UNIT 1

• The study of motion is called kinematics

• Uniform motion is movement at a constant speed in a straight line

• Nonuniform motion is movement that involves changes in speed, direction or both

• Scalar quantities have a magnitude and usually some unit of measure, but no direction

• Vector quantities have a magnitude, usually some unit of measure and a direction

• Position: The location of an object relative to a reference point.

• Ex. Jimmy is 12m [W] of the school

• Displacement: Represents the change in an object’s position. No reference is needed.

• Ex. Jimmy moved 33km [E]

• We represent vectors using vector diagrams. Vectors are drawn using a scale and an arrow-

head to indicate direction.

• We add vectors by drawing them tip to tail. Each vector starts where the previous one left off.

We call the result a resultant.

• If the vectors are collinear, we can use the algebraic method. All you need to do is define one

direction as positive and one as negative and then add the vectors together.

• When the vectors form right angle triangles, you can use trigonometry and the Pythagorean

theorem to solve for the resultant

• When the vectors are not right angle triangles but do form the arms of a triangle you can use

the sine and cosine laws to solve for the resultant.

• Velocity is the ratio of the displacement to the elapsed time. Since more than one displacement

is involved, the average velocity is described using the resultant displacement:

A position-time graph depicts the relationship between position and time and can be used to

determine:

Whether velocity is constant

The average velocity of an interval

An object with a constant velocity will have a position time graph with a straight line slope:

We can find the average velocity of an object by calculating the slope of its position-time graph.

If the object is accelerating, the position time graph will not be linear

If the object accelerates uniformly we will observe a curved position time graph

We can find the instantaneous velocity which is the velocity at one particular instant in time by

taking the slope of a tangent at that time. In the above diagram the slope of the tangent would

tell us the instantaneous velocity at t=2.5

If the graph is curved we can still find the average velocity for any interval by connecting the two

end points. In the above graph the red line represents the average velocity for the entire time

Acceleration is the rate of change of velocity. We can calculate acceleration using:

• Where is acceleration in m/s2 or km/h2

• Uniform Motion is when an object moves at a steady speed along a straight line (not common)

• Accelerated motion occurs when the object is changing speeds, directions or both (like a car in

traffic)

• Uniformly accelerated motion occurs when an object is moving in a straight line and changes

speed uniformly with time.

• The slope of a velocity time graph gives us the average acceleration!

• We can find the displacement from a velocity time graph by calculating the area under the curve

for that given interval.

• Formulas for uniformly accelerated motion

Forces are any push or pull and are capable accelerating, twisting, compressing or distorting

matter.

All forces are vector quantities and are measured in the SI unit called the Newton (N)

Forces are represented using the letter F and appropriate subscripts to describe the type of

force.

There are four fundamental forces in the universe as summarized below:

The most common force we experience is the force of gravity between the Earth and the

objects on it. If an object is stationary on a surface it must be experiencing an equal force in the

opposite direction or it would move towards the Earth. This opposite upwards force is called the

normal force.

The force of friction acts between two surfaces in contact parallel to the surfaces. It always act

in the opposite direction of the motion of an object or the intended motion.

The force of tension is the force exerted by strings or ropes or fibers.

The vector sum of all the forces acting on a body is called the resultant or net force. The net

force represents on force equivalent to all the other forces acting on the object together.

We can find the net force by resolving the individual vectors.

Law of Universal Gravitation:

The force of gravitational attraction between any two objects is directly proportional to the

product of the masses of the objects, and inversely proportional to the square of the distance

between their centres.

The law represented as an equation is:

Where:

FG is the force of gravitational attraction between any two objects.

m1 is the mass of one object in kg.

m2 is the mass of a second object in kg.

d is the distance between the centres of the two objects in m. (Objects are assumed to be spherical.)

G is the Universal Gravitational Constant

(G = 6.67x10–11 N•m2/kg2)

Friction is the force between two objects that opposes the motion of objects

Friction makes many things possible but also presents us with many problems

There are two key types of friction that we will investigate

Static friction is the force that tends to prevent a stationary object from moving

The maximum static friction is the starting friction or limiting static friction, which is the force

which must be overcome before an object will move.

Once an object is in motion it will experience kinetic friction.

Kinetic friction operates opposite the direction of movement.

