# Electrical Energy and Capacitance

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Electrical Energy and Capacitance
Chapter 16

Review What is potential energy?
Energy at rest or energy due to position

What is a conservative force?
A conservative force is a force that does work in such a way that the work done depends only upon the initial and final positions.

Frictional force is dissipative.
The Coulomb force is conservative.

What is meant by the conservation of energy?
Energy cannot be created or destroyed, only transformed.

Gravitational force is conservative.
Gravitational potential energy depends upon mass, gravity, and position.

Introduction New concepts Electric potential energy Electric potential
Voltage between two points Electric potential difference Capacitance

Work Done on a Charge Electrostatic force is conservative
Work may be done by a conservative force

The equation for work done on a charge:
Since F = qE W = (F)d = (qE)d

Electric Potential Electric potential (V) is a scalar quantity
It is defined as the energy per unit charge (J/C) at a given point The unit for electric potential is the volt (1 volt = 1 Joule/Coulomb)

Potential Difference Definition of the potential difference (DV) between points A and B DV = VB - VA = DPE/q = -E.d The units are Volts or Joules /Coulomb

Useful relationships:
1 V = 1 J/C 1 N/C = 1 V/m

Electrical PE and KE A positive charge gains electrical PE when it moves against the field. A positive charge gains KE when it moves in the same direction as the field. 166, 16.2

A negative charge gains KE when it moves against the field.
A negative charge gains electrical PE when it moves in the same direction as the field. A negative charge gains KE when it moves against the field. 167

Potential Difference And Electric Potential
A 12-volt automobile battery Maintains a potential difference across its terminals The positive terminal is at a higher potential. (+ 12 volts) The negative terminal is at a lower potential (0 volts) and is connected to the car frame. Charge moves around the circuit. 16.3

Zero Potential A point of zero potential is usually defined by grounding some point in the circuit.

A point at infinity may be considered to be at zero potential in relation to a positive charge.

Electric Potential at a Point
The electric potential, at a particular location, created by a point charge can be found by using: V = ke(q/r)

Electric Potential The electric potential depends upon only two things:

The electric potential depends upon only two things:
Charge Location

The electric potential exists at every point surrounding a given charge.
A second charge is not needed.

Electric potential is a scalar quantity.
If there are two or more charges, the potentials add algebraically at a given point. no vectors to worry about

Electric PE Electric potential energy is the energy that a charge has due to its position in the electric field produced by another charge. It is measured in Joules. 133

The electric potential (PE) energy of a pair of charges can be found by using:
PE = q2V1 = q2(keq1/r) PE = ke (q1q2/r) 16.7

The electric potential energy is positive if the charges are identical and negative if they are different.

Equipotentials No work is required to move a charge between two points that are at the same potential. W = -q(VB – VA)

All points on the surface of a charged conductor which is in electrostatic equilibrium are at the same potential.

The electric potential is constant everywhere on the surface of a charged conductor in equilibrium.

The electric potential is constant everywhere inside a conductor and equal to its value at the surface.

The Electron-Volt The electron-volt is the energy of an electron after it has been accelerated across a potential difference of 1 volt. It is a very small unit of energy. 1 eV = 1.6 x J

Equipotential Surfaces
What is an equipotential surface? An equipotential surface is one where all points are at the same potential. 169

No work is required to move a charge at a constant speed along an equipotential surface.
134

The electric field at every point of an equipotential surface is perpendicular to the surface.
16.7

Equipotential Lines Equipotential lines Two-dimensional views
Equipotential lines are always perpendicular to electric field lines. 16.10, 170, 16.6

Applications Electrostatic precipitator Electrostatic air cleaners
Power company smokestacks Electrostatic air cleaners Furnace filters Smoke eaters at party halls

How does a copy machine work?
Corotron Selenium drum Heated pressure rollers 165

How does laser printer work?
16.12

QUESTIONS 1, 4 – 7, 11 Pg. 564

Capacitors What is a capacitor?
A capacitor is made up of two parallel metal plates with a surface area (A) separated by a dielectric with thickness (d) 171

How it works: 68 Each plate is connected to one side of a battery
Charge flows until the plates have the same potential difference as the battery One is positive while the other is negative (+ Q and –Q) 68

The Definition Of Capacitance
What is capacitance? Capacitance is the ratio of the magnitude of the charge on either conducting surface to the potential difference between the two conducting surfaces. C = Q/DV Therefore: Q = DV.C

What is the unit of capacitance?

Capacitance Applications
Tuning stations on radio and television receivers Storing charge in electronic flash units Computer keyboards

The Parallel Plate Capacitor
Factors affecting capacitance: Area (A) Separation (d) Permittivity of free space (eo) C = eoA/d (in air) Also: ke = 1/4peo

eo = 8.85 x C2/N.m2

How things work: Flash attachment

How things work: Computer keyboard 173

Circuit Symbols Symbols for circuit elements Battery Capacitor
Resistor Wires

Types of Electrical Circuits
Complete Circuits Series Parallel Combination 7, 16.15

Capacitors in Parallel
The potential differences across each of the capacitors is equal to the battery voltage 16.17

In Parallel: The equivalent capacitance of the circuit is equal to the sum of the individual capacitors Ceq = C1 + C2 + …

In Parallel: The total charge stored by the capacitors is: Q = Q1 + Q2 + …

In Parallel: The equivalent capacitance of a parallel combination is always greater than any of the individual capacitances

Capacitors in Series In Series:
The potential differences across each of the capacitors add up to the battery voltage 16.19

In Series: The equivalent capacitance of the circuit can be found by using: 1/Ceq = 1/C1 +1/C2 + … There is a Shortcut!

The equivalent capacitance of two capacitors in series can be found by using:

In Series: All of the capacitors must have the same charge: QT = Q1 = Q2 = …

In Series: The equivalent capacitance of a series combination is always less than any individual capacitance in the combination 187, 188

Combinations Of Capacitors
Some circuits involve combinations of series and parallel capacitors

Energy Stored In A Charged Capacitor
A capacitor stores electrical energy in its field Discharges can be dangerous if high voltages are present.

Work is done in charging a capacitor
W = 0.5 QDV 50

The energy stored in a capacitor is given by:
E = 0.5 CDV2

Electrical breakdown limits the amount of energy that can be stored in a capacitor

Capacitors charge to a high voltage Charging takes time

Capacitors With Dielectrics
A dielectric is an insulating material Examples of dielectrics Rubber Glass Plastic Waxed paper

Dielectrics can increase capacitance
The dielectric constant (k) See Table 16.1 (Pg. 557) Air has a dielectric constant of 1 C = keoA/d 172, 16.23

Types of Capacitors Tubular High voltage Electrolytic (polarized)
Variable

Application: DNA And Forensic Science
DNA fragments are separated by mass and by charge

QUESTIONS 8, 9, 10, Pg. 564