All physics to date has led to one primary conclusion:
• There are four fundamental forces:
1)
2)
3)
4)
Strong nuclear
Electromagnetic
Weak nuclear
Gravitational
But why four?
Why not just one master force?
The quest for a single unified master force is on!!!
Idea: There is one force only which manifest itself
differently in different situations
GUT - grand unified theory :
Higgs boson
~250 yrs or so since we first learned what electricity is
“Electricity” – from the Greek word electron (elektron) - meaning “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
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.
– positive charge
– negative charge
Benjamin Franklin
1706 - 1790,
American statesman,
philosopher and scientist)
Electricity has origin within the atom itself.
10-15 m
Name
Symbol Charge
Electron
e
-e
Proton
Neutron
p
n
e
none
Mass
9.11x10-31 kg
1.67x10-27 kg
1.67x10-27 kg
10-10 m
mnucleon ≈ 2000 x melectron
ratom ≈ 100000 x rnucleus
Atom is electrically neutral = has no net charge, since it contains equal
numbers of protons and electrons.
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 are formed and…chemistry…
• charge is measured in Coulombs [C]
French physicist Charles A. de
Coulomb
1736 - 1806
Every electron has charge -1.6 x 10-19 C,
and every proton 1.6 x 10-19 C
1C represents the charge of 6.25 billion billion (6.25x1018) electrons !
Yet 1C is the amount of charge passing through a 100-W light
bulb in just over a second. A lot of electrons!
The smallest amount of the free positive
charge is the charge on the proton.
quarks have 1/3, but they
come in triplets
The smallest amount of the free negative
charge is the charge on the electron.
let e = 1.6 x 10-19 C
Charge of the single proton is qproton = e
Charge of the single electron is qelectron = - e
• 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.
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.


• Which object gains the electrons depends on their electron affinity:
Conclusion:
 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!
 Another Law of Conservation:
Charge is always conserved: charge cannot be created or
destroyed, but can be transferred from one object to another.
Electrical conductors, insulators, semiconductors and
superconductors
- distinction based on their ability to conduct electric charge.
Any material that allow charges to move about more or less freely is called conductor.
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.
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!!
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.
The markings caused by electrical breakdown in
this material – look similar to the lightening bolts
produced when air undergoes electrical
breakdown.
Materials like amber, pure water, plastic, glass, rubber, wood… are called
insulators.
They do not let electricity flow through them. Electrons are tightly bound to nuclei,
so it is hard to make them flow. Hence, poor conductors of current and of heat.
Conductors and Insulators
REMEMBER:
Electrons are free to move in a
conductor
Electrons stay with their atom in an
insulator
Most things are in between perfect conductor/ insulator
Semiconductors
• Materials that can be made to behave sometimes as insulators,
sometimes as conductors.
Eg. Silicon, germanium. In pure crystalline form, are insulators. But if
replace even one atom in 10 million with an impurity atom (ie a different
type of atom that has a different # of electrons in their outer shell), it
becomes an excellent conductor.
• Transistors: thin layers of semiconducting materials joined together.
Used to control flow of currents, detect and amplify radio signals, act as
digital switches…An integrated circuit contains many transistors.
The movement of electrons in semiconductors is impossible to
describe without the aid of quantum mechanics.
As the conductivity of semiconductors can be adjusted by adding
certain types of atomic impurities in varying concentrations, you can
control how much resistance the product will have.
ADVANTAGE – A HUGE ONE
Superconductors
• Have zero resistance, infinite conductivity
• Not common! Have to cool to very, very low temperatures.
• Current passes without losing energy, no heat loss.
• Discovered in 1911 in metals near absolute zero
(recall this is 0oK, -273oC)
• Discovered in 1987 in non-metallic compound (ceramic) at “high”
temperature around 100 K, (-173oC)
• Under intense research! Many useful applications eg. transmission of
power without loss, magnetically-levitated trains…
•
http://science.nasa.gov/science-news/science-at-nasa/2003/05feb_superconductor/
•
http://www.scicymru.info/sciwales/indexphpsectionchoose_scienceuser_typePupilpage_id11696languageEnglish.htm
Example:
Van de Graaff
The sphere gives the girl a large negative charge. Each
strand of hair is trying to:
1) Get away from the charged sphere.
