Electric Circuits (Chapter 23)
Review from Chapter 22
Electric current is the flow of electric charge just as water current is the flow of water
molecules.
Units of measurement: AMPERES = Amps
What do we mean by electric current in a copper wire? Since copper has one weakly
bound electron (the 29th one), the wire has copper ions that are fixed in place within the
wire. The weakly bound electrons (called the conduction electron) are bound to the solid
as a whole, but not to any particular atom. They are free to move around.
DEMO Fluorescent light tube.
Electric Potential Difference or Voltage sets up the electrical landscape that charges
will follow.
potential difference ( ∆V ≠ 0)

→ current flow
no potential difference ( ∆V =
0) 
→ no current flow
Clicker Question
In which of the circuits below does a current exist to light the bulb?
Overview: Basic Elements of Electric Circuits
Most people come into contact with electric phenomena through electric circuits in their
homes and cars. In its most basic form, an electric circuit is an unbroken path of material
that carries electricity (wires). Every circuit consists of three parts:
1. Source of energy: voltage source or battery
2. Transfer of energy: a closed path that carries current and has resistance
3. Power Absorption: Load Device and Electric Power: mp3 player, light bulb that
uses the electric energy.
1. The Source of Energy in a Circuit (or role of the Voltage Source/Battery)
Analogy: Water circuit – fountain
i. Water
• never builds up in one place, just keeps flowing
• only flows in a closed loop
ii. What is the role of the water pump? It applies the pressure (it’s the water
push or force) required to move water from one local to another. However,
it is much deeper than that.
Lecture 7-1
Analogy: sliding book with friction
Suppose you want to slide a book across the table. You give it a quick push to start it
moving, but it begins slowing down because of friction as soon as you take your
hand off of it. The book's kinetic energy is transformed into thermal energy, leaving
the book and the table slightly warmer. The only way to keep the book moving at a
constant speed is to continue pushing it.
So in the case of the water fountain system, if a gallon of water is poured down the
incline of the water fountain, then the water flows down and uses all its PE, and is
now at rest at the bottom of the pool. The only way to keep the water circulating
continuously is to pump water back up to the top so that the water can again
flow down the slide of the water fountain. That is, when water flows from a high
potential to a low potential, there is loss in PE of the water. A water pump “reenergizes” the water and brings low potential water up to high potential water.
iii. So where does this loss in potential energy show up?
Suppose we put a turbine in the middle of the pipe so that the flow of the
water turns the turbine. Water flows through the turbine. It is not consumed
by the turbine, and the number of gallons of water per minute leaving the
pipe is exactly the same as that entering. Nonetheless, the water must do
work to turn the turbine, so there is an energy change as the water passes
through.
Electric Circuit
DEMO Setup a single lightbulb circuit
i
Similar to water current, electric current never builds up in one place and only flows
in a closed loop.
ii. An E-field is transmitted through the wires instantaneous such that there is an
electrical pressure that pushes all of the charges in one direction (from high to low
potential).
What is the role of the battery? It applies an electrical pressure (it’s the electrical
push or force) required to move electric charge from one local to another. There are
two ways to see this role: E-field (the force picture) or potential field (incline) picture.
E-field Picture
Something similar happens in a conductor as with the sliding book with friction.
Suppose we take a piece of metal and apply an electric field, the E-field pushes on
the electrons in a conductor and they begin to move. But the electrons aren't moving
in a vacuum. Collisions between the electrons and the atoms of the metal slow them
down, transforming the electrons' kinetic energy into the thermal energy of the metal,
making the metal warmer. The motion of the electrons will cease unless you continue
pushing. To keep the electrons moving, we must maintain an electric field. In a
Lecture 7-2
constant field, an electron's average motion will be opposite the field. We call this
motion the electron's drift velocity.
Potential Field Picture
The battery sets up a voltage (electrical incline) and charges move down the incline
from a high potential to a low potential. Electrical PE lost so that the charge is at a
low energy at the bottom of the electrical incline. The role of the battery is to “reenergizes” charge from low potential to high potential charge via a chemical process.
So how does the battery do this? The chemicals inside the battery do chemical work
on the charges and “lift them” from low electrical PE to high electrical PE. That is, the
charges gain electrical potential energy. As a result, the charges are able to
continuously circulate through the electrical circuit.
Once again, in an electric circuit there is a loss in electric potential as a charge
goes around a closed circuit. The job of the battery is to “re-energize” the
charge from a low to a high electric potential. Therefore, the charges are able
to continuously circulate through the circuit as the battery continuously adds
electrical PE to the circuit.
iii. So where does this loss in potential energy show up?
Similarly to the water turbine, the lightbulb doesn't "use up" current, but,
like the turbine, it does use energy. The energy is dissipated by atomiclevel friction as the electrons move through the wire, making the wire
hotter until, in the case of the lightbulb filament, it glows.
2. Energy Transfer – Current and Resistance
As stated early, in an electric circuit there is a loss in electric PE. Where does this
electrical PE go? It is dissipated by atomic-level friction as the electrons move through
the wire and whatever electrical device (radio, toaster …) is using this PE. The question
we need to ask is how it does this and the answer leads to understanding what electrical
resistance is.
Current is the number of electrons flowing past a fixed point when a potential difference
is created. The charge carriers in metals are (conduction) electrons while in ionic
solutions (seawater, blood) are both positive and negative ions. Picture wise the picture
you should have is
Lecture 7-3
more
→ higher resistance 
→ lower current
collisions
 