If the applied force and the kinetic friction forces are equal in magnitude, the object will move at

a constant rate

The coefficient of Friction is the ratio of the magnitude of friction to the magnitude of the

normal force

Newton described the property of bodies tending to stay in motion as inertia.

Inertia is the property of an object to resist changes to its motion.

Example: Ways to fall on a bus

Inertia is directly proportionate to mass.

The larger the mass of an object the greater the interia

Newton summarized Galileo’s findings in his first law which states:

“Every object will continue in a state of rest or with constant speed in a straight line unless

acted upon by an external unbalanced or net force.”

Newton’s second law:

If the net external force on an object is not zero, the object accelerates in the direction of the

net force. The magnitude of the acceleration is proportional to the magnitude of the net force

and is inversely proportional to the object’s mass.

UNIT 2

Energy is defined as the capacity to do work.

We can determine the rest mass energy of an object using the formula:

E = mc2

Where E is the energy in joules, m is the mass in kg and c is the speed of light in a vacuum,

3.0x108m/s

Work is the energy transferred to an object by an applied force over a measured distance.

The amount of work done depends of the force applied and the displacement of the object in

the direction of the applied force.

In order for mechanical work to scientifically be considered done, it must meet the following

requirements:

A force must be exerted on the object

The object must be displaced by the force

At least part of the force must be in the same direction as the displacement

Work is the product of the magnitude of the force applied on an object and the magnitude of

the displacement of the object in the direction of the force

W = FΔd

Where W is work in Joules, F is the applied force in N and Δd is the displacement in m

1 J = 1 N·m

Positive work is done to increase the speed of an object whereas negative work tends to

decrease the speed of an object.

For example friction does negative work on a moving object.

When lifting an object a force upward must be applied to overcome the downward force of

gravity. The work done against gravity is positive when the applied force and displacement are

both vertical upward than the work done against gravity is positive.

Torque is a twisting force. We encounter torque in many different facets of our lives:

The Ideal Mechanical Advantage (IMA) for a system is the mechanical advantage neglecting

friction. To predict the IMA for a pulley system you count the number of strings pulling the load

up. Because the AMA includes friction it is always less than the IMA.

To find the percent efficiency for a pulley we use the following equation:

Power is defined as the rate at which work is done. Power is a scalar quantity

To calculate power we use:

Power is measured in joules per second or watts, named after James Watt who is the inventor

of the modern steam engine

Thermal energy is the total kinetic energy and potential energy (caused by electric forces) of the

atoms or molecules of a substance

Temperature is a measure of the average kinetic energy of the atoms or molecules of a

substance, which increases if the motion of the particles increases.

heat is the transfer of energy from a hot body to a colder one

a measure of the amount of energy needed to raise the temperature of 1.0kg of a substance by

1.0°C

We represent the heat capacity of a substance as c and it is measured in J/kg·0C

The quantity of heat gained or lost by a body, Q, is directly proportional to the mass, m, of the

body, its specific heat capacity, c, and the change in the body’s temperature, Δt. The equation

relating these factors is:

Q = mcΔt

When heat is transferred from one body to another, it normally flows from the hotter body to

the colder one. The amount of heat transferred obeys the principle of heat exchange, which is

stated as follows:

When heat is transferred from one body to another, the amount of heat lost by the hot body

equals the amount of heat gained by the cold body.

Heat Exchange equations:

Qlost + Qgained = 0

or m1c1Δt1 + m2c2Δt2 = 0

|heat lost| = |heat gained|

We can use these equations when heat is transferred from a warm body to a cold one.

UNIT #3 - Sound and Waves

Section 6.1 - Vibrations

periodic motion: motion that occurs when the vibration, or oscillation, of an object is repeated in equal time intervals

transverse vibration: occurs when an object vibrates perpendicular to its axis longitudinal vibration: occurs when an object vibrates parallel to its axis torsional vibration: occurs when an object twists around its axis

Cycles

A cycle is considered one complete oscillation. This means the object travels through its entire range of motion

Frequency

frequency: (f ) the number of cycles per second. Frequency is measured in the SI units hertz (Hz) named after the scientist who first produced

electromagnetic waves in a lab

Period

period: (T ) the time required for one cycle. The period of motion is usually measured in seconds, but can be days (like the moon) or years

(like the Earth around the sun)

Relating Frequency and Period

Since frequency is measured in cycles per second and period is measured in seconds per cycle, frequency and period are reciprocals of each other.

