Resistance

1
Resistance
Water flows through a pipe with no effort at all,
right? It takes the same amount of force to move
water at a certain rate through a soda straw or a
firehose, right? Of course not!
2
Resistance
Water flows through a pipe with no effort at all,
right? It takes the same amount of force to move
water at a certain rate through a soda straw or a
firehose, right? Of course not!
Small pipe requires more pressure
Large pipe requires less pressure (for the same
flow rate)
A pipe has resistance to the flow of water. A
small pipe has more resistance, a large pipe has
less.
3
Resistance
Any wire also has resistance to the flow of
charge. The resistance depends on the material
the wire is made of. Copper is better than steel,
for instance. It also depends on the length and
thickness of the wire.
Long, thin wire has higher resistance
Short, thick wire has lower resistance.
A pipe has resistance to the flow of water. A
small pipe has more resistance, a large pipe has
less.
4
Resistance
The unit of resistance is the Ohm, which is often
abbreviated by the greek letter W (Omega). The
symbol for resistance is usually R
This is the schematic symbol for a resistor
designate R1, with a resistance of 15 KW (15,000
Ohms).
R1
5
Resistance
The resistance of an electrical conductor is
given by
A
l
6
Resistance
In some tabulations of resistivity for standard
wire sizes, the cross-sectional area A may be
given in units of circular mils (CM). The units
of r are then CM-Ohms/ft. (at 20 degrees C). The
meaning of circular mils is illustrated below. A
mil is 0.001 inch. To find the area of a circle
in circular mils, find the area in square mils of
a square just big enough to hold the circle. If
ACM is the area of the circle in circular mils,
and A is the area of the square in square mils,
then
ASM
ACM
D
7
Resistance
To increase s the resistance of a wire, increase
its length, reduce its cross-section area (reduce
its diameter), or substitute a material with a
greater resistivity. To reduce the resistance of
a wire, reduce its length, increase its cross
section, or substitute a material with a smaller
resistivity. Materials with small values of
resistivity are called conductors. Most metals
are classified as conductors, along with some
plastics and ceramics, and ionic solutions of
water. The resistivity of copper is 1.72 x 10-9
W-m Materials with large values of resistivity
are called insulators. Examples are glass, most
plastics, dry wood and deionized water. The
resistivity of glass is 1000 x 109 W-m, about
1021 times the resistivity of copper.
8
Resistance
Materials with resistivities too great to be
called conductors but too small to be good
insulators are called semiconductors. Examples
are germanium and silicon. Diodes and
transistors are called semiconductor devices
because their operation depends on special
properties of certain semiconductors. The first
transistors were made of germanium, with a
resistivity of 0.47 W-m. Most transistors today
are made of silicon, whose resistivity is 640
W-m.
9
Resistance Characteristic
Resistance is a measure of the difficulty with
which electrical current flows through a circuit
or circuit element. For a given resistance, the
current can be increased by using additional
force (increased voltage) to push current through
the resistance.
I
I
This can be illustrated by plotting the current
through a resistor versus the voltage applied
across the resistor. For an ideal resistor, this
is a straight line passing through the origin
Iwith slope equal to the reciprocal of the
resistance.
V
10
Conductance
Resistance is a measure of the difficulty wit h
which electrical current flows through a circuit
or circuit element. Conductance is a measure of
the ease with which currenst flows through a
circuit element. Mathematically, the conductance
of an element (usually represented by the symbol
G) is the reciprocal of its resistance
The unit of conductance is the mho (Ohm spelled
backwards). Seriously, 30 years ago it was the
mho, now its the Siemen, abbreviated S. A
resistance of 1 W has a conductance of 1 S.
11
Resistance Characteristic
We can construct the resistance characteristic
using an adjustable power supply, an ammeter and
a voltmeter. Apply voltage across the resistor
as shown, using the adjustable
power supply. Vary the applied voltage,
measuring the voltage and current with the
meters. Record the voltage and current fory a
variety of voltage settings, and then plot. A
curve tracer is an instrument which does this
automatically.
V2
I

