Transcript dielectric
20.9 Energy Stored in a Capacitor Assume a capacitor has a charge q on it and is being charged at the some point, The work needed to transfer a charge dq from one plate to the other is dW Vdq q dq C The total work required to charge the capacitor from q=0 to q=Q is W Q 0 q Q2 dq C 2C 1 Energy in a Capacitor The work done in charging the capacitor appears as electric potential energy U Q2 1 1 U QV C( V )2 2C 2 2 This applies to a capacitor of any geometry The stored energy increases as the charge increases and as the potential difference increases 2 Energy Density in an Electric Field 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 (eoAd)E2 It can also be expressed in terms of the energy density (energy per unit volume) in an electric field E uE = ½ eo E2 3 4 5 6 7 8 9 10 11 12 20.10 Capacitors with Dielectrics A dielectric is an insulating material that, when placed between the plates of a capacitor, increases the capacitance Dielectrics include rubber, plastic, or waxed paper When viewing in an atomic scale, the molecules that make up the dielectric are modeled as dipoles The dipoles are randomly oriented in the absence of an electric field 13 Dielectrics – An Atomic View An external electric field is applied This produces a torque on the molecules The molecules partially align with the electric field 14 Dielectrics – An Atomic View An external field can polarize the dielectric whether the molecules are polar or nonpolar The charged edges of the dielectric act as a second pair of plates producing an induced electric field in the direction opposite the original electric field 15 A charged capacitor before and after insertion of a dielectric 16 Capacitor with a Dielectric With a dielectric, C = κCo The capacitance is multiplied by the factor κ when the dielectric completely fills the region between the plates For a parallel plate capacitor, this becomes C = κεo(A/d) Dielectrics provide the following advantages Increase in capacitance Increase the maximum operating voltage Possible mechanical support between the plates This allows the plates to be close together without touching This decreases d and increases C If the electric field inside a capacitor exceeds some value, called the dielectric strength of the dielectric material, the dielectric medium will begin to conduct and the capacitor will break down by discharging 17 18 Types of Capacitors – Tubular Metallic foil may be interlaced with thin sheets of paper or Mylar The layers are rolled into a cylinder to form a small package for the capacitor 19 Types of Capacitors – Oil Filled Common for high voltage capacitors A number of interwoven metallic plates are immersed in silicon oil 20 Types of Capacitors – Variable Variable capacitors consist of two interwoven sets of metallic plates One plate is fixed and the other is moveable The capacitor generally vary between 10 and 500 pF 21 Types of Capacitors – Electrolytic Is used to store large amounts of charge at relatively low voltages The electrolyte is a solution that conducts electricity by virtue of motion of ions contained in the solution 22 23 24 25 26 27 28 29 30 Exercises of Chapter 20 6, 16, 22, 30, 35, 37, 44, 48, 51, 54, 70, 78, 88 31