2) Get away from the ground.
3) Get near the ceiling.
4) Get away from the other strands of hair.
5) Get near the wall outlet.
Like charges attached to the hair strands repel,
causing them to get away from each other.
What is his secret?
Seeing the effects of charge:
the 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 negatively charged rod is placed near the ball,
the electrons move away because of the repulsion.
The two sides of the metal foil then separate.
Charge polarization is why a charged object can attract a neutra
one :
•DEMO: Rub balloon on your hair – it will then stick to the wall !
Why?
Balloon becomes charged by friction when rub on hair,
picking up electrons. It then polarize molecules on the
surface, induces + charge layer on the wall’s surface
closest to it , and next 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.
• Charge a comb by rubbing it
through your hair, and then see it
attracts bits of paper and fluff…
You can bend water with charge!
The water molecule
has a positive end and
a negative end.
charged rod
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?
stream of water
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?
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.
q1q2
F k 2
r
k  8.99 109 N  m 2 / C 2
Force is a vector, therefore it must
always have a direction.
SHE accumulates a charge q1 of 2.0 x 10-5 C
(sliding out of the seat of a car).
HE has accumulated a charge q2 of – 8.0 x 10-5 C
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 a factor of 0.5?
a) They exert equal forces on each other only in opposite direction
F k
q1q2
 0.40 N
2
r
(“-“ = attractive force)
b) r’ = 0.5 r
q1q2
F '  k 2  1.6 N  4 F
r'
Strong force at very small separation
How many electrons is 2.0 x 10-5 C ?
2.0 10 5 C
14

10
electrons
19
1.6 10 C
spark
When you comb your hair with a plastic comb, some electrons
from your hair can jump onto it making it negatively charged.
Your body contains more than 1028 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 equal to the force that
1023 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.
Three point charges : 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?
1.30 m
230
q1
q2
230
1.30 m
Force diagram
F3
q3
q1
F2
F2  k
q1q2
 0.213 N
2
r
q1q2
F3  k 2  0.213 N
r
𝐹𝑥 = 0 , 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑜𝑓 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦; x-components will cancel each other
𝐹𝑦 = 𝐹2 sin 230 + 𝐹3 sin 230 = 0.213 sin 230 + 0.213 sin 230 = 0.166 𝑁
F = Fy = 0.166 N
𝑎=
𝐹
0.166
𝑚
=
=
111
𝑚 1.50 × 10−3
𝑠2
𝑖𝑛 𝑦 − 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
electric force is very-very strong force, and resulting acceleration can be huge
A positive and negative charge with equal magnitude are connected by a rigid rod,
and placed near a large negative charge. In which direction is the net force on the
two connected charges?
1) Left
2) Zero
3) Right
Positive charge is attracted (force to left)
Negative charge is repelled (force to right)
Positive charge is closer so force to left is larger.
-
+
-
Calculate force on +2mC charge due to other two charges
– Calculate force from +7mC charge
– Calculate force from –3.5mC charge
– Add (VECTORS!)
q1q2
F k 2
r
(9 109 )(2 10 6 )(7 10 6 )
F7 
N
25
(9 109 )(2 10 6 )(3.5 10 6 )
F3 
N
25
F7
Q=+2.0mC
F3
4m
•
F7  5 103 N
F3  2.5 103 N
Q=+7.0mC
6m
Q=-3.5 mC
Fx = F7 cos q + F3 cos q = F7(3/5) + F3(3/5) = 3  10-3 N + 1.5  10-3 N = 4.510-3 N
Fy = F7 sin q + F3 sin q = F7(4/5) + F3(4/5) = 4  10-3 N – 2.0  10-3 N= 2.010-3 N
F  Fx2  Fy2
 4.9 103 N
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.