Rest Position and Amplitude

The rest position is the initial position of the object with no force acting upon it other than gravity

The amplitude is the maximum distance the object moves from the rest position.

Phase

in phase: objects are vibrating in phase if they have the same period and pass through the rest position at the same time

out of phase: objects are vibrating out of phase if they do not have the same period or if they have the same period but they do not pass through the rest position at the same time

Section 6.3 and 6.4 Transverse Waves

In a transverse wave the particles in the medium vibrate at right angles to the direction that the wave travels.

The high point is called a crest and the low point is called a trough.

Wavelength of Transverse Wave The distance from the midpoint of one crest to the midpoint of the next crest (or from

the midpoint of one trough to the midpoint of the next) is called the wavelength and is represented by the Greek letter λ (lambda).

Longitudinal Waves A longitudinal wave is one in which the particles of the medium vibrate parallel to the

direction of wave compression: region in a longitudinal wave where the particles are closer together than

normal rarefaction: region in a longitudinal wave where the particles are farther apart than

normal

The Universal Wave Equation The frequency of the wave is exactly the same as that of the source. It is the source alone

that determines the frequency of the wave. Once the wave is produced, its frequency never changes, even if its speed and

wavelength do change. This behaviour is characteristic of all waves. Universal Wave Equation:

Section 6.5 - Wave Behaviour Interference of Waves

Wave interference occurs when two waves act simultaneously on the same particles of a medium

For transverse pulses, destructive interference occurs when a crest meets a trough For longitudinal pulses, destructive interference occurs when a compression meets a

rarefaction. Constructive interference occurs when pulses build each other up, resulting in a larger

amplitude In transverse waves when two crests or two troughs meet, constructive interference

occurs, resulting in a larger amplitude called a supercrest or supertrough.

Principle of Superposition

The concept of amplitude addition is summarized in the principle of superposition, which states that at any point the resulting amplitude of two interfering waves is the algebraic sum of the displacements of the individual waves.

Refraction and Diffraction

When the wave travels from deep to shallow water, in such a way that it crosses the boundary between the two depths straight on, no change in direction occurs.

On the other hand, if a wave crosses the boundary at an angle, the direction of travel does change. This phenomenon is called refraction.

If waves pass by the sharp edge of an obstacle or through a small opening in the obstacle, the waves change direction. This bending is called diffraction.

Factors Effecting Diffraction How much the wave bends depends on both the wavelength and the size of the opening

in the barrier. For the same opening, long-wavelength waves are diffracted more than short-wavelength waves.

Decreasing the size of the opening will increase the amount of diffraction.

Section 7.1 and 7.3 - Producing Sound and the Speed of Sound Sound

Sounds are a form of energy produced by rapidly vibrating objects. We hear sounds because this energy stimulates the auditory nerve in the human ear. The ears of most young people respond to sound frequencies of between 20 Hz and 20

000 Hz infrasonic: any sound with a frequency lower than the threshold of human hearing

(approximately 20 Hz) ultrasonic: any sound with a frequency above the range of human hearing

(approximately 20000 Hz)

Producing Sound Sound is produced by vibrating objects. Sound is transmitted by vibrating molecules of air Sound cannot travel through a vacuum

Loudness and Pitch Loudness is determined by the amplitude of the wave. The larger the amplitude the

higher the loudness.

Pitch is related to the frequency of the wave. The higher the frequency the higher the pitch.

The Speed of Sound Sound travels significantly slower than light resulting in many “delayed sound”

scenarios. At normal atmospheric pressure and 0°C, the speed of sound in air is 331 m/s This is called the Standard Temperature and Pressure (STP) If the air pressure remains constant, the speed of sound increases as the temperature

increases. For every rise in temperature of 1°C, the speed of sound in air increases by 0.59m/s.

Section 7.4 - Interference and Diffraction Interference

Interference can occur between waves both in phase and out of phase. For in phase, both constructive and destructive interference occur. Destructive interference produce nodal lines where sound intensity is decreased and

constructive interference produce regions of increased intensity

Beat Frequency beats: periodic changes in sound intensity caused by interference between two nearly

identical sound waves The number of maximum intensity points that occur per second is called the beat

frequency. To determine the beat frequency, the lower frequency is subtracted from the higher

frequency. For example, if a tuning fork of 436 Hz is sounded with a 440-Hz tuning fork, the beat

frequency will be 4 Hz.

