Lecture 11 Lecture 11 --CapacitanceCapacitanceChapter 30 Chapter 30 --Thursday February 15thThursday February 15th•Review: capacitors in series and parallel•Energy stored in an electric field•Capacitor filled with a dielectric•DC circuits and electromotive force (if time)Reading: pages 701 thru 716 (chapter 31) in HRKReading: pages 701 thru 716 (chapter 31) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssign: deadline Fri. Feb. 16th at 11:59pmWebAssign: deadline Fri. Feb. 16th at 11:59pmNext weekNext week’’s set will be from chapter 31s set will be from chapter 31Graded problems (Ch.29) Graded problems (Ch.29) ––P. 6, 10; (Ch.30) P. 6, 10; (Ch.30) ––E. 7, 12, 23, P. 9, 20E. 7, 12, 23, P. 9, 20Practice problems (Ch. 30): Ex. 25, 35, 37, 39; Prob. 13, 23Practice problems (Ch. 30): Ex. 25, 35, 37, 39; Prob. 13, 23Practice problems (Ch. 30):Practice problems (Ch. 30):Ex. 3, 5, 7, 19; Prob. 3Ex. 3, 5, 7, 19; Prob. 3CapacitorsCapacitors•The transfer of charge from one terminal of the capacitor to the other creates the electric field.•Where there is a field, there must be a potential gradient, i.e. there has to be a potential difference between the terminals.qCV=Δ•qrepresents the magnitude of the excess charge on either plate. Another way of thinking of it is the charge that was transferred between the plates.SI unit of capacitance: 1 farad (F) = 1 coulomb/volt(after Michael Faraday)•This leads to the definition of capacitance C:Capacitances more often have units of picofarad (pF) and microfarad (μF)Capacitors connected in parallelCapacitors connected in parallelΔV+q2-q2-q1+q1+(q1+q2)-(q1+q2)ΔV11qCV=Δ22qCV=Δ12 eqqqCV+= Δ()12 eqCC VCV+Δ= Δ12eqCCC=+Capacitors connected in seriesCapacitors connected in series12111eqCCC=+11neq nCC=∑In fact:Energy stored in electric fieldsEnergy stored in electric fieldsdqdU = ΔV × dqqdU dqC=()2221201122QqQUdU dq Q CVCCC== =≡××=Δ∫∫212ouEε=Energy densityA dielectric in an electric fieldA dielectric in an electric fieldElectric dipoles in an electric fieldNon-polar atoms in an electric fieldA dielectric in an electric fieldA dielectric in an electric field0'=+EE EGGGE = E0− E' E' opposes E0A dielectric in an electric fieldA dielectric in an electric fieldLinear materials: E' ∝ E, ⇒ E0= (1 + χe)E0011(1)1eeeeEEEκχχκ⇒= = =++χeis the electric susceptibility (dimensionless)κeis the dielectric constant (dimensionless)ε = κeεοis the permittivityDielectrics in capacitorsDielectrics in capacitorsoencencoe encencdqq'dqdqεεκε⋅= −⋅=⋅=∫∫∫EAEAEAGGGGGGvvveC' Cκ=DC CircuitsDC CircuitsemfDC CircuitsDC CircuitsKirchoff’s first law:At any junction in an electrical circuit, the total current entering the junction must equal the total current leaving the junction.Electromotive force (emf)Electromotive force (emf)•Source of electrical energy in a circuit.•Represents the potential energy provided to each coulomb of charge that passes through the device.•IT IS NOT A FORCE!!!•Most often, emf is provided by a battery (a chemical cell).•The emf is the same as the potential difference between the negative and positive terminals of a battery WHEN NO CURRENT FLOWS.•In general, when a current flows, the potential difference at the terminals of a battery is lower than the emf.•An emf can also store energy.E = dW/dq SI unit: joule/CoulombCircuit analysisCircuit analysisKirchoff’s second law:The algebraic sum of all differences in potential around a complete circuit loop must be
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