R
V
-
Ground
12
Resistance Characteristic
This plot is the characteristic, or I-V
characteristic of the resistor. Since the
resistance is the reciprocal of the slope, we can
write
I
I
If the resistor is ideal (a common simplifying
assumption) with a straight-line characteristic
passing through the origin, we can simply write
V
This is Ohms Law.
13
Resistance Characteristic
Note that increasing the slope of the I-V
characteristic is equivalent to increasing
conductance or decreasing resistance. A
vertical characteristic indicates a resistance
value of zero.
I
I
Conversely, reducing the slope indicates reduced
resistance. A slope of zero (a horizontal
characteristic) indicates infinite resistance (or
zero conductance).
V
14
Short Circuit
A resistance value of zero is called a short
circuit, and the circuit below shows why.
Connect a short circuit (a wire resistance 0)
around the resistor. This gives electrical
current a path from the batterys positive
terminal back to its negative terminal with much
less resistance than the path through the
resistor. Its like a
shortcut around the resistor. Current tends to
take the easiest (least resistance) path, so it
all flows through the short circuit and none
flows through the resistor. If the resistance of
the new path were greater than zero but less than
R, some current would still flow through R but
most would flow through the new path.
IR

ISC
V
-
R
Ground
15
Open Circuit
Conversely, a resistance value of infinity (zero
conductance) is called an open circuit. No
current flows through an open circuit. As shown
below, an open circuit between the battery and
the resistor means no current flows through the
resistor it has no way to get to the resistor.
Because no current flows through the
resistor, the battery current is zero.
IR0

V
-
R
Ground
16
Switch
A switch is a circuit element which can be either
a short circuit or an open circuit. In the
circuit on the left, the switch is open open
circuited. No current flows. On the right, the
switch is closed, connecting R to the battery.
The current on the right is determined by V and
R, according to Ohms law. This is a
single-pole, single-throw (SPST) switch, the
simplest kind. It is either on or off.
IRV/R
IR0


V
V
-
-
R
R
Ground
Ground
17
SPDT Switch
Heres a single-pole, double-throw (SPDT) switch.
It has two positions, which can be used to
select one of two voltage sources to connect to
the resistor, as shown.
IR0


V2
V1
-
-
R
Ground
18
DPST Switch
Heres a double-pole, single throw (DPST) switch.
Its equivalent to two SPST switches, operated
by the same button, lever or knob.
19
DPDT Switch
This is a double-pole, Double throw (DPDT)
switch. Its equivalent to two SPDT switches,
operated by the same button, lever or knob.
20
Diode
A diode is a semiconductor element, represented
by the schematic symbol shown below. It has two
terminals, called the anode and the cathode.
Ideally, when VD is positive (the anode is
positive with respect to the cathode), the
diodes resistance is zero.
ID
Anode

VD
ID
VD
-
Cathode
21
Diode
The diode acts like a short circuit, or an on
SPST switch when the anode is more positive than
the cathode (a condition referred to as forward
biased or biased on) and like an open circuit or
an off SPST switch when the anode is more
negative (reverse, or off, bias).
ID
Anode

VD
ID
VD
-
Cathode
22
Diode
The characteristic of the ideal resistor was a
straight line. The characteristic of the ideal
diode is not. It is a nonlinear circuit element
the resistor is a linear element.
ID
Anode