Sound Diffraction Diffraction is the property of waves spreading out after encountering an obstacle.

The Doppler Effect Doppler effect: when a source of sound approaches an observer, the observed

frequency increases; when the source moves away from an observer, the observed frequency decreases.

1

Super and Subsonic Speed subsonic speed: speed less than the speed of sound in air supersonic speed: speed greater than the speed of sound in air

Mach Number It is sometimes more convenient to use an objects mach number rather than m/s or

km/h Mach number: the ratio of the speed of an object to the speed of sound in air.

Section 8.1 - Standing Waves

Music vs. Noise

music: sound that originates from a source with one or more constant frequencies noise: sound that originates from a source where the frequencies are not constant

Standing Waves

A standing wave is produced in objects such as strings when they vibrate due to the interactions of the initial wave and reflected wave

Vibration

fundamental mode: simplest mode of vibration producing the lowest frequency fundamental frequency: (f0) the lowest natural frequency overtones: the resulting modes of vibration when a string vibrates in more than one segment

emitting more than one frequency

Section 8.2 and 8.3 - Stringed Instruments and Acoustical Resonance in Air Columns

Stringed Instruments

A variety of factors affect the frequency of a vibrating string on an instrument: Length Tension Diameter Density

We can quantify and calculate changes in string frequency WRT to length.

Relating Frequency and String Length

To relate frequency and string length we can use the following equality:

Resonance in Air Columns

Resonance will occur in closed end air columns when the length of the column and the frequency of the wave are such that a node is produced in the end of the tube. This is acoustical resonance.

The shortest length of column is called the first resonant length, the next the second and so on. Resonance first occurs when the column is 1/4 λ in length, since a single node is formed The next possible lengths are 3/4 λ, 5/4λ, 7/4 λ etc. For a 256-Hz tuning fork, ¼ λ would be approximately 34 cm at room temperature (20°C).

Acoustical Resonance in an Open Air Column

We can apply the same concept in open air columns, where acoustical resonance occurs when an anti-node is produced at both ends of the column

The first resonant length occurs at 1/2 λ followed by λ, 3/2 λ, 2 λ and so on.

UNIT 4-LIGHT AND GEOMETRIC OPTICS

CHAPTER 9-SOURCES, TRANSMISSION, AND REFLECTION OF LIGHT

Light is emitted from a source and travels in straight lines in all directions. Our eyes will either absorb it

directly or indirectly. When light bounces off of objects, some of the light is absorbed and the rest is

reflected.

Particle model: describes light as consisting of microscopic particles radiating away from the source.

Wave model: describes light as consisting of transverse waves radiating away from the source.

Quantum model: combines the particle and wave models. It describes light as consisting of microscopic

particles called photons, which have wave properties.

Rectilinear propagation: one of the properties of light; describes light as travelling in straight lines

Reflection: When light takes a different direction after bouncing off of something

Refraction: When light travels from one material into another than angle other than 90.

Beam: bundle of rays

Parallel: Converging: Diverging:

Transparent: Transmits light very well. Objects can be seen clearly through them.

Translucent: Transmits some light. Objects cannot be seen clearly through them

Opaque: Does not transmit light at all.

Optical illusions: When our mind perceives something as, but it is not the reality of the truth

Laws of Reflection: The angle of reflection is equal to the angle of incidence.

The incident ray, normal and reflected ray all lie on the same plane.

Characteristic of Mirror Images:

Characteristics of Image Description

Magnification Enlarged, same size, diminished

Attitude Erect, Inverted

Kind Real, Virtual

Position Displacement measured from reflecting surface

Converging Mirrors: causes parallel rays to come to a focus.

Diverging Mirrors: Causes parallel rays to spread apart

CHAPTER 10-REFRECTION AND TOTAL INTERNAL REFLECTION

refraction: the change in direction of light as it passes from one medium into another of differing density

Look at Example 1, pg 367. IMPORTANT (I think).

