Chapter 27 Capacitance and Dielectrics 第二十七章 電容及介電質

Capacitors

The uses of capacitors Capacitor or condenser is a charge storage device. It is also an energy storage device. Capacitors have many uses beyond the energy or charge storage, such as in tuning circuits, filter circuits, memories, etc. What else can you think of?

Capacitance Two isolated conductors of any shape comprise a capacitor. We call these two conductors plates. When the capacitor is charged, there are equal amount but opposite charges on the two plates. The amount of charge is proportional to the potential difference between them. The proportionality constant C is called capacitance.

Parallel-plate capacitor Neglecting the edges, we have The capacitance of a parallel plate capacitor:

The unit of capacitance The SI unit of capacitance is faraday (F). How large is one faraday? If d = 10 m, then Not easy to achieve!

Charging the capacitor

A cylindrical capacitor

A spherical capacitor

An isolated sphere R

Sample problem 1 A storage capacitor on a random access memory (RAM) chip has a capacitance of 55 fF. If the capacitor is charged to 5.3 V, how many excess electrons are on its negative plate? 1.8  106 electrons

Some circuit symbols

Capacitors in parallel

Capacitors in series

Sample problem 2

Sample problem 3

Energy stored in a capacitor The work is stored as the potential energy U in the capacitor.

The medical defibrillator About ¼ of the stored energy is sent to the patient during a period of 2.0 ms.

Energy stored in an electric field Neglecting the edges, Ad is the volume in which the electric field is present. Thus the energy density of the electric field is:

Sample problem 4 An isolated conducting sphere whose radius R is 6.85 cm has a charge q = 1.25 nC. (a) How much potential energy is stored in the electric field of this charged conductor? (b) What is the energy density at the surface of the sphere? (a) 103 nJ. (b) 25.4 J/m3.

Capacitor with a dielectric + + + + + + + V       

Schematics of real capacitors

Capacitor with a dielectric

Space filled with a dielectric material For a point charge: Just outside a conductor:

Sample problem 5 A parallel-plate capacitor whose capacitance C is 13.5 pF is charged by a battery to a potential difference V = 12.5 V between its plates. The charging battery is now disconnected and a porcelain slab ( = 6.50) is slipped between the plates. What is the potential energy of the capacitor-porcelain device, both before and after the slab is put into place? Ui = 1055 pJ and Uf = Ui/ = 160 pJ

Dielectrics: an atomic view

Induced dipole moment

Capacitance: an atomic view

Sample problem 6 What is the electric field in (a) the gap between the plates and the dielectric slab? (b) the dielectric slab? What is the capacitance?

Metal slab in a capacitor

Capacitor partially filled with a dielectric

Sample problem 7 What is the ratio of the capacitance of the capacitor with dielectrics shown below to that of the same capacitor without any dielectric?

Force exerted on a dielectric in a capacitor

Force exerted on a dielectric in a capacitor

Home work Question (問題): 1, 6, 19 Exercise (練習題): 11, 16, 19 Problem (習題): 10, 20, 24, 38