Electrical Energy and Capacitance

•Chapter 16

ReviewReview

•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.

IntroductionIntroduction

•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 (V) between points A and B

V = VB - VA = PE/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 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 10-19 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–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, 11Pg. 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:– 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/V

Therefore: Q = V.C

•What is the unit of capacitance?–Farad (F)

•Named after Michael Faraday•1 farad = 1 Coulomb/volt•Microfarads (F) and picofarads (pF) are more commonly used

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 (o)

C = oA/d (in air)

Also: ke = 1/4o

o = 8.85 x 10-12 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

•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:

21

21

CC

CCCe +

∗=

•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 QV

50

•The energy stored in a capacitor is given by: E = 0.5 CV2

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

Medical Applications

•Defibrillators–Paddles–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 ()

•See Table 16.1 (Pg. 557)– Air has a dielectric constant of 1

C = oA/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, 12 - 14Pg. 564