VD
ID
VD
-
Cathode
23
Diode
An ideal diode conducts (exhibits zero
resistance) for any VD greater than zero. A real
diode requires a small positive voltage to
conduct. Common switching or rectifier diodes
are made of silicon, for which the minimum
forward bias voltage is about 0.7 V. This is
illustrated byt the characteristic below.
ID
This means that whenever a silicon diode conducts
current, it has a positive voltage across its
terminals of 0.7 V. Germanium diodes have a
forward bias voltage of about 0.2 V.
VD
24
Diode
A real diode conducts a small reverse leakage
current when reverse biased. This is shown in
the characteristic below. For a good diode, this
current is very very small.
ID
This means that whenever a silicon diode conducts
current, it has a positive voltage across its
terminals of 0.7 V. Germanium diodes have a
forward bias voltage of about 0.2 V.
VD
25
Diode
Finally, a real diode does not have an abrupt
transition (a sharp corner in the characteristic)
between the forward biased region and the reverse
biased region. The transition is smooth, as
shown below.
ID
VD
26
Light-Emitting Diode (LED)
A light-emitting diode (LED) is an interesting
device. It behaves like other diodes, except
that it emits light of a particular wavelength
(color) when conducting a forward current. LEDs
are made of gallium arsenide (GaAs), with small
amounts of other elements to determine the color.
LED symbol
27
Resistance
If we know A and l, we can get R using the
formula
If we A but not l, we can get the resistance per
unit length using
A
l
Or, if the wire is a standard guage and material,
we can look up the resistance per unit length in
a wire table like the one of p. 1180 of Herrick.
28
Resistance of Wire
Since wire has resistance, it dissipates power by
converting it to heat. The power dissipated in a
length of wire is proportional to the resistance
of the wire, and also proportional to the square
of the current flowing through the wire
Wire of a given diameter has a certain resistance
per unit length, so for a given current and wire
diameter, the wire will dissipate a certain power
per unit length. This causes the wire to heat
up. Excessive heat may be a fire hazard, so each
wire size (gauge) has a current rating. The
current rating is the greatest current the wire
can carry without excessive heating. The current
ratinga are also given in the wire table on page
1080. For example, 12 gauge wire is rated for 20
Amperes, and 14 gauge wire is rated for 15 A.
29
Fuses
A fuse is a device which is used to prevent wires
or other conductors from carrying more current
than they are rated for, which might cause a
fire. A fuse is a short length of a conductor
made of a metal which melts at a relatively low
temperature, such as tin. The length and cross
sectional area of the fuse are chosen so it will
melt (blow) at a specified current. It is then
placed in series with the circuit it is supposed
to protect. If the rated current is exceeded,
the fuse blows and the circuit opens.
Fuse
Circuit
30
Fuses
Note that the current rating of the fuse must not
exceed the current rating of the circuit it is
supposed to protect. If we use a 20 amp fuse in
series with a circuit rated at 15 A, the circuit
will protect the fuse by blowing first. While
this saves us the trouble of replacing a blown
fuse, the circuit is probably more expensive to
replace. Fast-blow and slow-blow fuses are
available. Slow blow fuses are used in
applications where brief overcurrents may be
tolerated fast-blow fuses are used where even
brief current spikes would cause damage. Always
use the appropriate type.
Fuse
Circuit
31
Circuit breakers
Circuit breakers are protective devices that
serve the same purpose as fuses. Instead of
blowing and destroying themselves, circuit
breakers trip to open the circuit. A tripped
circuit breaker is reset, instead of being
replaced.
32
Resistance of Circuit Boards
Suppose the conductor does not have a circular
cross section. Maybe its rectangular. A
circuit board trace is an example of a conductor
with a rectangular cross-section. We still use
the formula
But now the units of r are perhaps
Ohm-centimeters, and l and A are given in
centimeters and cm2.
A
l
33
Resistance
RESISTANCE IS USELESS!
No, it isnt. Resistance is deliberately used in
nearly all circuits, for reasons well discover
soon. Resistors are among the most common
circuit elements. A fixed value resistor is
represented by this schematic symbol
R
34
Resistance
Ohmmeters
To measure resistance, use an Ohmmeter. This
places a low voltage across the resistor, and
measures the current flowing through it. As
weve seen, the current is inversely proportional
to resistance.
R
35
Resistance
Variable Resistors
There are also variable resistors. These are
used for such things as volume controls. The
symbol is
R
This type of variable resistor is called a
rheostat.
36
Resistance
Potentiometer
These are three-terminal elements. are also
variable resistors. These are used for such
things as volume controls. The symbol is
1
R
3
2
37
Resistance
Potentiometers
