Physics 1161: Pre-Lecture 05 Capacitors Sections 20-5 – 20-6

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

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 + DUAB = q DVAB

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 i.e. it doesn’t matter how far away the plates are from each other This is called a parallel plate capacitor

Parallel Plate Capacitor Potential Difference Charge Q on plates Charge 2Q on plates V = VA – VB = +E0 d V = VA – VB = +2E0d E=2E0 E=E0 + - + - + - A B A B d d Potential difference is proportional to charge: Double Q  Double V E0 = 4πkQ/A

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

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 Q = CV E d + - Stores Energy U = (½) Q V

Capacitance of Parallel Plate Capacitor V = Ed AND E = Q/(e0A) (Between two large plates) So: V = Qd/ /(e0A) Remember: CQ/V So: Equation based on geometry of capacitor V + E - A A d If there is adielectric (κ>1) between plates C = κ C0 e0= 8.85x10-12 C2/Nm2

Dielectric Placing a dielectric between the plates increases the capacitance. C = k C0 Dielectric constant (k > 1) Capacitance without dielectric Capacitance with dielectric

Dielectrics Material Constant Vacuum 1 Germanium 16 Polyvinyl chloride 3.18 Strontium titanate 310 Mica 3 - 6 Water 80.4 Mylar 3.1 Glycerin 42.5 Neoprene 6.70 Benzene 2.284 Plexiglass 3.40 Glass 5 – 10 Polyethylene 2.25 Air (1 atm) Liquid ammonia (-78oC) 25 Titanium dioxide (rutile) 173 perp 86 para

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.” Vwire 1= 0 V Vwire 2= 5 V Vwire 3= 12 V Vwire 4= 15 V C1 C2 C3 VC1= _____ V VC2= _____ V VC3= _____ 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.” Vwire 1= 0 V Vwire 2= 5 V Vwire 3= 12 V Vwire 4= 15 V C1 C2 C3 VC1= 5 V VC2= 7 V VC3= 3 V

Capacitors in Parallel Both ends connected together by wire Share Charge: Qeq = Q1 + Q2 Total Cap: Ceq = (Q1 + Q2)/V = C1 + C2 Same voltage: V1 = V2 = Veq Ceq C1 C2

Capacitors in Parallel Both ends connected together by wire Share Charge: Qeq = Q1+ Q2 Total Cap: Ceq = (Q1+ Q2)/V = C1+ C2 Same voltage: V1 = V2 = Veq 15 V 15 V 15 V Ceq C1 C2 10 V 10 V 10 V

Capacitors in Series Connected end-to-end with NO other exits Same Charge: Q1 = Q2 = Qeq Share Voltage: V1+V2=Veq + + +Q -Q + +Q + + Ceq C1 + - + - + + +Q -Q + + + C2 -Q - - - + + + + +

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