Chapter 24Capacitance & DielectricsDr. Ray KwokSJSUCapacitance & Dielectrics - Dr. Ray KwokGoals for Chapter 24• To consider capacitors and capacitance• To study the use of capacitors in series and capacitors in parallel• To determine the energy in a capacitor• To examine dielectrics and see how different dielectrics lead to differences in capacitanceCapacitance & Dielectrics - Dr. Ray KwokKeep charges apart and you get capacitancedAdAEdQVQCooε=εσσ==≡parallelplatesCapacitance & Dielectrics - Dr. Ray KwokThe unit of capacitance, the farad,is very large Commercial capacitors for home electronics are often cylindrical, from the size of a grain of rice to that of a large cigar. Capacitors like those mentioned above and pictured at right are microfarad capacitors.dAVQCoε=≡εois a very small number.Capacitance & Dielectrics - Dr. Ray KwokApplications of Capacitors –e.g. Computers  Computers use capacitors in many ways Some keyboards use capacitors at the bases of the keys When the key is pressed, the capacitor spacing decreases and the capacitance increases The key is recognized by the change in capacitanceCapacitance & Dielectrics - Dr. Ray KwokCapacitance of a Spherical Capacitor−πε=−πε==−πε=πε−=⋅−=πε=ε=π∫ ∫a1b12a1b12QQVQCa1b12Qrdr4QdEVr4QEQ)r4(Eoooba2o2oo2lCapacitance & Dielectrics - Dr. Ray KwokCapacitance of a Cylindrical Capacitorπε=≡πε=πελλ==πελ−=πελ−=⋅−=πελ=ελ=π∫ ∫abln2LC'CablnL2abln2LVQCabln2rdr2dEVr2EL)rL2(EoooobaooolCapacitance & Dielectrics - Dr. Ray KwokCircuit Symbols A circuit diagram is a simplified representation of an actual circuit Circuit symbols are used to represent the various elements Lines are used to represent wires The battery’s positive terminal is indicated by the longer lineCapacitance & Dielectrics - Dr. Ray KwokCapacitors may be connected one or many at a timeIn series,same Q.V = V1+ V2+…In parallel,same V.Q = Q1+ Q2+ …Capacitance & Dielectrics - Dr. Ray KwokCalculations regarding capacitanceOne step at a time !More examples…Capacitance & Dielectrics - Dr. Ray KwokDielectrics change the potential difference• The potential between to parallel plates of a capacitor changes when the material between the plates changes. It does not matter if the plates are rolled into a tube as they are in Figure 24.13 or if they are flat as shown in Figure 24.14.KVVo=Capacitance & Dielectrics - Dr. Ray KwokTable 24.1—Dielectric constantsCapacitance & Dielectrics - Dr. Ray KwokMolecular models• Figure 24.18 (at right) and Figure 24.19 (below) show the effect of an applied field on individual molecules.Capacitance & Dielectrics - Dr. Ray KwokPolarization and electric field linesCapacitance & Dielectrics - Dr. Ray KwokEnergy Stored in a Capacitor Assume the capacitor is being charged and, at some point, has a charge q on it The work needed to transfer a charge from one plate to the other is The total work required isqdW Vdq dqC= ∆ =202Qq QW dqC C= =∫Capacitance & Dielectrics - Dr. Ray KwokEnergy, cont The work done in charging the capacitor appears as electric potential energy U: This applies to a capacitor of any geometry The energy stored increases as the charge increases and as the potential difference increases In practice, there is a maximum voltage before discharge occurs between the plates221 1( )2 2 2QU Q V C VC= = ∆ = ∆= ½ CV2Capacitance & Dielectrics - Dr. Ray KwokEnergy, final The energy can be considered to be stored in the electric field  For a parallel-plate capacitor, the energy can be expressed in terms of the field as U = ½(εoAd)E2 It can also be expressed in terms of the energy density (energy per unit volume)uE= ½εoE2Capacitance & Dielectrics - Dr. Ray KwokExamples to consider, capacitors with and without dielectrics222121EkEoεε==Electric energy density( Joules/m3)Capacitance & Dielectrics - Dr. Ray KwokDielectric breakdown• A very strong electrical field can exceed the strength of the dielectric to contain it. Table 24.2 at the bottom of the page lists some limits.Capacitance & Dielectrics - Dr. Ray KwokCapacitance & Dielectrics - Dr. Ray KwokGauss’s Law in