Speed of Light: 3.00x108

Index of Refraction (n): the ratio of the speed of light in a vacuum (c) to the speed of light in a given

material (v). (n=c/v) Because c and v have the same units, n is dimensionless (no units)

Snell’s Law of Refraction

The angle of incidence (θi) is the angle between the incident ray and the

normal at the point of incidence

The angle of reflection (θr) is the angle between the reflected ray and the

normal

The angle of refraction (θR) is the angle between the refracted ray and the

normal.

The term “optically dense” is used when referring to a medium in which the speed of light decreases

The slower the medium, the greater the amount of refraction in that medium

The medium in which the light travels more slowly is said to be the more refractive medium

Snell’s law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a

constant.

It has been found that the constant of proportionality and the index of refraction (n) are one and the

same.

The two laws of refraction are:

-The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant (also

known as Snell’s law).

-The incident ray and the refracted ray are on opposite sides of the normal at the point of incidence, and

all three are in the same plane.

We can generalize Snell’s law for any two mediums by using the following equation:

Light is reversible and will travel the same path going one direction or the other, thus it doesn’t matter

which media is 1 and which is 2.

When a light ray passes from air into glass and then back into air, it is refracted twice

If the two refracting surfaces are parallel, Snell’s law can prove that the emergent ray is parallel to the

incident ray but it is no longer moving in the same path

As the angle of incidence increases, the intensity of a reflected ray becomes progressively stronger and

the intensity of a refracted ray progressively weaker.

As the angle of incidence increases, the angle of refraction increases, eventually reaching a maximum of

90°

Beyond this point, there is no refracted ray at all, and all the incident light is reflected at the boundary,

back into the optically denser medium

When all the light is reflected and none is refracted we observe total internal reflection

total internal reflection: the reflection of light in an optically denser medium; it occurs when the angle of

incidence in the more dense medium is equal to or greater than a certain critical angle

critical angle: (θc) the angle in an optically denser medium at which total internal reflection occurs; at

this angle the angle of refraction in the less dense medium is 90°

The critical angle is unique for different substances and is dependent on the index of refraction

sinθc = n2/n1

Where medium 1 is the more refractive medium (higher n value) and medium 2 is the less refractive

medium

Apparent Depth

Apparent Depth: The location of a virtual image of an object within a different medium.

Objects in a different medium than the observer appear to be at a different depth than the actual depth

We can calculate the apparent depth of an object by using the following formula:

d’ = d(n2/n1)

Where:

-d’ is the apparent depth

-d is the actual depth

-n1 is the refractive index of the medium the object is in

-n2 is the refractive index of the medium the observer is in

Only 90% of the light energy is reflected by most metallic reflectors, the other 10% being absorbed by

the reflective material

To remedy some of the difficulties with front surface mirrors, total internal reflection prisms are used.

They reflect nearly all the light energy and have nontarnishing reflective surfaces.

Another important application of total internal reflection is communication by the transmission of light

along fibre optic cables. The most basic optic fibre is a transparent glass or plastic rod.

(The Diver’s Field of view)

CHAPTER 11-LENSES AND TECHNOLOGICAL DEVICES

lens: transparent device with at least one curved surface that changes the direction of light passing

through it

converging lens: lens that causes parallel light rays to come together so that they cross at a single focal

point

diverging lens: lens that causes parallel light rays to spread apart so that they appear to emerge from

the virtual focal point

optical centre: (O) the geometric centre of all lenses

optical axis: (OA) a vertical line through the optical centre

Principal axis: (PA) a horizontal line drawn through the optical centre

principal focus: (F ) the point on the principal axis through which a group of rays parallel to the principal

axis is refracted

focal length: (f ) the distance between the principal focus and the optical centre, measured along the

principal axis

focal plane: the plane, perpendicular to the principal axis, on which all focal points lie

Magnification of the Image

The height of an object is written as ho; the height of the image is written as hi.To compare their

heights, the magnification (M) of the image is found by calculating the ratio of the image height to the

object height:

Images can be enlarged, unchanged, diminished or undefined

Attitude of the Image

The attitude of the image refers to its orientation relative to the object.

For example, when an image forms on film in a camera, the image is inverted relative to the object that

was photographed. An image is either upright or inverted, relative to the object.

