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All physics to date has led to one primary conclusion:
 There are four fundamental forces:
1) Gravitational
2) Electromagnetic
all based on the
3) Strong nuclear
Electromagnetic Theory
4) Weak nuclear
GUT - grand unified theory
~250 yrs or so since we first learned what electricity is
“Electricity” – from the Greek word electron () - “amber”.
The ancients knew that if you rub an amber rod with a piece of
cloth, it attracts small pieces of leaves or dust.
“amber effect”– the object becomes electrically charged
Electric forces
 charges exert electric forces on other charges
◊ two positive charges repel each other
◊ two negative charges repel each other
◊ a positive and negative charge attract each other
• The repulsive electric force between 2 protons is
1,000,000,000,000,000,000,000,000,000,000,000,000
times stronger than the attractive gravitational force!
• Attractive force between protons and electrons cause them to
form atoms. Electrical force is behind all of how atoms bond …
chemistry
•
charge is measured in Coulombs [C]
Electricity & Magnetism
• static electricity (Electrostatics)
◊ Why do I get a shock when I walk across the rug and touch
the door knob?
◊ Why do socks stick to my pants in the dryer?
◊ Why does my hair stick to my comb, and I hear a crackling
sound ?
◊ Why does a piece of plastic refuse to leave my hand when I
peel it off a package?
◊ What is lightning?
• What is that all about? It’s the CHARGE
No one has ever seen electric charge;
it has no weight, color, smell, flavor, length, or width.
Charge is an intrinsic property of matter – electron has it, proton
has it, neutron doesn’t have it – and that’s all
• Electric charge is defined by the effect (force) it produces.
• Matter (stuff) has two basic properties
◊ mass  is what gives the gravitational force
◊ charge  is wh at gives electric and magnetic forces
There are two kinds of charge:
◊ positive charge
◊ negative charge
Named by
Benjamin Franklin (1706 - 1790,
American statesman,
philosopher and scientist)
Electricity has origin within the atom itself.
French physicist Charles A. de Coulomb
1736 - 1806
-19
◊ every electron has charge -1.6 x 10
C,
-19
◊ every proton 1.6 x 10
C
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6.25 billion billion (6.25 x 10 ) electrons has charge of 1 C !
Yet 1C is the amount of charge passing through a 100-W light bulb
in just over a second. A lot of electrons!
let e  1.6  1019 C
• The smallest amount of the free positive
charge is the charge on the proton. q
= e
proton
• The smallest amount of the free negative
charge is the charge on the electron. q
=-e
electron
• quarks have 1/3, but they come in triplets

Charge is quantized: cannot divide up charge into smaller
units than that of electron (or proton) i.e. all objects have
a charge that is a whole-number multiple of charge of
the smallest amount (a single e).
• The net charge is the algebraic sum of the individual charges
(+ 5 - 3 = 2).
• Everyday objects - electronically neutral – balance of charge
– no net charge.
• Objects can be charged – there can be net charge on an
object. How?
The only type of charge that can move around is the negative
charge, or electrons. The positive charge stays in the nuclei. So, we
can put a NET CHARGE on different objects in two ways
◊ Add electrons and make the object negatively charged.
◊ Remove electrons and make the object positively charged.
mnucleon  2000  melectron
ratom  100000  rnucleus
Atom is electrically neutral = has no net charge,
since it contains equal numbers of protons and electrons.
Some materials have atoms that have outer electrons (farthest
from nucleus) loosely bound. They can be attracted and can
actually move into an outer orbit of another type of atom. The
atom that has lost an electron has a net charge +e (positive ion). An
atom that gains an extra electron has a net charge of – e (negative
ion).
This type of charge transfer often occurs when two different
materials (different types of atoms) come into contact.
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•
Which object gains the electrons depends on their
electron affinity
So, electrons can be transferred from one object to another
During that process, the net charge produced is zero. The charges
are separated, but the sum is zero. The amount of charge in the
universe remains constant (we think!!) It is CONSERVED!
• Electrons in insulators are tightly bound to atomic nuclei and so
cannot be easily made to drift from one atom to the next. Only if
a very strong electric field is applied, the breakthrough
(molecules become ionized resulting in a flow of freed electrons)
could result in destruction of the material.
Most things are in between perfect conductor/ insulator
 Law of Conservation of charge: Charge is always conserved:
charge cannot be created or destroyed, but can be transferred
from one object to another.
When objects are charged by rubbing, they don’t stay charged for
ever. They eventually return to neutral state – very often the
charge will “leak off” onto water (polar) molecules in the air.
Sometimes they will be neutralized by charged ions in the air
(formed, for example, by collisions with charged particles known as
cosmic rays).
