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Circuits
Current
Electricity
![](3D"slide0068_image002.gif")
=
The term electricity can be used to refer to any =
of the
properties that particles, like
protons and electrons, have as a result
of their charge. Typically, though, electricity refers to electrical current as a source of power. Whenever
valence electrons move in=
a
wire, current flows, by definition, in the =
opposite direction. As the electrons move, their
electric potential energy=
can
be converted to other forms like light, heat, and sound. The source of this energy can be=
a
battery, generator, solar =
cell,
or power plant.
![](3D"slide0070_image003.gif")
Curren=
t
By
definition, current is the rate of flow of positive charge. Mathematically,
current is given by:
I =3D
q
t
If 15 C of charge flow p=
ast
some point in a circuit over a period of 3 s, then the current at th=
at
point is 5 C/s. A coulomb per second is also called an ampere and its symbol is A. So, the current is =
5 A.
We might say, “There is a 5 amp current in this
wire.”
It is current that can kill a someone who is electrocuted. A sign reading “Beware, High Voltage!” is really a warn= ing that there is a potential difference high enough to produce a deadly current.
![](3D"slide0071_image004.gif")
Charge
Carriers & Current
A charge carrier is any charged particle capable of
moving. They are usually=
ions
or subatomic particles. A stream of protons, for example, heading toward Earth from the sun (in the solar wi=
nd) is
a current and the pr=
otons
are the charge carriers. In this case the current is in the =
direction of motion of protons, since protons are
positively charged. In a wire
on Earth, the charge carriers are electrons, and the current is in the opposite direction of the electrons. Negative char=
ge
moving to the left is equiva=
lent
to positive charge moving to the right. The size of the current depends on how much charge each carrier possesses,=
how
quickly the carrie=
rs are
moving, and the number of carriers passing by per unit time.
wire
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electrons
I
protons
I
![](3D"slide0062_image022.gif")
A circuit is a path through=
which
an electricity
can flow. It often consists of a wire made of a highly conductive metal <=
/span>like copper. The circuit sh=
own
consists of a =
battery ( =
;
), a resistor ( =
;
), and lengths of wire ( =
;
). The battery is the source of energy for the circuit. Th=
e potential difference across=
the
battery is V. Valence electrons have a clockwise motion, opposite the direct=
ion of
the current,
I. The resistor is a circuit =
component that dissipates t=
he
energy that the
charges acquired from the battery, usually as heat. (A light bulb, for exam=
ple, would act as a resistor.) T=
he
greater the resistance, R, of the resistor, the more it restricts the flow of current.
=
![](3D"slide0062_image023.gif")
![](3D"slide0062_image024.gif")
![](3D"slide0062_image025.gif")
A
Simple Circuit
Building Analogy
![](3D"slide0061_image028.gif")
![](3D"slide0061_image029.gif")
To understand circuits, circuit components, current, energy =
transform=
ations
within a circuit, and devices used to make measureme=
nts in
circuits, we will make an analogy to a building.
=
; &n=
bsp; =
; &n=
bsp; =
; &n=
bsp; =
;
Continued…
![](3D"slide0061_image030.gif")
![](3D"slide0061_image031.gif")
![](3D"slide0061_image033.gif")
![](3D"slide0061_image034.gif")
![](3D"slide0061_image035.gif")
![](3D"slide0061_image036.gif")
![](3D"slide0061_image037.gif")
V
R
![](3D"slide0061_image038.gif")
I
Buildi=
ng
Analogy Correspondences
Battery ↔ =
Elevator that only =
goes
up and all the way to the top floor
Voltage of battery ↔ =
Height of buildin=
g
Positive charge carriers ↔ People who move through the building
= ; &n= bsp; = ; &n= bsp; en masse (as a large group)
= ; &n= bsp; = ; &n= bsp; en masse (as a large group)
Current ↔ Traffic (number of people per unit time moving past
= ; &n= bsp; some point in the building)
= ; &n= bsp; some point in the building)
Wire w/ no=
internal resistance &#=
8596;
Hallway (with no slope)
Wire w/ internal resistance ↔ Hallway sloping downward slightly
Resistor ↔ Stairway, ladder, f=
ire
pole, slide, etc. that only goes down
Voltage drop across resistor ↔ =
Length
of stairway
Resistance of resistor ↔ =
Narrowness
of stairway
Ammeter ↔ Turnstile (measures
traffic without slowing it down)
Voltmeter ↔ Tape measure (for measu=
ring
changes in height)
Current and the Building Analogy
In our analogy people correspond to positive char=
ge
carriers and a hallway corresponds to a wire.