How to measure/find the strength (magnitude and direction)
of electric field at particular location P due to charge Q?
A test charge, q, placed at P will experience an electric
force, F - either attractive or repulsive.
r
Q
P F
q
r
Q
P F
q
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.
F
E=
q
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.
N
E ) 
C
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=qE
E
E
q
F
F
q
Electric field of a charged particle/point charge
A charged particle Q creates an electric field.
Q
F
E Field independent
◊ magnitude E  q = k r2
of test charge
the same value on the sphere of radius r around
◊ direction – radially outward or inward
example:
Q=1.6x10-19 C
+
q
E
r = 1x10-10 m
-19
E = 9109 1.610
(10-10)2
= 2.91011 N/C
q positive test charge
(to the right)
Question
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.
We use “Electric Field Lines” to visualize el. field.
Convention / agreement
Direction indicates direction in which a positive test
charge would be pushed – direction of the force!!!.
321011 N/C
Electric Field of a Point Charge
2.91011 N/C
+
This is becoming a mess!!!
E
Electric Field Lines
1. Density gives strength
# lines proportional to Q
lines never cross!
2. Arrow gives direction
Start on +, end on -
negative
charge
So always point away from
+ charges, towards – charges…
positive
charge
Denser lines - stronger field
el. field decreases with distance
more lines revels stronger
field due to greater 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.
Question?
What is the direction of the electric field at point C?
1) Left
2) Right
3)
Zero
Away from positive charge (right)
Towards negative charge (right)
y
Net E field is to right.
C
x
Question?
What is the direction of the electric field at point A?
1) Up
2) Down
3) Left
4) Right
5) Zero
A
x
Question?
What is the direction of the electric field at point B?
1) Up
2) Down
3) Left
4) Right
5) Zero
y
B
x
Question?
What is the direction of the electric field at point A, if the
two positive charges have equal magnitude?
1) Up
2) Down
3) Left
4) Right
5) Zero
A
x
Electrical Energy and Electrical Potential
Two different things that sound alike!
Recall Work: W = F d cos(q)
In order to bring two like charges together work must be done.
In order to separate two opposite charges, work must be done.
As the monkey does + work on the positive
charge against electric force, he increases the
energy of that charge. The closer he brings it,
the more electrical potential energy it has.
This work done by external force against
electrical force is stored as electrical PE, U.
When he let it go, the charge will gain kinetic energy and can do a work.
Try the same thing with grav. force. It is the same!!!! charge → mass
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 doesn’t depend on
the amount of charge.
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 
U
V
q
electric potential energy
charge
1J
1V 
1C
The SI unit of electric
potential is the volt.
• 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 – could
do more work.
Potential Difference Between Two Points (ΔV = VB – VA)
The difference between the potentials at two different
points, A & B, is equal to the change in electric potential
energy between these two points or the work done per
unit of positive charge in order to move it from one point
to the other.
∆U W
∆V=
=
q
q
Law of conservation of energy:
change in potential energy = change in kinetic energy
To place a charge in electric field a work has to be done on the charge.
That work is stored as potential energy, U, of the charge. The point
where the charge is, has potential V (charge q placed there has
potential energy U = qV). Charge placed in electric field E will
experience electric force, F= qE. If the charge is free to move it will
accelerate, it will gain kinetic energy and can do a work.
surprise, surprise ! We use the same name for different things, and even
worse we use couple of different names to express the same thing, like:
1. The variable we use for potential, potential difference, and the unit
for potential difference (volts) is V. Cute!!!!!
2. Don't let that confuse you when you see V = 1.5V
3. Electric potential energy is not the same as electrical potential.
4. The electron volt is not a smaller unit of the volt, it's a smaller unit of
the Joule.
5. Electrical potential can also be described by the terms, potential
difference, voltage, potential drop, potential rise, electromotive force,
and EMF. These terms may differ slightly in meaning depending on
the situation.
Electrical Energy Storage
◊ We can store electric energy in a capacitor :
◊ Found in nearly all electronic circuits eg. in photo-flash units.
