Slide 1Chapter 26Capacitors = that which have capacitance to hold = containersCapacitanceMore About CapacitanceCapacitance of a one conductor system is small: for example, Isolated SphereHow to Make a Capacitor?A Real Parallel Plate Capacitor charged up with a battaryOther type of capacitors a Cylindrical CapacitorEnergy stored in a charged capacitorHow Much Energy Stored in a CapacitorEnergy in a Capacitor, the formulaEnergy in a Capacitor, final discussionCapacitors with DielectricsDielectrics, contDielectrics, finalSlide 17Types of Capacitors – TubularTypes of Capacitors – Oil FilledTypes of Capacitors – ElectrolyticTypes of Capacitors – VariableDielectrics – An Atomic ViewDielectrics – An Atomic View, 2Dielectrics – An Atomic View, 3Dielectrics – An Atomic View, 4Dielectrics – An Atomic View, finalInduced Charge and FieldChargespositive (+) negative (-)conservationForce (field)Potential (energy)121212rrF221022141rqqrqqkeForce between point chargeseq=F Er rForce on charge in the field0AEqdEConnect field with its source: chargeBAdV sEqVU Connect field with energyWhat for?To understand the worldOr to move on to capacitor, one of the three passive components in circuitsChapter 26Capacitance andDielectricsCapacitors = that which have capacitance to hold = containersCapacitors are devices that store electric chargeAny conductors can store electric charge, butCapacitors that specially designed devices to story a lot of chargesExamples of where capacitors are used include:radio receiversfilters in power suppliesto eliminate sparking in automobile ignition systemsenergy-storing devices in electronic flashesHow is my English?CapacitanceThe capacitance, C, is defined as the ratio of the amount of the charge Q on the conductor to the potential increase ΔV of the conductor because of the charge:This ratio is an indicator of the capability that the object can hold charges. It is a constant once the object is given, regardless there is charge on the object or not. This is like the capacitance of a mug which does not depend on there is water in it or not. The SI unit of capacitance is the farad (F)VQCQVC=1V1C F1 More About CapacitanceCapacitance will always be a positive quantityThe capacitance of a given capacitor is constantThe capacitance is a measure of the capacitor’s ability to store chargeThe farad is an extremely large unit, typically you will see microfarads (F=10-6F), nanofarads (nF=10-19F), and picofarads (pF=10-12F)Capacitance of a one conductor system is small: for example, Isolated SphereAssume a spherical charged conductor with radius RThe sphere will have the same capacitance as it would if there were a conducting sphere of infinite radius, concentric with the original sphereAssume V = 0 for the infinitely large shellEven for R=1m, C = 0.1 nFNote, this is independent of the charge and the potential differenceeekRRQkQVQC How to Make a Capacitor?Requirements:Hold chargesThe potential increase does not appear outside of the device, hence no influence to other devices.Is there such a good thing?For this parallel plate capacitor, the capacitance isarea surface theis ,00AdAdAEdAVQC02 E0022 E0E0E0EdEdV Quiz x: Isn’t Physics easy once you really understand it?A Real Parallel Plate Capacitor charged up with a battaryEach plate is connected to a terminal of the batteryThe battery is a source of potential differenceIf the capacitor is initially uncharged, the battery establishes an electric field in the connecting wiresThis field applies a force on electrons in the wire just outside of the platesThe force causes the electrons to move onto the negative plateThis continues until equilibrium is achievedThe plate, the wire and the terminal are all at the same potentialAt this point, there is no field present in the wire and the movement of the electrons ceasesThe plate is now negatively chargedA similar process occurs at the other plate, electrons moving away from the plate and leaving it positively chargedIn its final configuration, the potential difference across the capacitor plates is the same as that between the terminals of the batteryVOther type of capacitorsa Cylindrical CapacitorV = -2ke ln (b/a) = Q/lThe capacitance is( )2 ln /eQCV k b a= =DlEnergy stored in a charged capacitor Consider the circuit to be a systemBefore the switch is closed, the energy is stored as chemical energy in the batteryWhen the switch is closed, the energy is transformed from chemical to electric potential energyThe electric potential energy is related to the separation of the positive and negative charges on the platesA capacitor can be described as a device that stores energy as well as chargeHow Much Energy Stored in a Capacitorq -qdqTo study this problem, recall that the work the field force does equals to the electric potential energy loss:VQUWEEVdqCqVdqdWBWhen the charge buildup is q, move a dq, the work isThis also means that when the battery moves a charge dq to charge the capacitor, the work the battery does equals to the buildup of the electric potential energy:UWBWe now have the answer to the final charge Q: UCQdqCqdWWQQBB2200Energy in a Capacitor, the formulaWhen a capacitor has charge stored in it, it also stores electric potential energy that isThis applies to a capacitor of any geometryThe energy stored increases as the charge increases and as the potential difference increasesIn practice, there is a maximum voltage before discharge occurs between the plates22)(212VCCQUEEnergy in a Capacitor, final discussionThe 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)E2It can also be expressed in terms of the energy density (energy per unit volume)uE = ½ E2Capacitors with DielectricsA dielectric is a nonconducting material that, when placed between the plates of a capacitor, increases the capacitanceDielectrics include rubber, glass, and waxed paperWith a dielectric, the capacitance becomes C = κCo The capacitance increases
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