So, when a large group of people move together=
down
a hallway, this is like charge carriers flowing through a wire.
Traffic is the rate at which people are passing, say, a water fountain
in the hall. Current is rate at which positive charge flows past =
some
point in a wire. This is why traffic corresponds to current.
<=
/span>
Suppose you count 30 people passing by the founta=
in
over a 5 s interval. The traffic rate is 6 peo=
ple
per second. This rate does not tell us how f=
ast
the people are moving. We don’t know if the hall is crowded
with slowly moving people or if the hall is relatively empty but
the people are running. We only know how many go by per second. Similarly,
in a circuit, a 6 A current could be due to many slow moving charges
or fewer charges moving more quickly. The only thing for <=
span
lang=3DEN-US style=3D'font-family:Times;font-size:96%;mso-ansi-language:EN=
-US'>certain
is that 6 coulombs of charge are passing by each second.
![](3D"slide0058_image039.gif")
el<=
/span>e<=
/span>v<=
/span>a<=
/span>t<=
/span>o<=
/span>r<=
/span>
![](3D"slide0058_image040.gif")
top floor hallway: high Ugrav
Battery=
&
Resistors and the Building Analogy
![](3D"slide0058_image041.gif")
![](3D"slide0058_image042.gif")
![](3D"slide0058_image043.gif")
![](3D"slide0058_image044.gif")
![](3D"slide0058_image045.gif")
![](3D"slide0058_image046.gif")
![](3D"slide0058_image047.gif")
![](3D"slide0058_image048.gif")
V
R
bottom
floor hallway: zero Ugrav
![](3D"slide0058_image049.gif")
![3D"Text](3D"slide0058_image050.gif")
staircase
=
flow of
+ = charges
+ = charges
![](3D"slide0058_image051.gif")
+
-
flow of
people
people
Our up-only elevator will only take people to the =
top
floor, where they have maximum
potential and, thus, where they are at the maximum gravitational potential. The elevator “energizes” pe=
ople,
giving them potential energy. Likewise,
a battery energizes positive charges. Think of a 10 V battery as an elevator that goes up 10 stories. The greater the
voltage, the greater the difference
in potential, and the higher the building. As reference points, let’=
s choose the negative terminal of the battery to be =
at
zero electric potential and the
ground floor to be at zero gravitational potential. Continued…
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Current flows from the positive terminal of the ba=
ttery,
where + charges are at high potential,
through the resistor where they give up their energy as heat, to the negative terminal of the battery, where they have =
zero
potential energy. The battery then
“lifts them back up” to a higher potential. The charges lose no
energy moving the a
length of wire (with no internal resistance). Similarly, people walk from =
the top floor where they are at a high potential, down=
the
stairs, where their potential energy
is converted to waste heat, to the bottom floor, where they have zero potential energy. The elevator them lifts them bac=
k up
to a higher potential. The people
lose no energy traveling down a (level) hallway.
Battery
& Resistors and the Building (con=
t.)
elevator
![](3D"slide0072_image053.gif")
top floor hallway: high Ugrav
![](3D"slide0072_image054.gif")
![](3D"slide0072_image055.gif")
![](3D"slide0072_image056.gif")
![](3D"slide0072_image057.gif")
![](3D"slide0072_image058.gif")
![](3D"slide0072_image059.gif")
![](3D"slide0072_image060.gif")
![](3D"slide0072_image061.gif")
V
R
bottom floor hallway: zero Ugrav
![](3D"slide0072_image062.gif")
![3D"Text](3D"slide0072_image063.gif")
staircase
=
flow of
+ = charges
+ = charges
![](3D"slide0072_image064.gif")
+
-
flow of
people
people
Resistance
Resistance is a measure of a resistors ability to
resist the flow of current in a circui=
t. As
a simplistic analogy, think of a battery as a water pump; it’s voltage
is the strength of the pump. A pipe with flowing water is like a wire
with flowing current, and a partial clog in the pipe is like a resistor in=
the
circuit. The more clogged the pipe is, the more resistance it puts up to <=
/span>the
flow of water trying to flow through it, and the smaller that flow will be.