Location of the Image

The distance between the subject of a photograph and the lens of a camera is the object distance,

designated by do. An image of the object is formed on the film inside the camera. The distance between

the image on the film and the lens is the image distance, di.

The image is located either on the object side of the lens, or on the opposite side of the lens.When

discussing object and image distances, we refer to the location as “between F and the lens,” “between F

and 2F,” or “beyond 2F.”

Type of the Image

An image can be either real or virtual

A real image can be placed onto a screen, a virtual image cannot

The location of virtual images can be found by tracing rays backwards to where the appear to originate

from. These are virtual rays

Virtual rays are always drawn as dashed lines

Rules for Rays in a Converging Lens

1. A light ray travelling parallel to the principal axis refracts through the principal focus (F).

2. A light ray that passes through the secondary principal focus (F) refracts parallel to the principal axis.

3. A light ray that passes through the optical centre goes straight through, without refracting.

Sign Convention

1. Object and image distances are measured from the optical centre of the lens.

2. Object distances are positive if they are on the side of the lens from which light is coming; otherwise

they are negative.

3. Image distances are positive if they are on the opposite side of the lens from which light is coming; if

they are on the same side, the image distance is negative. (Image distance is positive for real images,

negative for virtual images.)

4. Object heights and image heights are positive when measured upward and negative when measured

downward from the principal axis.

An image can form either in front of a lens or behind it, and measurements are made either above or

below the principal axis. Therefore, we need a sign convention to distinguish between real and virtual

images and to interpret magnification calculations.

Rules for Rays in a Diverging Lens

1. A light ray travelling parallel to the principal axis refracts in line with the principal focus (F ).

2. A light ray that is aimed toward the secondary principal focus (F’) refracts parallel to the principal axis.

3. A light ray that passes through the optical centre goes straight through, without refracting.

For all positions of the object, the image is virtual, upright, and smaller.

The image is always located between the principal focus and the optical centre.

To find magnification we use:

Because real images for converging lenses will have a negative hi we must make the equation involving

di and do negative

UNIT 5-ELECTRICTY AND MAGNETISM

CHAPTER 12-ELECTRIC CHARGE, CURRENT, AND POTENTIAL DIFFERENCE

electric charge: a basic property of matter described as negative or positive

static electricity: a buildup of stationary electric charge on a substance

atom: sub-microscopic particle of which all matter is made

electron: negatively charged particle which moves around the nucleus of an atom

proton: positively charged particle found in the nucleus of an atom

nucleus: the central region of an atom, where protons and neutrons are found

elementary charge: (e) electric charge of magnitude equal to the charge on a proton and an electron

neutron: a neutral particle found in the nucleus

negative ion: an atom that has at least one extra electron and is negatively charged

positive ion: an atom that has lost at least one electron and is positively charged

fundamental laws of electric charges: Opposite charges attract each other. Similar electric charges repel

each other. Charged objects attract some neutral objects.

Coulomb found that the magnitude of the force between two charged objects is directly proportional to

the product of the charges and inversely proportional to the square of the distance between them.

The charge on one electron is

–e = –1.6 × 10–19 C,

the charge on one proton is

e = 1.6 × 10–19 C.

If a charged object has an excess or deficit of N electrons, each with a charge e (the elementary charge),

then the total charge, Q, on the object, measured in coulombs, is given by:

Q = Ne

In metals, electrons conduct electric current which have a negative charge.

Consider a cylindrical wire of known cross-sectional area, with a total charge Q (in coulombs) flowing

through the area A in a time t (in seconds)

Then the electric current I through the wire is

When electric charges move from one place to another, this constitutes an electric current

electric potential difference: (V ) the amount of work required per unit charge to move a positive charge

from one point to another in the presence of an electric field

volt: (V) the SI unit for electric potential difference.

1 V = 1 J/C

In Series: It=I1=I2=In

In Parallel: It=I1+I2+...+In

At any junction in an electric circuit, the total current flowing into a junction is equal to the total current

flowing out of the junction.

In Series: Vt=V1+V2+...+Vn

In Parallel: Vt=V1=V2=Vn

The algebraic sum of the potential differences around any closed pathway or loop must equal zero.

CHAPTER 13-ELECTRICAL RESISTANCE, POWER, AND ENGERGY

resistance: an opposition to the flow of charge, resulting in a loss of potential energy

Ohm’s law: The potential difference between any two points in a conductor varies directly as the current

between the two points if the temperature remains constant.