more heat
less
collisions
→ lower resistance 
→ higher current



 
less heat
DEMO
The motion of a ball rolling down and bouncing off pegs in its path is analogous
to the motion of an electron in a metallic conductor with an electric field
present.
DEMO Lichtenberg Figure from SLAC
Here is a computer simulation of electron flow in a conductor (in a 2-dimensional
electrical landscape)
Resistance ≡ R is the ability of a materia lto resist the flow of charge
smaller the resistance ⇒ larger current
larger the resistance ⇒ smaller current
Units of measurement: Ohms (Ω)
Electrical resistance depends on 4 things: area, length, material, and temperature
1. Area Dependence: with water, as the diameter of the pipe increases, so does the
amount of water that can flow through it. With electricity, conducting wires take the
place of the pipe. As the cross-sectional area of the wire increases, so does the
amount of electric current (number of electrons) that can flow through it.
larger area
→ larger current
smaller area → smaller current


bigger diameter wire
smaller diameter wire
Examples: Electrical fires
Electrical fires are usually caused by having too much current in a smaller wire.
Why the difference in size between the outlet plug for a home clothes drier verses
the outlet plug for a lamp?
DEMO Compare a power supply wire vs. lamp lead
2. Length Dependence: if the length of a wire is increased, does the number of
collisions increase? Yes!
longer length
→ smaller current → higher resistance



more collisions
shorter length



→ higher current
→ lower resistance
less collisions
Example: Cray-2. No wire was longer than 6 inches. Why?
Lecture 7-4
The Cray-2, installed in 1985 at LLNL, has 240,000 computer chips packed into the
C-shaped cabinet. A liquid coolant must wash continuously over the circuits to
dissipate heat that would otherwise melt the machine.
3. Material Dependence: Conductors move charge whereas insulators do not.,
conductors → lower resistance
insulators
→ higher resistance
4. Temperature Dependence: If one heats up a metal so that the temperature of the
metal increases, the resistance goes up. As the copper ions acquire KE from the
heat energy, these once stationary ions are now moving. It is now more likely that
the electrons will collide more frequent with the copper ions, which results in a higher
resistance and reduce current flow.
higher temperature → higher resistance

more collisions
lower
temperature


→ lower resistance
less collisions
Examples: lightbulbs change brightness as they heat up; rear car windows and
resistors
OHM”S LAW & POWER
George Ohm discovered that in many materials, especially metals, the current that flows
through a material is proportional to the voltage and inversely proportional to the
resistance. The relationship between the current, voltage, and the resistance is called
Ohm’s Law:
Ohm’s Law – The current in a circuit is inversely proportional to the resistance and
directly proportional to the voltage.
Lecture 7-5
=
Current
( Voltage Difference ) ⋅ (Resistance )
I=
ΔV
R
or
∆V =
IR
Remarks
1. Current ∝ voltage
I ∝ ΔV