Similarly, if a resistor has a high resistance, the current flowing it wil=
l be
small. Resistance is defined mathematically by the equation:
V =3D I R
Resistance
is the ratio of voltage to current. The current flowing through
a resistor depends on the voltage drop across it and the resistance
of the resistor. The SI unit for resistance is the ohm, and =
its
symbol is capital omega: Ω. An ohm
is a volt per ampere:
1 Ω =3D 1 V /<=
/span> A<=
/span>
![](3D"slide0073_image065.gif")
Resist=
ance
and Building Analogy
In our building analogy we’re deal=
ing
with people instead of water molecules and staircases instead of clog=
s. A
wide staircase allows many people to travel down it simultaneously, but a narrow <=
/span>=
staircase restricts the flo=
w of
people and reduces traffic. So, a resistor with low resistance is like a w=
ide
stairway, allowing a large current though it, and a resistor with h=
igh
resistance is like a narrow stairway, allowing a smaller current.
![](3D"slide0073_image066.gif")
![](3D"slide0073_image067.gif")
![](3D"slide0073_image068.gif")
![](3D"slide0073_image069.gif")
![](3D"slide0073_image070.gif")
![](3D"slide0073_image071.gif")
![](3D"slide0073_image072.gif")
V =3D 12 V=
R =3D 6 Ω
![](3D"slide0073_image073.gif")
I =3D 2
A
![](3D"slide0073_image074.gif")
![](3D"slide0073_image075.gif")
![](3D"slide0073_image076.gif")
![](3D"slide0073_image077.gif")
![](3D"slide0073_image078.gif")
![](3D"slide0073_image079.gif")
![](3D"slide0073_image080.gif")
![](3D"slide0073_image081.gif")
V =3D 12 V=
R =3D 3 Ω
![](3D"slide0073_image082.gif")
I =3D 4
A
Narrow staircase means reduced traffic.
Wide staircase means
more traffic.
more traffic.
![](3D"slide0001_image084.jpg")
The definition of resistance, V =3D I R, is often confused with Ohm’s law, which only states that the R in this formula is a constant. In other words, the resistance of a resistor is a constant no matt=
er how
much current is flowi=
ng
through it. This is like saying a clog resists the flow of water to the same extent regardless of how much water is flowing
through it. It is also like
saying a the width of a staircase does not change: no matter what rate
Georg Simon Ohm =
;
1789-1854
1789-1854
Ohm=
217;s
Law
people are going downstairs, the stairs hinder the=
ir progress to the same extent. In real life, OhmR=
17;s
law is not exactly true.=
It is
approximately true for voltage drops
that aren’t too high. When voltage drops are high, so is the current, and high current causes m=
ore heat to generated. More heat means more random thermal motion of the atoms in the resistor. This,=
in turn, makes it harder for current to flow, so resi=
stance
goes up. In the circuit proble=
ms we
do we will assume that
Ohm’s law does hold true.
![](3D"slide0003_image085.gif")
If
Ohm’s law were always true, then as V across a resistor =
increases,
so would I through it, and their ratio,
R (the slope of the graph)
would remain constant.
In
actuality, Ohm’s law holds only for currents that aren’=
;t
too large. When the current is small, not much heat is <=
span
style=3D'position:absolute;top:27.0%;left:45.13%;width:54.86%;height:5.25%=
'>produced
in a real, so resistance is constant and Ohm’s law holds
(linear portion of graph). But large currents cause
R to increase (concave up =
part of
graph).