◊ Simplest is: two close but separated parallel plates.
When connected to a battery electrons get transferred from
one plate to the other until the potential difference between
them = voltage of battery.
◊ How?
Positive battery terminal attracts electrons on LH plate; these
are then pumped through battery, through the terminal to the
opposite plate. Process continues until no more potential
difference btn plate and connected terminal.
◊ Discharging: when conducting path links the two charged plates.
◊ Discharging is what creates the flash in a camera.
♦If very high voltages (eg caps in tv’s), its dangerous if you are this path!
Potential difference or Voltage (symbol V)
• When the ends of an electric conductor are at different
electric potential, charge flows from one end to the other.
Voltage is what causes charge to move in a conductor.
Charge moves toward lower potential energy the same way
as you would fall from a tree.
• Voltage plays a role similar to pressure in a pipe; to get
water to flow there must be a pressure difference between
the ends, this pressure difference is produced by a pump
• That’s why we call voltage “electric pressure”
• A battery is like a pump for charge, it provides the energy for
pushing the charges around a circuit
Voltage and current are not the same thing
• You can have voltage, but without a
path (connection) there is no current.
An
electrical
outlet
voltage
Current– flow of electric charge
If I connect a battery to the ends of the copper bar the
electrons in the copper will be pulled toward the positive
side of the battery and will flow around and around.
 this is called current – flow of charge
copper
An electric circuit!
Duracell
+
Electric current (symbol I)
◊ the flow of electric charge q that can occur in solids, liquids and gases.
q
• DEF: the rate at which charge flows
by a given cross-section.
• measured in amperes (A)
q
I=
t
1C
1A =
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.
Electrical resistance (symbol R)
• 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.
path
atoms
(actually
positive ions)
free electron
.
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
• DEF: Current through resistor (conductor) is
proportional to potential difference on the resistor
if the temperature of a resistor is constant
(than the resistance of a conductor is constant).
Other way:
V
I=
R
current =
voltage
resistance
• if resistance R is constant/ temperature is constant
• I – current
V – potential difference across R
Examples
• 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 
Effects of electric current on the BODY- electric shock
Current (A)
Effect
0.001
can be felt
0.005
painful
0.010
involuntary muscle contractions (spasms)
0.015
loss of muscle control
0.070
if through the heart, serious disruption; probably
fatal if current lasts for more than 1 second
questionable circuits: live (hot) wire ? how to avoid being electrified?
1. keep one hand behind the body (no hand to hand current through the body)
2. touch the wire with the back of the hand. Shock causing muscular contraction
will not cause their hands to grip the wire.
human body resistance varies:
100 ohms if soaked with salt water;
moist skin - 1000 ohms;
normal dry skin – 100 000 ohms,
extra dry skin – 500 000 ohms.
What would be the current in your body if you touch the
terminals of a 12-V battery with dry hands?
I = V/R = 12 V/100 000  = 0.000 12 A
quite harmless
But if your hands are moist (fear of AP test?) and you
touch 24 V battery, how much current would you draw?
I = V/R = 24 V/1000  = 0.024 A
a dangerous amount of current.
Factors affecting resistance
Conductors, semiconductors and insulators differ
in their resistance to current flow.
Wires, wires, wires
The resistance of a wire can be completely ignored – if it
is a thin wire connecting two, three or more resistors, or
can become very important if it is a long, long wire as in
the case of iron, washing machine, toaster ……
The resistance of a conducting wire depends on four main
factors: • length • cross-sectional area • resistivity • temperature
Resistance of a wire when the temperature is kept constant is:
R=ρ
L
A
L – length
A – cross-sectional area
Of course, resistance depends on the material being used.
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.
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?
The current can be found from Ohm's Law, V = IR. The V is the battery
voltage, so if R can be determined then the current can be calculated.
The first step, then, is to find the resistance of the wire:
L = 1.60 m.
r = 1.00 mm
r = 1.72x10-8 m, copper - books
The resistance of the wire is then:
R = r L/A = (1.72x10-8 m)(1.67)/(7.85x10-7m2 ) = 3.50 
The current can now be found from Ohm's Law:
I = V / R = 1.5 / 3.5 = 0.428 A
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.
