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**Electrical Energy and Capacitance**

Chapter 16

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**Review What is potential energy?**

Energy at rest or energy due to position

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**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.

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**Frictional force is dissipative.**

The Coulomb force is conservative.

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**What is meant by the conservation of energy?**

Energy cannot be created or destroyed, only transformed.

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**Gravitational force is conservative.**

Gravitational potential energy depends upon mass, gravity, and position.

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**Introduction New concepts Electric potential energy Electric potential**

Voltage between two points Electric potential difference Capacitance

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**Work Done on a Charge Electrostatic force is conservative**

Work may be done by a conservative force

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**The equation for work done on a charge:**

Since F = qE W = (F)d = (qE)d

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**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)

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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

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**Useful relationships:**

1 V = 1 J/C 1 N/C = 1 V/m

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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

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**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

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**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

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

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

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**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)

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Electric Potential The electric potential depends upon only two things:

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**The electric potential depends upon only two things:**

Charge Location

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**The electric potential exists at every point surrounding a given charge.**

A second charge is not needed.

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**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

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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

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**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

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

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

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

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

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

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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

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**Equipotential Surfaces**

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

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

134

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

16.7

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**Equipotential Lines Equipotential lines Two-dimensional views**

Equipotential lines are always perpendicular to electric field lines. 16.10, 170, 16.6

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**Applications Electrostatic precipitator Electrostatic air cleaners**

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

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**How does a copy machine work?**

Corotron Selenium drum Heated pressure rollers 165

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**How does laser printer work?**

16.12

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QUESTIONS 1, 4 – 7, 11 Pg. 564

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**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

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**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

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**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

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**What is the unit of capacitance?**

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

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**Capacitance Applications**

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

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**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

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eo = 8.85 x C2/N.m2

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How things work: Flash attachment

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How things work: Computer keyboard 173

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**Circuit Symbols Symbols for circuit elements Battery Capacitor**

Resistor Wires

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**Types of Electrical Circuits**

Complete Circuits Series Parallel Combination 7, 16.15

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**Capacitors in Parallel**

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

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

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

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

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**Capacitors in Series In Series:**

The potential differences across each of the capacitors add up to the battery voltage 16.19

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

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

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

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

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**Combinations Of Capacitors**

Some circuits involve combinations of series and parallel capacitors

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**Energy Stored In A Charged Capacitor**

A capacitor stores electrical energy in its field Discharges can be dangerous if high voltages are present.

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**Work is done in charging a capacitor**

W = 0.5 QDV 50

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**The energy stored in a capacitor is given by:**

E = 0.5 CDV2

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

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**Medical Applications Defibrillators Paddles**

Capacitors charge to a high voltage Charging takes time

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**Capacitors With Dielectrics**

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

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**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

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**Types of Capacitors Tubular High voltage Electrolytic (polarized)**

Variable

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**Application: DNA And Forensic Science**

DNA fragments are separated by mass and by charge

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QUESTIONS 8, 9, 10, Pg. 564

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18-3: Capacitance Objectives: Relate capacitance to the storage of electrical potential energy in the form of separated charges. Calculate the capacitance.

18-3: Capacitance Objectives: Relate capacitance to the storage of electrical potential energy in the form of separated charges. Calculate the capacitance.

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