chapter24

= __**Chapter 24: Electrostatic Energy and Capacitance**__  =

** Navigation of this chapter by section: **
 * Electrostatic Potential Energy **
 * Capacitance **
 * Storage of Electrical Energy **
 * Capacitors, Batteries, and Circuits **
 * Dielectrics **
 * Capacitor/Dielectric Lab **

= **__Introduction to capcitance and potential:__** = === When we bring a point charge q from far away to a region where other charges are present, we must do work qV. where V is the potential at the final position due to the other charges in the vicinity. The work done is stored as electrostatic potential energy. The electrostatic potential energy of a system is the work needed to assemble the system. when positive charge is placed on an isolated conductor, the potential of the conductor increases. The ratio of the charge to the potential is called the capacitance of the conductor (C= Q/V). ===

= = = __ **Vital Equations for Electrostatic Potential** __ =

The potential at point 3, a dirstance r from q1 and a distance R from q2, is given by **V3= (kq1/r) + (kq2/R)**
= __ **Electrostatic Potential Energy** __ =

**U= (kQ^2)/(2R)= (1/2)QV**
= = = = = **__Capacitance__** =

=== A device consisting of two conductors carrying equal but opposite charges is called a capacitor. A capacitor is usually charged by transferring a charge Q from one conductor to the other conductor, which leaves one of the conductors with a charge +Q and the other with a charge of -Q. ===

=__ Storage of Electrical Energy  __=

=== When a capacitor is being charged, typically electrons are transferred from the positively charged conductor to the negatively charged conductor. This leaves the positive conductor with an electron deficit and the negative conductor with an electron surplus. Alternatively, transferring positive charges from the negative to the positive conductor can also charge capacitors. Either way, work must be done in order to charge a capacitor, and at least some of this work is stored as electrostatic potential energy. ===

=** __Capacitors,__  ** __ **Batteries, and Circuits** __ = = = === When two capacitors are connected, as shown in the figure below, so that the upper plates of the two capacitors are connected by a conducting wire and are therefore at a common potential, and the lower plates are also connected together and are at a common potential. These Capacitors are said to be connected in parallel. Devices connected in parallel share a common potential difference across each wire due solely to the way they are connected. === === In the figure below, assume that points A and B are connected to a battery or some other device that provides a potential difference. V= Va-Vb between the plates of each capacitor. If the capacitances are C1 and C2, the charges Q1 and Q2 stored on the plates are given by: ===

Q = Q1 + Q2 = C1V + C2V = (C1+C2)V
= = = = = = === A Combination of Capacitors in a circuit can sometimes be substituted with a single capacitor that is operationally equivalent to the combination. the Substitute capacitor is said to have an equivalent capacitance. That is, if a combination of initially uncharged capacitors is connected to a battery, the charge Q that flows through the battery as the capacitor combination becomes charged is the same as the charge that flows through the battery if connected to a single uncharged capacitor of equivalent capacitance. Therefore, the equivalent capacitance of two capacitors in parallel is the ratio of the Charge Q1 + Q2 to the potential difference. ===

Ceq = Q/V = (Q1+Q2)/V = Q1/V + Q2/V = C1 + C2
= =



=== In the figure below, two capacitors are connected so that the potential difference across the pair is the sum of the potential difference across the individual capacitors. Devices connected in this manner are said to be connected in series. Both the capacitors in the figure below are connected in series and initially they are without charge. If points A and B are then connected to the terminals of a battery, electrons will be pumped from the upper plate of the first capacitor and the bottom plate of the second capacitor. This leaves the upper plate of C1 with a charge +Q and the lower plate of C2 with a charge of -Q. When a charge +Q appears on the upper plate of C1, the electric field produced by that charge induces an equal negative charge, -Q, on the lower plate of C1. This Charge comes from electrons drawn from the upper plate of C2. Thus, there will be an equal charge +Q on the upper plate of the second capacitor and the corresponding charge -Q on its lower plate. The potential difference across the first capacitor is ===

1/Ceq = 1/C1 + 1/C2


= = = =

=** __ Dielectrics __ **= = = === ** A nonconducting material (e.g. air, glass, paper, or wood) is called a dielectric. When the space between two conductors of a capacitor is occupied by a dielectric, the capacitance is increased by a factor of K that is characteristic of the dielectric, a fact discovered experimentally by Michael Faraday. The reason for this increase is that the electric field between the plates of the capacitor is weakened by the dielectric. Thus, for a given charge on the plates, the potential difference is reduced and the capacitance (Q/V) is increased. Consider am isolated charged capacitor without a dielectric between its plates. A dielectric slab is then inserted between the plates, completely filling the space between the plates. If the Electric field is Eo before the dielectric slab is inserted, after the dielectric slab is inserted between the plates the field is: ** ===

** E = Eo/K Where K (Kappa) is the dielectric constant. **
= =

C = Q/V = Q/(Vo/K) = K(Q/Vo) OR C = KCo
=﻿= = __Capacitance/Dielectric Lab__  =

This lab was conducted using a simulator on []

**Goals:** Determine the Capacitance and explore the effects of space and dielectric materials inserted between the conductors of a capacitor in a circuit

**Materials:** **-**Capacitor -Multimeter -1.5 V Power Source -Paper Dielectric -Teflon Dielectric -Glass Dielectric

**Procedure:** The Plate separation and area will remain constant throughout the lab, only the dielectric material will vary in this lab.

**Units: V- Volts mm- milimeters K- dielectric constant pF- picofarads = 1 X 10^-12 F** **Conclusion:** From this data we can conclude that adding a dielectric while keeping other factors constant will increase the capacitance of the plates. From this, we can derive the fundamental equation **C= KCo** = = = Sources: = = -The Textbook = = -My Brain =
 * Voltage || Plate Separation || Area of the Plates || Dielectric || Capacitance ||
 * 1.5 V || 10.0mm || 100.0mm^2 || none (air) || 0.09pF ||
 * 1.5 V || 10.0mm || 100.0mm^2 || Teflon K=2.1 || 0.19pF ||
 * 1.5 V || 10.0mm || 100.0mm^2 || Paper K=3.5 || 0.31pF ||
 * 1.5 V || 10.0mm || 100.0mm^2 || Glass K=4.7 || 0.42pF ||

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