Given enough time, the particles in the air will remove the excess
charge from the object leaving it neutrally charged. This explains
why on dry days we tend to have more trouble with static
electricity build-up than on humid (moist) days. On moist days
there are more water molecules in the air to steal charge more
rapidly. On dry days there are fewer particles in the air to steal
charges so we accumulate charge until we touch something and get
discharged (shocked).
Electrical conductors, insulators, semiconductors and
superconductors
- distinction based on their ability to conduct or transmit electric
charge.
 Conductor: Any material that contains movable charges and
allows charges to move about more or less freely.
So, if you transfer some electrons to the metal rod, that excess of
charge will distribute itself all around rod. Tap water, human body
and metals are generally good conductors.
 Insulator: is a a material that doesn’t contain movable charges
and resists the flow of electric current
Materials like amber, teflon, glass, pure water, plastic, glass,
rubber, wood are good insulators.
ELECTROSTATIC CHARGING
1.
Charging by Friction:
The transfer of charge is due to the rubbing – friction between
two previously neutral materials.
When you move your comb through your hair, the friction (rubbing)
between the comb and hair can pull some of the electrons out of
your hair and onto the comb. As a result your comb ends up with a
net negative charge and attracts your hair which is now positive.
Rubbing: rubber rod with fur or cloth, glass rod with silk, hair with
balloon, shuffling across a carpeted floor.
2.
Charging by Conduction (Contact):
2.1 Conductors:
When a charge is placed on a conductor, the mutual repulsion of
the individual charges causes them to move as far away from each
other as possible. Thus, a charge deposited on a conductor quickly
spreads out over its surface.
Metal sphere on
insulating stand
2. 2 Insulators:
When a charge is placed on an insulator, it remains where it is
deposited and surrounding molecules become polarized. An
external (negative) charge distorts the shape of an atom by forcing
its negatively-charged electron clouds to shift away from the charge
and the positively charged nuclei to shift toward the charge.
Such a distorted atom is said to be polarized.
That’s all very nice, but why is that so?
 What makes conductors conduct?
• Atoms have equal numbers of positive and negative charges, so
that a chunk of stuff usually has no net charge  the plusses
and minuses cancel each other.
• However, in metal atoms the valence electrons – the electrons
in the outermost orbits - are loosely bound, so when you put a
bunch of metal atoms together (to form a metal) an amazing
thing happens: valence electrons from each atom get confused
and forget which atom they belong to.
• They now belong to the metal as the whole. As the result,
positive ions which are tightly bound and can only oscillate
around their equilibrium positions,
form a positive background. All the
homeless electrons - “Free electrons”wander around freely keeping ions
from falling apart – metallic bond!!
Question:
Consider a negatively charged rod touching a conductor versus an
insulator. What is the difference between how the electrons are
arranged on the conductor and insulator?
• charges can be transferred from/to conductors or
non-conductors but they can only move through conductors.
Would spread out evenly on a good conductor, because the
transferred electrons repel each other.
But on insulator would be localized at where the rod touched.
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3. Charging by Induction
Example::
A charged rod is brought close to two metal spheres touching
each other. Free electrons: since free to move, they will!
3.1 Conductors:
Steps:
1. Neutral conductor with free electrons
2. free electrons in the metal are repelled
as far as possible from the charged object.
Charge has been separated, but metal
sphere is still neutral.
3.. The Earth is reservoir of any charge.
It can easily accept or give up electrons.
Connect conductor with a conducting wire
to the ground - many of free electrons in
metal are able to move even further from
charged object down the wire into the
Earth. Or you can touch it with finger,
electrons flow through your finger,
through you, to the ground.
4. Object is left positively charged.
5. cut the wire, remove the rod and the
metal sphere has evenly distributed
positive charge.
Once separated from each other with rod still close they’ll
remain charged. Charge is conserved, so charges on spheres A
and B are equal and opposite.
Question:
A metal ring receives a positive charge by
contact.
What happens to the mass of the ring?
Does it increase, stay the same, or decrease?
When the positively charged ball touches the ring, electrons
inside it are attracted to the ball. Some will leave the ring trying
to neutralize the ball. Only a tiny fraction leaves the ring. The
mass of the electrons is so small compared to the atoms, so
although the mass of the ring decreases, measuring it would not
be possible. (By the way, both will be positively charged, but the
ball will be less then before)
3.2 Insulators:
When insulator is charged by induction, there will be no change of
charge. Instead of that, charge within the molecule/atom move
slightly in opposite directions (the net charge is kept zero)
Therefore we call it rather:
Positive
Charging by Polarization
surface charge
A charge placed near an insulator
polarizes its atoms. While the
insulator’s interior remains electrically
neutral, a net charge appears on the
surface, and can produce force on
other charges near the insulator.
Even though sphere is neutral
there is attraction force acting between the rod and sphere.
 What is polarization?