R is the total resistance which would be measured
by an Ohmmeter connected between terminals 1 and
2. Terminal 3 is connected internally to a
movable contact, which may be placed anywhere
along a strip of resistive material.
1
R
3
2
38
Resistance
Rheostat-Connected Potentiometer
A potentiometer may be used as a rheostat by
short-circuiting terminals 2 and three, as shown.
The resistance between terminal 1 and terminal 2
is now R1-3, the resistance between terminal 1
and the movable contact connected to terminal 3
1
R
3
1
2
R
2
39
Temperature Effects
The resistance of a conductor, resistor, or other
electrical device is affected by the temperature
of the device. Depending on the type of device,
increasing the temperature may either increase
its resistance or cause it to decrease.
In many cases, the variation of resistance as a
function of temperature may be approximated by a
straight line. The slope of the line is
R
The resistance R at a temperature T is given by
T
0
40
Temperature Coefficient
The temperature coefficient of a conductor,
resistor, or other device is the sensitivity of
its resistance to variations in temperature
R
A positive temperature coefficient means the plot
of R vs. temperature has positive slope
increasing temperature increases resistance.
Conductors have a positive temperature
coefficient, semiconductors and insulators have a
negative temperature coefficient.
T
0
41
Temperature Coefficient
Conductors have a lot of free electrons at room
temperature, and raising the temperatature does
not significantly increase the number, so raising
the temperature of a conductor does not increase
its conductivity. The existing free electrons
behave like molecules of a
gas when the temperature is raised They
continue to move around in a random fashion, but
their average speed is increased. This increases
the number of collisions, which actually
decreases the conductivity of the material.
Therefore, a conductors resistance has a
positive temperature coefficient.
R
T
0
42
Temperature Coefficient
The temperature coefficient of a conductors
resistance is constant over a very wide
temperature range, so over most of that range the
conductors resistance is a linear function of
temperature. However, as the temperature
approaches absolute zero (0 degrees K, or -273
degrees C) the resistance approaches 0 Ohms
superconductivity.
R
T
0
43
Temperature Coefficient
Semiconductor materials have a significant
number, but not an overabundance, of free
electrons at room temperature. Increasing the
temperature excites valence electrons to higher
energy states, and frees some of them
significantly increasing the number of charge
carriers. This reduces the resistivity of the
material. Therefore, semiconductors have a
negative temperature coefficient.
R
T
0
44
Temperature Coefficient
Resistors are typically made of carbon, or of
metal film. A carbon resistor typically has its
lowest resistance at room temperature, and the
resistance increases above or below room
temperature. The temperature coefficient is not
constant, so resistance is a nonlinear
function of temperature. Resistor usually
operate at greater than room temperature (because
of heating caused by power dissipation), where
they have a positive temperature
coefficient. The temperature coefficient of a
resistor is typically given in part per million
per degree C (PPM / deg C.) If 1000-Ohm
(nominal) resistor increases to 1002 Ohms for a
10 deg. C increas in temperature, its temperature
coefficitne is
R
T
Room Temp
0
45
Temperature Coefficient
The temperature coefficient of a resistor is
typically given in part per million per degree C
(PPM / deg C.) If 1000-Ohm (nominal) resistor
increases to 1002 Ohms for a 10 deg. C increas in
temperature, its temperature coefficitne is
R
T
Room Temp
0
46
Temperature Coefficient
Raising the temperature of an insulator increases
the very small number of free electrons in the
material. This slightly reduces the resistance,
so insulators have a negative temperature
coefficient.
R
T
Room Temp
0
47
Resistive Sensors
There are a number of types of sensors which are
based on the resistance of a material being
changed by variation in some physical quantity.
One good example is temperature sensors. Weve
seen that materials have temperature coefficients
of resistance the resistance of a material is
affected by its temperature. A temperature
sensor can be based on this behavior. A piece of
some material whose resistance is a well known
function of temperature
R
whose resistance is a well known function of
temperature is electrically connected to a
resistance measuring circuit, and is placed in an
environment where temperature is to be measured.
An estimate, or measurement, of the temperature
can be computed based on the resistance of the
sensor.
T
Room Temp
0
48
Resistive Sensors
Thermistors and Resistive Temperature Detectors
(RTDs) are two examples of resistive temperature
sensor. Photoconductive cells, devices whose
resistance decreases when exposed to light, are
another example.
R
A strain gauge is a mechanical sensor which is
based on resistance.
T
Room Temp
0