 ∝
I ΔV
→ small voltage difference ⇒ small current
→
large voltage difference ⇒ large current
2. Current ∝ 1/resistance
1

I ∝


 ∝ 1

R
R
I
→
→
large resistance ⇒ small current
small resistance ⇒ large current
Before we go start applying Ohm’s law to various types of circuits, let’s talk briefly about
what Electrical Power is.
Applications of Ohm’s Law
Electric circuits are all around us – because they can release a great deal of energy, we
have to be aware of this danger. There are two typical dangers that most encounter:
generation of fires due to short circuits and electric shock.
1. Generation of Fires due to Short Circuits
Because current flowing through a wire generates heat, there is always the danger that a
wire will overheat and ignite materials around it, and therefore, cause a potential fire.
There are codes that electrician must follow to reduce this: electric codes are set so that
every wire can only carry a specific maximum current.
2. Electric Shock
Nerves are on the order of 1micrometer (0.0000001 m), which is about the size of a
spider web. Because nerves are so thin, they cannot handle very much current
Effects of Current on the Human Body
Current (mA)
Effect
1 mA
can be felt
5 mA
painful
Involuntary muscle
10 mA
contractions
15 mA
Loss of muscle control
70 mA
Fatal if the heart is include
Suppose that you are interested in trying to find out how much electric shock you can get
out of a car battery (which has 12-volts). If you touch the two terminals of the car battery,
the current path is then from your right hand to your left hand, that includes your heart in
the circuit. How much electric shock you will receive will depend upon your electrical
resistance. There are three cases.
1. Dry fingers/hand: human resistance is 500,000Ω
Your skin of your hands gives you the highest electrical resistance of the human
body. So when you grab the two battery terminals, Ohm’s law predicts that
Lecture 7-6
ΔV
= I →
R
12 volts
= 0.024 mA
500,000Ω



too low of a resistance to be felt
2. Wet fingers/hand: human resistance is 1,000Ω
If you were able to bypass the skin of your figers/hands, your resistance dramatically
decreases because the current path is most made of water. So Ohm’s law tells us
that
ΔV
= I →
R
12 volts
= 12 mA
1,000
Ω


very painful shock but not enough to kill you
3. Salty Wet fingers: human resistance is 100Ω
If you add salt to water, water becomes a better conductor, which means that it
lowers the resistance. Since your organs/blood are really a salty water solution,
when you bypass your skin Ohm’s law tells us again that
ΔV
= I →
R
12 volts
= 120 mA
100Ω


A current this large is enough to stop the heart
True Story (Darwin Award Winner – 1999)
A US Navy safety publication describes injuries incurred while doing don't's. One page
described the fate of a sailor playing with a DMM in an unauthorized manner. He was
curious about the resistance level of the human body. He had a Simpson 260 DMM, a
small unit powered by a 9-volt battery. That may not seem powerful enough to be
dangerous… but it can be deadly in the wrong hands. The sailor took a probe in each
hand to measure his bodily resistance from thumb to thumb. But the probes had sharp
tips, and in his excitement he pressed his thumbs hard enough against the probes to
break the skin. Once the salty conducting fluid known as blood was available, the current
from the DMM travelled right across the sailor's heart, disrupting the electrical regulation
of his heartbeat. He died before he could record his resistance. The lesson? The Navy
issues very few objects which are designed to be stuck into the human body.
DC and AC Circuits
Series and Parallel Circuits
Voltage ≡ ∆V
Resistance ≡ R
Current ≡ I
Power ≡ ∆V∙ I
(brightness)
Series
Parallel
Voltages are divided between two
resistors (each lightbulb gets 5-volts).
Resistors in series increase the total
resistance
There is only one path for the current
follow and the overall battery current
decreases.
Voltages are not divided between two
resistors (each lightbulb gets 10-volts).
Resistors in parallel decrease to total
resistance
There two paths for the current to follow
and the overall battery current
increases.
Larger voltage, lower resistance implies
larger power, so lightbulbs are brighter.
The battery has to work harder to
maintain the current.
Smaller voltage, higher resistance
implies smaller power, so lightbulbs
are dim. The battery does not have to
work as hard to maintain the current.
ΔV ⋅ I = P
ΔV ⋅ I = P
Lecture 7-7