When a charged object is brought near an insulator, electrons are
not free to migrate throughout material. Instead, they redistribute
within the atoms/molecules themselves: “centers of charge”
move.
Example: Van de Graaff
The sphere gives the girl a large
negative charge. Each strand of
hair is trying to: Get away from the
other strands of hair.
Like charges attached to the hair
strands repel, causing them to get
away from each other.
Example: electroscope
the electroscope is a simple device for
observing the presence of electric charge
it consists of a small piece of metal foil (gold
if possible) suspended from a rod with a
metal ball at its top
If a positively charged rod is placed near the
ball, free electrons move closer to it leaving
leaves positively charged.The two sides of
the metal foil then separate.
Example: Attracting uncharged objects
In an usual atom center of electron
cloud is at the center of positive nucleus
When a negative charge is brought
near the right, electron cloud shifts to
the left. Centers of positive and
negative charges no longer coincide.
uncharged
metal sphere
A negatively charged rod will
push the electrons to the far
side leaving the near side
positive.
The force is attractive
because the positive charges are
closer to the rod than the
negative charges
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Example: Charge polarization is why a charged object can attract a
neutral one :
DEMO: Rub balloon on your hair – it will then stick to the wall !
Why?
Balloon becomes charged by friction when
rubbed on hair, picking up electrons. It then
polarizes molecules on the surface, inducing
+ charge layer on the wall’s surface closest
to it , and next layer negative furthest away.
So balloon is attracted to + charges and
repelled by – charges in wall , but the –
charges are further away so repulsive force
is weaker and attraction wins.
Example: You can bend water with charge!
The water molecule has a positive end
and a negative end.
When a negative rod is brought near the
stream of water, all the positive ends of
the water molecules turn to the right and
are attracted to the negative rod.
What happens if the rod is charged
positively?
• As we said like charges repel, and opposite charges attract.
• This is the fundamental cause of almost ALL electromagnetic
behavior.
• But how much?
• How Strong is the Electric Force between two charges?
a) They exert equal forces on each other only in opposite direction
F k
q1q2
 0.40 N
r2
(“-“ = attractive force)
b) r = 3 m
F k
q1q2
 1.6 N  4 F
r2
At very small separation - spark
-5
How many electrons is 2.0 x 10 C ?
2.0 10 5 C
 10 14 electrons
1.6 10 19 C
Trivia:
When you comb your hair with a plastic
comb, some electrons from your hair can
jump onto it making it negatively charged.
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Your body contains more than 10
electrons.
Suppose that you could borrow all the
electrons from a friend’s body and put them into your pocket. The
mass of electrons would be about 10 grams (a small sweet). With
no electrons your friend would have a huge positive charge. You,
on the other hand, would have a huge negative charge in your
pocket.
If you stood 10 m from your friend the attractive force would be
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equal to the force that 10 tons would exert sitting on your
shoulders – more 100,000 times greater than the gravitational
force between the earth and the Sun. Luckily only smaller charge
imbalances occur, so huge electrical forces like the one described
simply do not occur.
Example: Three point charges :
ELECTROSTATIC – ELECTRIC - COULOMB FORCE
The force between two point charges is proportional to the
product of the amount of the charge on each one, and inversely
proportional to the square of the distance between them.
F k
q1q2
r2
q1= +8.00 mC; q2= -5.00 mC and q3= +5.00 mC.
(a) Determine the net force (magnitude and direction)
exerted on q1 by the other two charges.
(b) If q1 had a mass of 1.50 g and it were free to move, what
would be its acceleration?
Force diagram
k  8.99 109 N  m 2 / C 2
Force is a vector, therefore it must
always have a direction.
F2 = k
Question:
-5
SHE accumulates charge q = 2.0 x 10 C
1
sliding out of the seat of a car.
-5
HE accumulates charge q = -8.0 x 10 C
2
while waiting in the wind.
What is the force between them a) when she opens the door 6.0 m
from him and b) when their separation is reduced by half to 3 m?
q1q2
= 0.213N
r2
F3 = k
q1q3
= 0.213N
r2
x-components will cancel, because of the symmetry
F = 0.213 sin230 + 0.213 sin230 = 0.166 N
.
a  F  0166
m / s2
m 1.5 103
a = 111 m/s2
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 Electric Field
Let's take a single electric charge, Q, and put it somewhere. The
space around it is different from the space without charge. We
have created a situation in which we could have an electric force.
All we have to do is bring in a second charge, q, to feel the force.
Without q, there is no force ....but we still have the condition that
we could have a force. We say that the space around charge
contains ELECTRIC FIELD.
Example:
Say the electric field from an isolated point charge has a certain
value at a distance of 1m. How will the electric field strength
compare at a distance of 2 m from the charge?
It will be ¼ as much – inverse square law for force between two
charges carries over to the electric field from a point charge.