1Ω is the electric resistance of a conductor that has a current of 1 A through it when the potential

difference across it is 1 V.

equivalent resistor: resistor that has the same current and potential difference as the resistors it

replaces

The equivalent resistance of resistors in series is equal to the sum of their individual resistances

The equivalent resistance of several resistors in series will be less than the resistance of the individual

resistors

We find equivalent resistance in parallel circuits using:

Where Rs is the equivalent resistance

power: (P) the rate at which energy is used or supplied:

P=VI

Where P is power in Watts

kilowatt hour: (kWh) the energy dissipated in exactly 1 h by a load with a power of exactly 1 kW

E=P∆t or E=IV∆t

E is measured in joules (J)

1J=1W x 1s=1W∙s

The Cost of Electricity: total cost=energy used x unit cost

1kw∙h=3.6x16J= 3.6MJ

CHAPTER 14-MAGNETISM

Naturally occurring magnets are made up of magnetite and are called lodestones

North on a compass seeks north and south seeks south

Similar magnetic poles repel while opposite magnetic poles attract

The magnetic field about a magnet is strongest at the poles

The North Pole and South Pole of the same bar magnet are normally equal in strength

If you cut a magnet in half, the half will still have one north and south pole. No matter how many times

you cut a magnet, it will still have both poles, but they will be generally weaker.

The magnetic field of a magnet is the area around the magnet throughout which the magnetic force of

the magnet can be detected.

Almost all substances are magnetic but only to a small extent. Some substances, such as iron, nickel,

cobalt and their alloys respond strongly to a magnetic field.

When a magnet is covered with clear acetate and then iron fillings, the imaginary magnetic field lines

will begin to appear.

The direction of a line of force is defined as the direction in which the north pole of a compass points

when paced along that line.

The lines inside of a magnet travel from the south pole to the north pole. The lines look 2d on a piece of

paper, but they actually travel around the magnet in a 3-dimensional form.

The further apart the lines, the smaller the force. The direction of the force is indicated with

arrowheads on the line. The arrows point from the north pole to the south pole on the outside. The

lines never intersect because if they did, they would be acting in two different directions at the same

time.

When lines of the same direction meet they produce an intensified field. Lines of opposite direction

produce a diminished field.

Electormagnets

Ampere’s rule: The magnetic field around a straight current carrying conductor is circular with the

conductor located at the centre.

Viewed from above, when the current flows down the wire (into the page, indicated with a cross), the

magnetic field is clockwise. Conversely, when the current flows up the wire (out of the page, indicated

with a dot), the magnetic field is counter clockwise.

Right hand rule: Tells us the direction of the current. Your thumb must face be pointed in the direction

of the current, and curl your finger, towards your palm. This will be the direction of the current.

The strength of the magnet decreases as the distance from the magnet increases. An increase in the

current also increases the strength of the magnetic field

Earth’s magnetic field: Earth`s magnetic north is not the exact north but about 1600km away from its

true geographic north. Similar is the south.

CHAPTER 15-MOTORS AND GENERATORS

When magnetic fields are parallel in direction there is repulsion and when they are opposite in direction

there is attraction.

Comment [T1]: Right Hand Rule

motor principle: A current-carrying conductor that cuts across external magnetic field lines experiences

a force perpendicular to both the magnetic field and the direction of electric current. The magnitude of

this force depends on the magnitude of both the External field and the current, as well as the angle

between the conductor and the magnetic field it cuts across.

right-hand rule for the motor principle: If the fingers of the open right hand point in the direction of the

external magnetic field, and the thumb represents the direction of electric current, the force on the

conductor will be in the direction in which the right palm faces.

law of electromagnetic induction: An electric current is induced in a conductor whenever the magnetic

field in the region of the conductor changes.

The induced potential difference (V) varies directly with the number of turns in the helix. Thus:

V1/V2 = N1/N2

Lenz’s law: For a current induced in a coil by a changing magnetic field, the electric current is in such a

direction that its own magnetic field opposes the change that produced it.

PLEASE READ SECTION 15.2

AND 15.6 ON YOUR OWN.

THEY WILL BE VITAL FOR THE

EXAM