SJSU EE 140 - ch24_Capacitance (21 pages)

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ch24_Capacitance

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ch24_Capacitance

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21
School:
San Jose State University
Course:
Ee 140 - Principles of Electromagnetic Fields
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Chapter 24 Capacitance Dielectrics Dr Ray Kwok SJSU Capacitance Dielectrics Dr Ray Kwok Goals 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 capacitance Capacitance Dielectrics Dr Ray Kwok Keep charges apart and you get capacitance C A o A Q Q V Ed d d o parallel plates Capacitance Dielectrics Dr Ray Kwok The 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 Q o A C V d o is a very small number Capacitance Dielectrics Dr Ray Kwok Applications 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 capacitance Capacitance Dielectrics Dr Ray Kwok Capacitance of a Spherical Capacitor Q E 4 r o 2 Q E 4 o r 2 b Q dr Q 1 1 V E dl 2 4 o a r 2 o b a Q Q 2 o C Q 1 1 1 1 V 2 o b a b a Capacitance Dielectrics Dr Ray Kwok Capacitance of a Cylindrical Capacitor L E 2 rL o E 2 o r b dr b V E dl ln 2 o a r 2 o a C C Q V L b ln 2 o a C 2 o L b ln a 2 o L b ln a Capacitance Dielectrics Dr Ray Kwok Circuit 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 line Capacitance Dielectrics Dr Ray Kwok Capacitors may be connected one or many at a time In series same Q V V1 V2 In parallel same V Q Q1 Q2 Capacitance Dielectrics Dr Ray Kwok Calculations regarding capacitance One step at a time More examples Capacitance Dielectrics Dr Ray Kwok Dielectrics 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 V Vo K Capacitance Dielectrics Dr Ray Kwok Table 24 1 Dielectric constants Capacitance Dielectrics Dr Ray Kwok Molecular 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 Kwok Polarization and electric field lines Capacitance Dielectrics Dr Ray Kwok Energy 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 q dW Vdq dq C The total work required is W Q 0 q Q2 dq C 2C Capacitance Dielectrics Dr Ray Kwok Energy cont The work done in charging the capacitor appears as electric potential energy U Q2 1 1 U Q V C V 2 CV2 2C 2 2 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 plates Capacitance Dielectrics Dr Ray Kwok Energy 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 oAd E2 It can also be expressed in terms of the energy density energy per unit volume uE oE2 Capacitance Dielectrics Dr Ray Kwok Examples to consider capacitors with and without dielectrics 1 1 2 Electric energy density E k o E 2 Joules m3 2 2 Capacitance Dielectrics Dr Ray Kwok Dielectric 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 Kwok Capacitance Dielectrics Dr Ray Kwok Gauss s Law in dielectrics EAGauss Qtotal inside o Q free inside K o

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