 Electric field lines
How to measure/find the strength (magnitude and direction) of
electric field at particular location P due to charge Q?
We use “Electric Field Lines” to visualize el.
field.
Convention / agreement
A test charge, q, placed at P will
experience an electric force, F either attractive or repulsive.
Instead of drawing vector E at every point
around certain charge (a huge mess) we
decided to go with direction of electric field
and density of electric field lines indicating
the magnitude of el. field.
Definition of electric field, E, at a point P distance r away from Q.
The magnitude of the electric field is defined as the force per unit
charge.
E=
F
q
E  
positive charge
negative charge
N
C
As F contains q, E DOESN’T depend on q at all, only on Q.
Electric field at any point P in space is always in the direction of
the force on a positive test charge if it were placed at the point P.
Denser lines - stronger field → el. field decreases with distance
 The other way around:
If you know electric field E at a point where you place a charge q ,
that charge will experience the force F:
F=Eq
more lines revels stronger field due to greater charge
 Electric field of a charged particle/point charge
◊ A charged particle Q creates an electric field.
◊ magnitude
E=
F
Q
=k 2
q
r
E Field independent
of test charge
the same value on the sphere of radius r around charge q
◊ direction – radially outward or inward.
Example:
q (test charge)
E  9 109
1.6 1019
10 
10 2
 2.9 1011 N / C to the right
El field always point away from + charges, towards – charge
Electric field lines can never cross. If they crossed, that would mean
that a charge placed at the intersection, would be accelerated in
TWO directions at once! This is impossible! If two sources are
creating electric fields in the same place, we have to add the two
vectors and get a resultant vector representing the NET ELECTRIC
FIELD.
Example:
What is the direction of the
electric field at point C if the
two charges have equal
magnitude??
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Example:
What is the direction of the
electric field at point A if
the two positive charges
have equal magnitude?
Example:
if not then electrons would respond to its presence and be
accelerated within the conductor. And that is not conductor in
electrostatic equilibrium.
Q.E.D

If such conductor has excess charge, it resides entirely
on the conductor’s outer surface running away from each
other as far as possible. El. field is still zero everywhere
inside the conductor.
Therefore, electric field of charged conducting sphere in
electrostatic equilibrium is:
What is the direction
of the electric field at
point B if the two
positive charges have equal magnitude??
Example:
What is the direction of
the electric field at point
A, if the two positive
charges have equal
magnitude?
 Electric field of a capacitor
Uniform electric field (the one
that has constant magnitude
and direction is generated
between two oppositely
charged parallel plates. Edge
effect is minimized when the
length is long compared to their
separation.
El. field just outside a charged conductor is perpendicular to
the conductor’s surface.
 Electric field of a charged conducting sphere in
electrostatic equilibrium
◊ Electric field outside a charged sphere (evenly distributed
charge q over surface) at distance r from its center is the same as
if the charge q is concentrated at the center of the sphere:
if not
◊ What is electric field inside the sphere?
OK. Let’s start. In general if you have many charges you have to find
el. field of each of them and then add them up as vectors to get net
el. field at certain point. So imagine a solid!!!!!!!!! Good luck.
Charge tends to accumulate where the curvature is greatest
(sharp points), resulting in strongest electric field.
◊ Different approach:
Conductor is in electrostatic equilibrium when there is no net
motion (flow ) of charge within a conductor or on its surface.
•
Conductor  electrons free to move
•
charges in electric field feel the force F = Eq
•
only free electrons can move in the conductor so they will
move until
 E = 0 inside a conductor
The fact that pointed objects
create strong electric fields if
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charged is the reason for the shape of lightning rod.
Electrical Energy and Electrical Potential
Two different things that sound alike!
Recall Work: W = F d cos(θ)
• In order to bring two like charges together work must be done.
• In order to separate two opposite charges, work must be done.
• This work done by external force against electrical force is stored
as electrical PE, U.
• If released , charges will gain KE while losing potential energy U .
• So essentially, potential energy is capacity for doing work which
arises from position or configuration.
• Greater amount of charge → greater force needed → greater
work done → greater stored potential energy U.
• → introducing the electrical potential energy per unit charge,
known as electrical potential, which does not depend on
the amount of charge.
 Electric potential
If a charge q at point P (in electric field E) has electric potential
energy U, the electric potential V at that point is:
electric potential 
V
electric potential energy
charge
U
q
◊ The SI unit of electric potential is the volt:
1V 
1J
1C
• Because the dependence on the charge q has been divided out,
the electric potential depends only on position.
V1 < V2
V1 > V2
Positive charge accelerates from
higher to lower potential.
• Note important difference between energy and potential:
• A point has potential, charge placed there
has electric potential energy
• Two points that are at the same distance
from the charged object have the same
potential.