Appliance
Power rating
Blow heater
Kettle
Toaster
1.2 kW
Iron
Vacuum cleaner
Television
2 kW
1.5 kW
850 W
1.2 kW
250 W
Deriving expressions for determining power
Basic definition of power:
Remember: W = qV → P =
W
P=
t
qV
t
P=IV
P = IV = V2/R = I2 R
and I = q/t, so
1W =
1J
= 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
1 kWh = 3.6 x 106 J
1W x 1s = 1J
$$$ example $$$
• At a rate of 14 cents per kWh, how much does it cost to keep a 100 W
light bulb on for one day?
• energy (kWh) = power (kW) x time (h)
• energy (kWh) = 0.1 kW x 24 h = 2.4 kWh
cost / day = 2.4 kWh x 14 cents/kWh = 33.6 ¢
 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
Duracell
+
The electrons go one way but the
current flows the opposite to the
direction that the electrons travel.
That’s convention.
hystoric explanation
click me
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
AC movement of electrons in a wire
_
+
The current in AC electricity alternates in direction. The back-and-forth 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.
current
How does the voltage and current change in time?
DC does not change
direction over time;
DC
current
time
AC
time
the actual voltage in
a 120-V AC circuit
varies between
+170V and -170V
peaks.
AC vs. DC current
• for heaters, hair dryers, irons, toasters, waffle makers,
the fact that the current reverses makes no difference.
They can be used with either AC or DC electricity.
• battery chargers (e.g., for cell phones) convert the AC
to DC
• Why do we use AC ?? DC seems simpler?
• late 1800’s  the war of the currents
• Edison (DC) vs Tesla (Westinghouse) (AC)
• Edison opened the first commercial power plane for
producing DC in NY in 1892
• Tesla who was hired by George Westinghouse
believed that AC was superior
• Tesla was right, but Edison never gave up!
Why AC is better than DC
• DC power is provided at one voltage only
• The major advantage: AC voltages can be transformed
to higher or lower voltages (can be stepped up or down
to provide any voltage required)
• This means that the high voltages used to send
electricity over great distances from the power station
can be reduced to a safer voltage for use in the house.
• This is done by the use of a transformer.
• DC is very expensive to transmit over large distances
compared to AC (more loss to heat), so many plants are
required
• DC power plants must be close to users
• AC plants can be far outside cities
• by 1895 DC was out and AC was in
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
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.
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 + I2 = I3 + I 4 + I 5
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 = V1 + V2 + V3
Resistors in Series
• connected in such a way that all components
have the same current through them.
• Burning out of one of the lamp filaments or simply
opening the switch could cause such a break.
Equivalent or total or effective resistance is the one that
could replace all resistors resulting in the same current.
Req = R1+ R2 + R3
logic: the total or effective resistance would have length L1+ L2+ L3
and resistance is proportional to the length
Resistors in Parallel
• 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.
• 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 curent.
1
1
1
1
=
+
+
Req R1 R2 R3
equivelent resistance
is smaller than the
smallest resistance.
RESISTORS IN COMPOUND CIRCUITS
Now you can calculate current, potential drop and
power dissipated through each resistor
http://www.saaphysics.com/CircuitsPractic
eQuiz.htm
http://www.glencoe.com/qe/science.php?qi
=2246
http://phet.colorado.edu/en/simulation/circu
it-construction-kit-dc-virtual-lab
example: Find power of the source, current in each resistor, terminal potential,
potential drop across each resistor and power dissipated in each resistor.
I = ε/Req = 0.3 A
Req = 120 
terminal potential:
V = ε – Ir = 36 – 0.3x6.7 = 34 V
current through resistors 100Ω and 50Ω :
0.3 = I1 + I2
100 I1 = 50 I2
I = I1 + I2
→ I1 = 0.1 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
I1R1 = I2R2
I2 = 0.2 A
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.
• 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.
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.