![](3D"slide0003_image086.gif")
![3D"Text](3D"slide0003_image087.gif")
ohmic
![](3D"slide0003_image088.gif")
![3D"Text](3D"slide0003_image089.gif")
non-ohmic
![](3D"slide0003_image090.gif")
![](3D"slide0003_image091.gif")
![](3D"slide0003_image092.gif")
I
V
Ohmic Resistor
Ohmic =
vs.
Nonohmic Resistors
Real Resistor
I
V
![](3D"slide0007_image093.gif")
Resistors in Series
Voltage
drops can be different; they sum to V.
Each voltage drop is identical
and equal to V.
![](3D"slide0007_image094.gif")
![](3D"slide0007_image095.gif")
![](3D"slide0007_image096.gif")
![](3D"slide0007_image097.gif")
![](3D"slide0007_image098.gif")
![](3D"slide0007_image099.gif")
![](3D"slide0007_image100.gif")
![](3D"slide0007_image101.gif")
I
V
R1
R2
R3
![](3D"slide0007_image102.gif")
![](3D"slide0007_image103.gif")
![](3D"slide0007_image104.gif")
![](3D"slide0007_image105.gif")
=
![](3D"slide0007_image106.gif")
![](3D"slide0007_image107.gif")
![](3D"slide0007_image108.gif")
![](3D"slide0007_image109.gif")
![](3D"slide0007_image110.gif")
![](3D"slide0007_image111.gif")
=
V
I
R1
R2
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Circuits
![](3D"slide0005_image129.gif")
![](3D"slide0005_image130.gif")
![](3D"slide0005_image131.gif")
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![](3D"slide0005_image133.gif")
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R3
![](3D"slide0007_image112.gif")
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![](3D"slide0007_image114.gif")
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Current
going through each resistor is the same and equal
to I.
Current going through each
resistor can be different; they
sum to I.
resistor can be different; they
sum to I.
Series=
&
Parallel Circuits
When
several circuit components are arranged in a circuit, they can be
done so in series, parallel, or a combination of the two.
Resistors in Parallel
Resistors in Series: Building Analogy
To
go from the top to the bottom floor, all people must take the same path. S=
o, by definition, the staircases are in series. With =
each
flight people lose some of the
potential energy given to them by the elevator, expending all of it by the=
time they reach the ground floor. So the sum of th=
e V drops across the resistors the
voltage of the battery. People lose more potential energy going down longe=
r flights of stairs, so from V =3D I R, long
stairways correspond to high resistance resistors.
The
double waterfall is like a pair of resistors in series because there is on=
ly
one route for the wat=
er to
take. The longer the fall, the greater the resistance.
3 steps=
6 steps
11 steps
=
Elevator (battery)
R1
R2
R3
R1
R2
I
![](3D"slide0005_image137.gif")
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Circuits
![](3D"slide0009_image147.gif")
![](3D"slide0009_image148.gif")
![](3D"slide0009_image149.gif")
![](3D"slide0009_image150.gif")
![](3D"slide0009_image151.gif")
![](3D"slide0009_image152.gif")
![](3D"slide0009_image153.gif")
![](3D"slide0009_image154.gif")
V
R1
R2
R3
Equiva=
lent
Resistance in Series
I
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V
Req
If you were to remove all =
the
resistors from a circuit and replace them with a single resist=
or,
what resistance should this replacement have in order to produce t=
he
same current? This resistance is called the equivalent resista=
nce,
Req.
In series Req is simply the=
sum
of the resistances of all the resistors, no matter how many there a=
re:
=
; &n=
bsp;
Req =3D R1 + R2 + R3 + ·
· ·
Mnemonic: Resistors
in Series are R=
eally S=
imple.
V1 + V2 + V3 =3D V =
;(energy losses sum to energy gained by battery)=
3;
V1=3D I R1, V2=3D =
I =
R2,
and V3=3D I R3 ( I is a constant in series) =
; &n=
bsp;
I
![](3D"slide0009_image155.gif")
![](3D"slide0009_image156.gif")
V
R1
R2
R3
}
V1
}
V2
}
V3
Proof =
of
Series Formula
I =