• So, when two charged object are placed
there, they are at the same potential, but
the one with more charge on it has higher
electric potential energy.
 Potential Difference Between Two Points (ΔV = VB – VA)
The amount of gravitational potential energy depends on the
reference point. In contrary, here we choose that:
. Law of conservation of energy:
change in potential energy = change in kinetic energy
The zero of electrical potential and potential energy is at infinity.
Work – kinetic energy theorem
work done by net force (electric force) = change in kinetic energy
Negative charge accelerates from
lower to higher potential.
The difference between the potentials at two different points (A &
B) measures the work done per unit positive charge in order to
move it from one point to the other.
V 
W U

q
q
So now we reformulate definition of electric potential:
 The potential, V at a point P in an electric field, is the work done
per unit of positive charge in order to bring it from infinity to
that point.
The zero of electrical potential is at infinity.
 Point charge Q:
Potential energy of charge q at point P r distance from charge Q:
Q
Qq and potential at point P is:
U=k
V k
r
r
Electrical potentials can be positive or negative.
→ If a charge, q, is moved through a potential difference, ∆V,
then the work done on it is equal to the change in its electric
potential energy which is converted into kinetic energy:
W = ∆U = q ∆V = ½ mv2
 electron-Volt (eV)
An electron volt is the amount of energy/work it takes to move
an electron through a potential difference of 1volt.
1 eV = ∆U = W = (1.6x10-19 C) (1V)
1 eV = 1.6x10-19 J
The electron volt is not a smaller unit for volts!!!
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 Electrical resistance (symbol R)
It is a smaller unit for energy.
 Uniform electric field, E
Why is it necessary to keep pushing the charges to make them
move?
The electrons do not move unimpeded through a conductor. As
they move they keep bumping into the ions of crystal lattice which
either slows them down or bring them to rest.
A ball accelerates as it loses
potential energy.
Similarly, a positive charge
accelerates from a region of higher
potential toward a region of lower
potential.
 The resistance (R) is a measure of the degree to which the
conductor impedes the flow of current.
 Resistance is measured in Ohms ()
 OHM’S LAW - Current, Voltage and Resistance
◊ The change in potential energy of a charge q is converted into
kinetic energy:
∆U = q ∆V = ½ mv2
◊ The change in kinetic energy is equal to the work done on charge
q by el. field:
Fd = qEd = ½ mv2
◊
relationship between uniform electric field E and potential
difference between two points distance d from each other along
electric field line:
ΔV = Ed
→ E = ΔV/d

and NC-1 = Vm-1
Electric current (symbol I)
◊ the flow of electric charge q that can occur in solids,
liquids and gases.
 DEF: the rate at which charge flows past a given cross-section.
I=
 measured in amperes (A)
 DEF: Current through resistor (conductor) is proportional to
potential difference on the resistor if the temperature of a
resistor is constant (the resistance of a conductor is constant).
 math def:
I=
V
R
if resistance R is constant/ temperature is constant
I – current
V – potential difference across R
Example:
If a 3 volt flashlight bulb has a resistance of 9 ohms, how much
current will it draw?
I = V / R = 3 V / 9  = 1/3 Amps
If a light bulb draws 2 A of current when connected to a 120 volt
circuit, what is the resistance of the light bulb?
R = V / I = 120 V / 2 A = 60 
 Factors affecting resistance
Conductors, semiconductors and insulators differ in their
resistance to current flow.
 DEF: The electrical resistance of a piece of material is defined by
the ratio of the potential difference across the material to the
current that flows through it.
R=
q
t
1C
1s
Solids – electrons in metals and graphite, and holes in
semiconductors
Liquids – positive and negative ions in molten and aqueous
electrolytes
Gases – electrons and positive ions stripped from gaseous
molecules by large potential differences.
1A =
V
I
 The units of resistance are volts per ampere (VA-1).
 However, a separate SI unit called the ohm Ω is defined as the
resistance through which a current of 1 A flows when a potential
difference of 1 V is applied.
Wires, wires, wires
As you are going to see, the resistance of a wire can be completely
ignored – if it is a thin wire connecting two, three or more resistors,
or becoming very important if it is a long, long wire as in the case of
iron, washing machine, toaster ….., where it becomes resistor itself.
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The resistance of a conducting wire depends on four main factors:
• length • cross-sectional area • resistivity • temperature
• Cross Sectional Area (A)
r = 1.00 mm
ρ = 1.72x10-8 Ωm, copper - books
R = r L/A = (1.72x10-8 )(1.67)/(7.85x10-7) = 3.50 Ω
I = V / R = 1.5 / 3.5 = 0.428 A
The cross-sectional area of a conductor
(thickness) is similar to the cross section of a
hallway. If the hall is very wide, it will allow a
high current through it, while a narrow hall
would be difficult to get through. Notice that
the electrons seem to be moving at the same
speed in each one but there are many more electrons in the larger
wire. This results in a larger current which leads us to say that the
resistance is less in a wire with a larger cross sectional area.
