 C2C2 + + + + + + + + + + + + + - + - + - + - + - +Q -Q +Q -Q +Q -Q Share Voltage: V 1 +V 2 =V eq

23. Physics 102: Lecture 4, Slide 23 Series Practice C eq C4C4 C6C6 + - + - + - +Q -Q +Q -Q +Q -Q A 4  F capacitor and 6  F capacitor are connected in series and charged to 5 volts. Calculate C eq, and the charge on the 4  F capacitor. Q = CV

24. Physics 102: Lecture 4, Slide 24 Series Practice C eq C4C4 C6C6 + - + - + - +Q -Q +Q -Q +Q -Q A 4  F capacitor and 6  F capacitor are connected in series and charged to 5 volts. Calculate C eq, and the charge on the 4  F capacitor. 5 V 0 V 5 V 0 V Q = CV

25. Physics 102: Lecture 4, Slide 25 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). C1C1 C2C2 C2C2 C1C1

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

27. Physics 102: Lecture 4, Slide 27 A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf . The capacitors obtain charges q 1, q 2,q 3, and have voltages across their plates V 1, V 2, and V 3. C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V1V1 V2V2 V3V3 1)q 1 = q 2 2)q 2 = q 3 3)V 2 = V 3 4)E = V 1 5)V 1 < V 2 6)C eq > C 1 Preflight 4.4

28. Physics 102: Lecture 4, Slide 28 A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf . The capacitors obtain charges q 1, q 2,q 3, and have voltages across their plates V 1, V 2, and V 3. C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V1V1 V2V2 V3V3 1) q 1 = q 2 Not necessarily C 1 and C 2 are NOT in series. 2) q 2 = q 3 Yes! C 2 and C 3 are in series. Preflight 4.4

29. Physics 102: Lecture 4, Slide 29 C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V1V1 V2V2 V3V3 3) V 2 = V 3 Not necessarily, only if C 2 = C 3 4) E = V 1 10V 0V 7V?? Yes! Both ends are connected by wires A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf . The capacitors obtain charges q 1, q 2,q 3, and have voltages across their plates V 1, V 2, and V 3. Preflight 4.4

30. Physics 102: Lecture 4, Slide 30 C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V1V1 V2V2 V3V3 5) V 1 < V 2 Nope, V 1 > V 2. (E.g. V 1 = 10-0, V 2 =10-7 6) C eq > C 1 10V 0V 7V?? Yes! C 1 is in parallel with C 23 (C eq = C 1 + C 23 ) A circuit consists of three initially uncharged capacitors C 1, C 2, and C 3, which are then connected to a battery of emf . The capacitors obtain charges q 1, q 2,q 3, and have voltages across their plates V 1, V 2, and V 3. Preflight 4.4

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