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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 2AnnouncementsAnnouncementsAnnouncementsAnnouncementsHomework 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/qΔVWUUUeifxsdExV)( 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 StrategiesGiven 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) useFor 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.enclosed0qAdExsdExV)(cosabba Note:1/25/07 184 Lecture 11 6Capacitors1/25/07 184 Lecture 11 7CapacitorsCapacitorsCapacitorsCapacitorsCapacitors are devices that store energy in an electric field.Capacitors are used in many every-day applications•Heart defibrillators•Camera flash unitsCapacitors 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 8CapacitanceCapacitanceCapacitanceCapacitanceCapacitors 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 CapacitorWe charge the capacitor by placing•a charge +q on the top plate•a charge -q on the bottom plateBecause 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 10The 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 qVqC1/25/07 184 Lecture 11 11Clicker QuestionClicker QuestionClicker QuestionClicker QuestionWhat 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 CapacitanceThe definition of capacitance isThe 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)VqCVqCV 1C 1 F 1 1/25/07 184 Lecture 11 14Charging/Discharging a CapacitorCharging/Discharging a CapacitorCharging/Discharging a CapacitorCharging/Discharging a CapacitorWe 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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MSU PHY 184 - Lec11drs

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