1. Capacitors Phy 1161: PreLecture 06 Today’s lecture will cover Textbook Sections 20-5 – 20-6

2. Comparison: Electric Potential Energy vs. Electric Potential  V AB : the difference in electric potential between points B and A  U AB : the change in electric potential energy of a charge q when moved from A to B  U AB = q  V AB q AB

3. Electric Potential: Summary E field lines point from higher to lower potential For positive charges, going from higher to lower potential is “downhill” For a battery, the (+) terminal is at a higher potential than the (–) terminal Positive charges tend to go “downhill”, from + to - Negative charges go in the opposite direction, from - to +  U AB = q  V AB

4. Important Special Case Uniform Electric Field ++++++++++ ---------- Two large parallel conducting plates of area A +Q on one plate -Q on other plate Then E is uniform between the two plates: E=4  kQ/A zero everywhere else This result is independent of plate separation This is call a parallel plate capacitor

5. Parallel Plate Capacitor Potential Difference A B E=E 0 d V = V A – V B = +E 0 d ++++++++++ ---------- A B d ++++++++++ ---------- ++++++++++ ---------- E= V = V A – V B = +2E 0 d Potential difference is proportional to charge: Double Q  Double V E 0 = 4πkQ/A Charge Q on platesCharge 2Q on plates

6. Capacitance The ability to store separated charge Definition: Units: Farad (F) – named in honor of Michael Faraday –1 F = 1C/V From Faraday’s notebook

7. Capacitor Any pair of 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

8. Capacitance of Parallel Plate Capacitor V = Ed AND E = Q/(  0 A) (Between two large plates) So: V = Qd/ /(  0 A) Remember: C  Q/V So: Equation based on geometry of capacitor A d A E+ - V  0 = 8.85x10 -12 C 2 /Nm 2 If there is adielectric (κ>1) between plates C = κ C 0

9. Dielectric Placing a dielectric between the plates increases the capacitance. C =  C 0 Capacitance with dielectric Dielectric constant (  > 1) Capacitance without dielectric

10. MaterialConstantMaterialConstant Vacuum1Germanium16 Polyvinyl chloride 3.18Strontium titanate 310 Mica3 - 6Water80.4 Mylar3.1Glycerin42.5 Neoprene6.70Benzene2.284 Plexiglass3.40Glass5 – 10 Polyethylene2.25Air (1 atm)1 Liquid ammonia (-78 o C) 25Titanium dioxide (rutile) 173 perp 86 para Dielectrics

11. 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.”

12. 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 = 5 V V C 3 = 3 VV C 2 = 7 V C1C1 C2C2 C3C3 The potential difference across an element is the element’s “voltage.”

13. 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

14. 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

15. 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

16. Electromotive Force Battery –Maintains potential difference V –Not constant power –Not constant current –Does NOT produce or supply charges, just “pushes” them. + -