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Capacitors

Capacitors. Physics 1161: Lecture 05. Textbook Sections 20-5 – 20-6. Capacitance Practice. Example. 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.

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Capacitors

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  1. Capacitors Physics 1161:Lecture 05 Textbook Sections20-5 – 20-6

  2. Capacitance Practice Example 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!

  3. Example 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. A A d

  4. + + + + - - - - -q +q d pull pull 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? • Increases • Constant • Decreases

  5. + + + + - - - - -q +q d pull pull 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? • Increases • Constant • Decreases Remember charge is real/physical. There is no place for the charges to go.

  6. + + + + - - - - -q +q d pull pull Checkpoint 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 40% C = e0A/d C decreases! 50% E= Q/(e0A) Constant 55% V= Ed 70% U = ½QV

  7. Checkpoint 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

  8. Example Parallel Practice 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 1161: Lecture 4, Slide 8

  9. +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

  10. 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).

  11. C 2 +q2 -q2 + V2 E +q1 +q3 C C V1 V3 - 1 3 -q1 -q3 Checkpoint 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

  12. Checkpoint 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 35% Not necessarily C1 and C2 are NOT in series. 55% 2) q2 = q3 Yes! C2 and C3 are in series.

  13. Checkpoint 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. 45% 3) V2 = V3 Not necessarily, only if C2 = C3 55% 4) E = V1 Yes! Both ends are connected by wires

  14. Checkpoint 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. 15% 5) V1 < V2 Nope, V1 > V2. (E.g. V1 = 10-0, V2 =10-7 50% 6) Ceq > C1 Yes! C1 is in parallel with C23 (Ceq = C1 + C23)

  15. Battery • Batteries produce electrons through chemical reactions.  • http://electronics.howstuffworks.com/battery.htm

  16. Recap of Today’s Lecture • Capacitance C = Q/V • Parallel Plate: C = 0A/d • Dielectric: C = kCo (k is dielectric constant) • Capacitors in parallel: Ceq = C1+C2 • Capacitors in series: Ceq = 1/(1/C1+1/C2) • Batteries provide fixed potential difference

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