 Ohmic and Non-Ohmic conductors
How does the current varies with potential difference for some
typical devices?
metal at const. temp.
filament lamp
diode
• Length of the Conductor (L)
The length of a conductor is similar to the length of a hallway.
A shorter hallway will result in less collisions than a longer one.
I = 1 is const.  R is const.
V
R
• Temperature
To understand the effect of temperature you must picture what
happens in a conductor as it is heated. Heat on the atomic or
molecular scale is a direct representation of the vibration of the
atoms or molecules. Higher temperature means more vibrations.
In a cold wire ions in crystal lattice are not vibrating much so the
electrons can run between them fairly rapidly. As the conductor
heats up, the ions start vibrating. As their motion becomes more
erratic they are more likely to get in the way and disrupt the flow of
the electrons. As a result, the higher the temperature, the higher
the resistance.
At extremely low temperatures, some materials, known as
superconductors, have no measurable resistance. This is called
superconductivity. Gradually, we are creating materials that
become superconductors at higher temperatures and the race is on
to find or create materials that superconduct at room
temperature. We are painfully far away from the finish line.
• Material used - resistivity
The resistivity, ρ (the Greek letter rho), is a value that only depends
on the material being used. It is tabulated and you can find it in the
books. For example, gold would have a lower value than lead or
zinc, because it is a better conductor than they are.
 The unit is Ω•m.
 Resistance of a wire when the temperature is kept constant is:
R=ρ
L
A
• In conclusion, we could say that a short fat cold wire makes the
best conductor.
• If you double the length of a wire, you will double the resistance
of the wire.
• If you double the cross sectional area of a wire you will cut its
resistance in half.
Example
A copper wire has a length of 160 m and a diameter of 1.00 mm. If
the wire is connected to a 1.5-volt battery, how much current flows
through the wire?
L = 1.60 m.
Devices for which current through them is directly proportional to
the potential difference across device are said to be ‘ohmic devices’
or ‘ohmic conductors’ or simply resistors. There are very few
devices that are truly ohmic. However, many useful devices obey
the law at least over a reasonable range.
Devices are non-ohmic if resistance changes
 Power dissipation in resistors
 DEF: Electric power is the rate at which energy is supplied to or
used by a device.
 DEF: Power is the rate at which electric energy is converted into
another form such as mechanical energy, heat, or light.
When a current is flowing through a load such as a resistor, it
dissipates energy in it. In collision with lattice ions electrons’ kinetic
energy is transferred to the ions, and as a result the amplitude of
vibrations of the ions increases and therefore the temperature of
the device increases.
That thermal energy (internal energy) is then transferred as heat
(to the air, food, hair etc.) by convection, or radiated as light
(electric bulb).
Where is that energy coming from?
This energy is equal to the potential energy lost by the charge as it
moves through the potential difference that exists between the
terminals of the load.
• Power is measured in J s-1 called watts W.
If a vacuum cleaner has a power rating of 500 W, it means
it is converting electrical energy to mechanical, sound and heat
energy at the rate of 500 J s-1. A 60 W light globe converts
electrical energy to light and heat energy at the rate of 60 J s -1.
 Deriving expressions for determining power
Basic definition of power:
P=
Remember: W = qV → P = qV/t
P = IV
W
t
and I = q/t, so
10
2
2
P = V /R = I R
1J
1W =
= 1A 1V
1s
In USA you can not get direct information on power of appliance
you buy.
Look at your hair dryer. If label says “10 A”, that means that the
power of the hair dryer is 10x120=1200 W, or 1.2 kW (using a
standard US 120 V outlet).
Comparison of US and other countries that use voltage of 240 V.
As the power of appliances is the roughly the same, the appliances
in USA have to draw a greater current, hence have to have less
resistance. As the consequence the wires (both used for
connecting and in appliances) are thicker in USA.
example
How much current is drawn by a 60 Watt light bulb connected to a
120 V power line?
P = 60 W = I V = I x 120
so I = 0.5 A
What is the resistance of the bulb?
I = V/R
R = V/I = 120 V/0.5 A
R = 240 
 Paying for electricity
You pay for the total amount of electrical energy (not power) that is
used each month
In Irving the cost of electric energy used is 14 ¢ per kilowatt-hour.
How do we get kilowatt-hour and what is that?
Power = energy/time
Energy = power x time, so energy can be expressed in units watts x
second what is simply a joule.
Physicists measure energy in joules, but utility companies
customarily charge energy in units of kilowatt-hours (kW h), where
Kilowatt-hour (kWh) = 103 W x 3600 s
1W x 1s = 1J
1 kWh = 3.6 x 106 J
$$$ example $$$
At a rate of 14 cents per kWh, how much does it cost to keep a 100
W light bulb on for one day?
