Chapter 16
Section 1 Electric Charge
•There are two kinds of electric charge.
–like charges repel
–unlike charges attract
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•Electric charge is conserved.
–Positively charged particles are called protons.
–Uncharged particles are called neutrons.
–Negatively charged particles are called electrons
•Electric charge is quantized. That is, when an object is charged, its charge is always a multiple of a fundamental unit of charge.
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•Charge is measured in coulombs (C).
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•The fundamental unit of charge, e, is the magnitude of the charge of a single electron or proton. e = 1.602 176 x 10–19 C
The Milikan Experiment
Transfer of Electric Charge
•An electrical conductor is a material in which charges can move freely.
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•An electrical insulator is a material in which charges cannot move freely.
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•Insulators and conductors can be charged by contact.
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•Conductors can be charged by induction.
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•Induction is a process of charging a conductor by bringing it near another charged object and grounding the conductor
•A surface charge can be induced on insulators by polarization.
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•With polarization, the charges within individual molecules are realigned such that the molecule has a slight charge separation.
Section 2 Electric Force
Coulomb’s Law
•Two charges near one another exert a force on one another called the electric force.
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•Coulomb’s law states that the electric force is propor-tional to the magnitude of each charge and inversely proportional to the square of the distance between them.
•The resultant force on a charge is the vector sum of the individual forces on that charge.
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•Adding forces this way is an example of the principle of superposition.
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•When a body is in equilibrium, the net external force acting on that body is zero.
•The Coulomb force is a field force.
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•A field force is a force that is exerted by one object on another even though there is no physical contact between the two objects.
Section 3 The Electric Field
Electric Field Strength
•An electric field is a region where an electric force on a test charge can be detected.
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•The SI units of the electric field, E, are newtons per coulomb (N/C).
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•The direction of the electric field vector, E, is in the direction of the electric force that would be exerted on a small positive test charge.
•Electric field strength depends on charge and distance. An electric field exists in the region around a charged object.
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•Electric Field Strength Due to a Point Charge
Electric Field Lines
•The number of electric field lines is proportional to the electric field strength.
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•Electric field lines are tangent to the electric field vector at any point.
Conductors in Electrostatic Equilibrium
•The electric field is zero everywhere inside the conductor.
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•Any excess charge on an isolated conductor resides entirely on the conductor’s outer surface.
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•The electric field just outside a charged conductor is perpendicular to the conductor’s surface.
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•On an irregularly shaped conductor, charge tends to accumulate where the radius of curvature of the surface is smallest, that is, at sharp points.
Chapter 17
Section 1 Electric Potential
Electrical Potential Energy
•Electrical potential energy is potential energy associated with a charge due to its position in an electric field.
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•Electrical potential energy is a component of mechanical energy.
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ME = KE + PEgrav + PEelastic + Peelectric
•Electrical potential energy can be associated with a charge in a uniform field.
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•Electrical Potential Energy in a Uniform Electric Field
PEelectric = –qEd
electrical potential energy = –(charge) ´ (electric field strength) ´ (displacement from the reference point in the direction of the field)
Potential Difference
•Electric Potential equals the work that must be performed against electric forces to move a charge from a reference point to the point in question, divided by the charge.
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•The electric potential associated with a charge is the electric energy divided by the charge:
V = PEelectric/q
•Potential Difference equals the work that must be performed against electric forces to move a charge between the two points in question, divided by the charge.
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•Potential difference is a change in electric potential.
•The potential difference in a uniform field varies with the displacement from a reference point.
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•Potential Difference in a Uniform Electric Field
∆V = –Ed
potential difference = –(magnitude of the electric field ´ displacement)
Sample Problem
Potential Energy and Potential Difference
A charge moves a distance of 2.0 cm in the direction of a uniform electric field whose magnitude is 215 N/C.As the charge moves, its electrical potential energy decreases by 6.9 ´ 10-19 J. Find the charge on the moving particle. What is the potential difference between the two locations?
•The reference point for potential difference near a point charge is often at infinity.
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•Potential Difference Between a Point at Infinity and a Point Near a Point Charge
•The superposition principle can be used to calculate the electric potential for a group of charges.
Section 2 Capacitance
Capacitors and Charge Storage
•A capacitor is a device that is used to store electrical potential energy.
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•Capacitance is the ability of a conductor to store energy in the form of electrically separated charges.
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•The SI units for capacitance is the farad, F, which equals a coulomb per volt (C/V)
•Capacitanceis the ratio of charge to potential difference.
•Capacitancedepends on the size and shape of a capacitor.
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•Capacitance for a Parallel-Plate Capacitor in a Vacuum
•The material between a capacitor’s plates can change its capacitance.
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•The effect of a dielectric is to reduce the strength of the electric field in a capacitor.
Capacitors in Keyboards
Energy and Capacitors
•The potential energy stored in a charged capacitor depends on the charge and the potential difference between the capacitor’s two plates.
