PHY 184AnnouncementsReview - Electric Potential, V(x)Review - Electric Potential (2)Problem-Solving StrategiesSlide 6CapacitorsCapacitanceParallel Plate CapacitorParallel Plate Capacitor (2)Clicker QuestionSlide 12Definition of CapacitanceCharging/Discharging a CapacitorCharging/Discharging a Capacitor (2)Demo: Big SparkSlide 17Slide 18Slide 19Parallel Plate Capacitor (3)Parallel Plate Capacitor (4)Demo: Parallel Plate CapacitorExample - Capacitance of a Parallel Plate CapacitorExample 2 - Capacitance of a Parallel Plate CapacitorExample - Capacitance, Charge and Electrons …1/25/07 184 Lecture 11 1PHY 184PHY 184PHY 184PHY 184Spring 2007Lecture 11Title: Capacitors1/25/07 184 Lecture 11 2AnnouncementsAnnouncementsAnnouncementsAnnouncementsHomework Set 3 is due Tuesday, Jan. 30 at 8:00 am.Homework Set 4 opened this morning.Today we will finish up the electric potential and start with capacitors.1/25/07 184 Lecture 11 3Review - Electric Potential, V(x)Review - Electric Potential, V(x)Review - Electric Potential, V(x)Review - Electric Potential, V(x))definition - potential (electric energy) (potential ΔU/qΔVWUUUeifxsdExV)( zVyVxVEEEzyx,,,,► If a charge q moves in an electric field…► For reference V=0 at infinity…► E is the gradient of V…1/25/07 184 Lecture 11 4Review - Electric Potential (2)Review - Electric Potential (2)Review - Electric Potential (2)Review - Electric Potential (2)rkQrV )()()(1xVxVnii► For a point source Q …► For many sources …(superposition)1/25/07 184 Lecture 11 5Problem-Solving StrategiesProblem-Solving StrategiesProblem-Solving StrategiesProblem-Solving StrategiesGiven a charge distribution, calculate the electric field and the electric potential: (i) Use Gauss Law to derive the electric field E: (ii) For the potential (V=0 at infinity) useFor an arrangement of charges, remember the superposition superposition principleprinciple! This holds for the electric force, the electric field, the electric potential and the electric potential energy.enclosed0qAdExsdExV)(cosabba Note:1/25/07 184 Lecture 11 6Capacitors1/25/07 184 Lecture 11 7CapacitorsCapacitorsCapacitorsCapacitorsCapacitors are devices that store energy in an electric field.Capacitors are used in many every-day applications•Heart defibrillators•Camera flash unitsCapacitors are an essential part of electronics.•Capacitors can be micro-sized on computer chips or super-sized for high power circuits such as FM radio transmitters.1/25/07 184 Lecture 11 8CapacitanceCapacitanceCapacitanceCapacitanceCapacitors come in a variety of sizes and shapes.Concept: A capacitor consists of two separated conductors, usually called plates, even if these conductors are not simple planes.We will define a simple geometry and generalize from there.We will start with a capacitor consisting of two parallel conducting plates, each with area A separated by a distance d .We assume that these plates are in vacuum (air is very close to a vacuum).1/25/07 184 Lecture 11 9Parallel Plate CapacitorParallel Plate CapacitorParallel Plate CapacitorParallel Plate CapacitorWe charge the capacitor by placing•a charge +q on the top plate•a charge -q on the bottom plateBecause the plates are conductors, the charge will distribute itself evenly over the surface of the conducting plates.The electric potential, V, is proportional to the amount of charge on the plates.q qe.g., using a batteryMore precisely, potential difference V(+)-V(-) = V1/25/07 184 Lecture 11 10The proportionality constant between the charge q and the electric potential difference V is the capacitance C.We will call the electric potential difference V the “potential” or the “voltage” across the plates.The capacitance of a device depends on the area of the plates and the distance between the plates, but does not depend on the voltage across the plates or the charge on the plates.The capacitance of a device tells us how much charge is required to produce a given voltage across the plates.Parallel Plate Capacitor (2)Parallel Plate Capacitor (2)Parallel Plate Capacitor (2)Parallel Plate Capacitor (2)CVq q qVqC1/25/07 184 Lecture 11 11Clicker QuestionClicker QuestionClicker QuestionClicker QuestionWhat is the NET CHARGE on the charged capacitor?q qA: +q+(-q)=0B: |+q|+|-q|=2qC: qD: none of the above1/25/07 184 Lecture 11 12Clicker QuestionClicker QuestionClicker QuestionClicker QuestionWhat is the NET CHARGE on the charged capacitor?A: +q+(-q)=0Charges are added with their signs.However, we refer to the charge of a capacitor as being q (the charge of a capacitor is not the net charge!)q q1/25/07 184 Lecture 11 13Definition of CapacitanceDefinition of CapacitanceDefinition of CapacitanceDefinition of CapacitanceThe definition of capacitance isThe units of capacitance are coulombs per volt.The unit of capacitance has been given the name farad (abbreviated F) named after British physicist Michael Faraday (1791 - 1867)A farad is a very large capacitance•Typically we deal with F (10-6 F), nF (10-9 F),or pF (10-12 F)VqCVqCV 1C 1 F 1 1/25/07 184 Lecture 11 14Charging/Discharging a CapacitorCharging/Discharging a CapacitorCharging/Discharging a CapacitorCharging/Discharging a CapacitorWe can charge a capacitor by connecting the capacitor to a battery or to a DC power supply.A battery or DC power supply is designed to supply charge at a given voltage.When we connect a capacitor to a battery, charge flows from the battery until the capacitor is fully charged.If we then disconnect the battery or power supply, the capacitor will retain its charge and voltage.A real-life capacitor will leak charge slowly, but here we will assume ideal capacitors that hold their charge and voltage indefinitely.1/25/07 184 Lecture 11 15Charging/Discharging a Capacitor (2)Charging/Discharging a Capacitor (2)Charging/Discharging a Capacitor (2)Charging/Discharging a Capacitor (2)Illustrate the charging processing using a circuit diagram.Lines represent conductorsThe battery or power supply is represented byThe capacitor is represented by the symbolThis circuit has a switch (ab)(open) When the switch is between positions a and b , the circuit is open (not
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