 DEF: The electrons go one way but the current
flows the opposite to the direction that the
electrons travel. That’s convention.
 Drift speed
When a battery is connected across the ends of a metal wire, an
electric field is produced in the wire. All free electrons in the circuit
start moving at the same time. Free electrons are accelerated
along their path reaching enormous speeds of about 106 ms-1.
They collide with positive ions of crystal lattice generating heat that
causes the temperature of the metal to increse. After this event,
they are again accelerated because of the electric field, until the
next collision occurs. Due to the collisions with positive ions of
crystal lattice, hence changing
direction, it is estimated that
the drift velocity is only a small
fraction of a metre each
second (about 10-4 m s-1).
example: in an el. circuit of a car, electrons have average drift
speed of about 0.01 cm/s, so it takes ~ 3 hour for an electron to
travel through 1m.
it’s not even a snail’s pace!!!!!
The electricity that you get from the power company is not DC it is
AC (alternating) created by an AC electric generator.
In an AC circuit the current reverses direction periodically
The current in AC electricity alternates in direction. The back-andforth motion occurs at freq. of 50 or 60 Hz, depending on the
electrical system of the country.
!!!!!!! the source of electrons is wire itself – free electrons in it !!!!!!
If you are jolted by electric shock, electrons making up the current
in your body originate in your body. They do NOT come from the
wire through your body into the ground. Alternating electric field
causes electrons to vibrate. Small vibrations – tingle; large
vibrations can be fatal.
• How does the voltage and current change in time?
energy (kWh) = power (kW) x time (h)
DC does not change direction over
time;
energy (kWh) = 0.1 kW x 24 h = 2.4 kWh
cost / day = 2.4 kWh x 14 cents/kWh = 33.6 ¢
the actual voltage in a 120-V AC circuit
varies between +170V and -170V
peaks.
 for one month that amounts to $ 10.1.
 Direct Current (DC) electric circuits
a circuit containing a battery is a DC circuit
in a DC circuit the current always flows in the same direction.
The direction of the current depends on how you connect the
battery Either way the bulb will be on.
a circuit must provide a closed path for the current to circulate
around
when the electrons pass through the light bulb they loose some of
their energy  the conductor (resistor) heats up
the battery is like a pump that re-energizes them each time they
pass through it
 Electromotive force (emf – ε or E)
We have defined potential difference as the amount of work that
has to be done to move a unit positive charge from one point to the
other in an electric field.
ΔV =
W
ΔU
=
q
q
A battery or an electric generator that transforms one type of
energy into electric energy is called source of electromotive force
11
 DEF: emf (ε) of the source is the potential
difference between the terminals when NO
current flows to an external circuit.
IT IS A VOLTAGE NOT A FORCE.
In the true sense, electromotive force (emf) is the work (energy)
per unit charge made available by an electrical source.
 2. loop rule – conservation of energy principle: Energy supplied
equals the energy released in this closed path
In a closed loop, the sum of the emfs
equals the sum of the potential drops
V = V 1 + V2 + V3
 Resistors in Series
 D.C. circuit analysis
Electric Circuits: Any path along which electrons can flow is a
circuit. For a continuous flow of electrons, there must be a
complete circuit with no gaps. A gap is usually provided by an
electric switch that can be opened or closed to either cut off or
allow electron flow.
An electric circuit has three essential components
• connected in such a way that all components
have the same current through hem.
• Burning out of one of the lamp
filaments or simply opening the
switch could cause such a break.
 Equivalent or total or effective or resistance is the one that
could replace all resistors resulting in the same current.
1. A source of emf.
2. A conducting pathway obtained by
conducting wires or some alternative.
3. A load to consume energy such as a
filament globe, other resistors and
electronic components.
When the switch is closed, a current exists almost immediately in
all circuit. The current does not “pile up” anywhere but flows
through the whole circuit. Electrons in all circuit begin to move at
once. Eventually the electrons move all the way around the circuit.
A break anywhere in the path results in an open circuit, and the
flow of electrons ceases.
Req = R1+ R2 + R3
logic: the total or effective resistance would have length L1+ L2+ L3
and resistance is proportional to the length
 Terminal voltage, emf and internal resistance
 Resistors in Parallel
In the circuit the total energy supplied is determined by the value
of the emf. When electrons flow around a circuit, they gain
potential energy in the cell and then lose the energy in the
resistors. In a closed circuits charge must flow between the
electrodes of the battery and there is always some hindrance to
completely free flow. So when the current I is drawn from the
battery there is some resistance called INTERNAL RESISTANCE (r ) of
the battery causing the voltage between terminals to drop below
the maximum value specified by the battery’s emf.