Sample Problem
Capacitance
A capacitor, connected to a 12 V battery, holds 36 µC of charge on each plate. What is the capacitance of the capacitor? How much electrical potential energy is stored in the capacitor?
Section 3 Current and Resistance
Current and Charge Movement
•Electric current is the rate at which electric charges pass through a given area.
Drift Velocity
•Drift velocity is the the net velocity of a charge carrier moving in an electric field.
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•Drift speeds are relatively small because of the many collisions that occur when an electron moves through a conductor.
Resistance to Current
•Resistance is the opposition presented to electric current by a material or device.
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•The SI units for resistance is the ohm (Ω) and is equal to one volt per ampere.
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•Resistance
•For many materials resistance is constant over a range of potential differences. These materials obey Ohm’s Law and are called ohmic materials.
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•Ohm’s low does not hold for all materials. Such materials are called non-ohmic.
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•Resistance depends on length, cross-sectional area, temperature, and material.
•Resistors can be used to control the amount of current in a conductor.
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•Salt water and perspiration lower the body's resistance.
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•Potentiometers have variable resistance.
Section 4 Electric Power
Sources and Types of Current
•Batteries and generators supply energy to charge carriers.
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•Current can be direct or alternating.
–In direct current, charges move in a single direction.
–In alternating current, the direction of charge movement continually alternates
Energy Transfer
•Electric power is the rate of conversion of electrical energy.
••Electric power
P = I∆V
Electric power = current ´ potential difference
Power dissipated by a resistor
•Electric companies measure energy consumed in kilowatt-hours.
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•Electrical energy is transferred at high potential differences to minimize energy loss.
Chapter 18
Section 1 Schematic Diagrams and Circuits
Schematic Diagrams
•A schematic diagram is a representation of a circuit that uses lines to represent wires and different symbols to represent components.
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•Some symbols used in schematic diagrams are shown at right.
Electric Circuits
•An electric circuit isa set of electrical components connected such that they provide one or more complete paths for the movement of charges.
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•A schematic diagram for a circuit is sometimes called a circuit diagram.
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•Any element or group of elements in a circuit that dissipates energy is called a load.
•A circuit which contains a complete path for electrons to follow is called a closed circuit.
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•Without a complete path, there is no charge flow and therefore no current. This situation is called an open circuit.
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•A short circuit is a closed circuit that does not contain a load. Short circuits can be hazardous.
•The source of potential difference and electrical energy is the circuits emf.
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•Any device that transforms nonelectrical energy into electrical energy, such as a battery or a generator, is a source of emf.
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•If the internal resistance of a battery is neglected, the emf equals the potential difference across the source’s two terminals.
•The terminal voltage is the potential difference across a battery’s positive and negative terminals.
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•For conventional current, the terminal voltage is less than the emf.
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•The potential difference across a load equals the terminal voltage.
Light Bulb
Section 2 Resistors in Series or in Parallel
Resistors in Series
•A series circuit describes two or more components of a circuit that provide a single path for current.
•Resistors in series carry the same current.
•The equivalent resistance can be used to find the current in a circuit.
•The equivalent resistance in a series circuit is the sum of the circuit’s resistances.
Req = R1 + R2 + R3…
•Two or more resistors in the actual circuit have the same effect on the current as one equivalent resistor.
•The total current in a series circuit equals the potential difference divided by the equivalent resistance.
Sample Problem
Resistors in Series
A 9.0 V battery is connected to four light bulbs, as shown at right. Find the equivalent resistance for the circuit and the current in the circuit.
•Series circuits require all elements to conduct electricity
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•As seen below, a burned out filament in a string of bulbs has the same effect as an open switch. Because the circuit is no longer complete, there is no current.
Resistors in Parallel
•Resistors in parallel have the same potential differences across them.
•The sum of currents in parallel resistors equals the total current.
•The equivalent resistance of resistors in parallel can be calculated using a reciprocal relationship
Resistors in parallel equation: 1/Req = 1/R1 + 1/R2 + 1/R3…
Sample Problem
Resistors in Parallel
A 9.0 V battery is connected to four resistors, as shown at right. Find the equivalent resistance for the circuit and the total current in the circuit.
Resistors in Series or in Parallel
Section 3 Complex Resistor
Resistors Combined Both in Parallel and in Series
•Many complex circuits can be understood by isolating segments that are in series or in parallel and simplifying them to their equivalent resistances.
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•Work backward to find the current in and potential difference across a part of a circuit.
Sample Problem
Equivalent Resistance
Determine the equivalent resistance of the complex circuit shown below.
Sample Problem
Current in and Potential Difference Across a Resistor
Determine the current in and potential difference across the 2.0 Ω resistor highlighted in the figure below.
Given:I = 0.71 A R = 2.7 Ω
Unknown: ∆V = ?
∆V = IR = (0.71 A)(2.7 Ω) = 1.9 V