• Electric devices connected in parallel are connected to the same
two points of an electric circuit, so all components have the same
potential difference across them.
• The current flowing into the point of splitting is equal to the sum
of the currents flowing out at that point: I = I1 + I2 + I3.
Thus the TERMINAL VOLTAGE (the
actual voltage delivered) is:
V = e - Ir
In the mid-nineteenth century, G.R. Kirchoff (1824-1887) stated two
simple rules using the laws of conservation of energy and charge to
help in the analysis of direct current circuits.
These rules are called Kirchoff’s rules.
 1. Junction rule – conservation of charge.
The sum of the currents flowing into a
point in a circuit equals the sum of the
currents flowing out at that point.
I1 + I 2 = I 3 + I 4 + I 5
1
1
1
1
=
+
+
Req R1 R2 R3
• A break in any one path does not interrupt the flow of charge in
the other paths. Each device operates independently of the other
devices. The greater resistance, the smaller current.
12
example: Find power of the source, current in each resistor,
terminal potential, potential drop across each resistor and power
dissipated in each resistor.
Req = 120 Ω
I = ε ∕ Req = 0.3 A
terminal potential: V = ε – Ir = 36 – 0.3x6.7 = 34 V
current through resistors 100Ω and 50Ω : I = I1 + I2
0.3 = I1 + I2
 Resistors in compound circuits
100 I1 = 50 I2
→ I1 = 0.1 A
I1R1 = I2R2
I2 = 0.2 A
potential drops
V = IR
power dissipated
P = IV
80 Ω
0.3x80 = 24 V
0.3x24 = 7.2 W
100 Ω
0.1x100 = 10 V
0.1x10 = 1 W
50 Ω
0.2x50 = 10 V
0.2x10 = 2 W
6.7 Ω
0.3x6.7 = 2 V
0.3x2 = 0.6 W
ε = Σ all potential drops:
36 V = 2 V + 24 V + 10 V
power dissipated in the circuit = power of the source
0.6 + 2 + 1 + 7.2 = 0.3x36
 Ammeters and voltmeters
In practical use, we need to be able to measure currents through
components and voltages across various components in electrical
circuits. To do this, we use AMMETERS and VOLTMETERS.
 An ammeter – measures current passing through it
• is always connected in series with a component we want to
measure in order that whatever current passes through the
component also passes the ammeter.
Now you can calculate current, potential drop and power
dissipated through each resistor
• has a very low resistance compared with the resistance of the
circuit so that it will not alter the current the current being
measured.
• would ideally have no resistance with no potential difference
across it so no energy would be dissipated in it.
13
 A potential divider
In electronic systems, it is often necessary to obtain smaller
voltages from larger voltages for the various electronic
circuits. A potential divider is a device that produces the
required voltage for a component from a larger voltage.
It consists of a series of resistors or a rheostat (variable
resistor) connected in series in a circuit.
 A voltmeter – measures voltage drop between two points
• is always connected across a device
(in parallel).
• has a very high resistance so that it
takes very little current from the device
whose potential difference is being measured.
• an ideal voltmeter would have infinite resistance
with no current passing through it and no energy
would be dissipated in it.
Potential divider equation
I=
V
R1+R 2
V1 =
V1 = IR1
R1
V
R1+R2
example:
In the potential divider shown, calculate:
(a) the total current in the circuit
(b) the potential difference across each resistor
(c) the voltmeter reading if it was connected
between terminals 2 and 6.
(a)
The total resistance
R = 12 Ω.
I = V / R = 12 V / 12 Ω = 1 A
(b) 6 x V = 12 V → V = 2 V
(12 V is equally shared by each 2 Ω resistor.
or
V = IR = 1x2 = 2 V
(c) R = 4 x 2 = 8 Ω
Between terminals 2 and 6 there are 4 resistors
potential difference between the terminals is
V = IR = 1 x 8 = 8 V
14
 Potentiometer
Because resistance is directly proportional to the length of a
resistor, a variable resistor also known as a potentiometer or as a
“pot” can also be used to control the potential difference across
some device.
Sliding contact A can
connect anywhere from
one end to the other of
the resistor chain. This
way it can control
voltage across a device
and therefore the
current through it, from
maximum down to zero.
1. step is to do a circuit
without device and then
adjust
point A in such a way that there is no current passing through
potentiometer. Potential difference across potentiometer is 6 V.
For some other battery point A would be somewhere else. If you
include a lamp into circuit and the pointer is at A, potential
difference across the lamp is zero. However, if the pointer is moved
up to two-thirds the length of the potentiometer as in the figure,
then the output voltage across the filament lamp would be
⅔ × 6V = 4V.
Pots have a rotating wheel mounted in plastic and they are
commonly used as volume and tone controls in sound systems.
They can be made from wire, metal oxides or carbon compounds.