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Applied Circuit Analysis
Chapter 2 - Resistance
Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Resistivity
• Materials tend to resist the flow of
electricity through them.
• This property is called “resistance.”
• The resistance of an object is a
function of its length, l, and cross
sectional area, A, and the material’s
resistivity:
R
l
A
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Resistivity of Common
Materials
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Ohm’s Law
• In a resistor, the voltage across a resistor is
directly proportional to the current flowing
through it.
V  IR
• The resistance of an element is measured in
units of Ohms, Ω, (V/A).
• The higher the resistance, the less current
will flow through for a given voltage.
• Ohm’s law requires conforming to the
passive sign convention.
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Circular Wires
• Most wires we use for connecting
circuit elements together are circular in
cross section.
• The diameter of the wire determines the
maximum current that it can handle,
with a larger diameter being able to
handle more current.
• The American Wire Gauge (AWG) is
frequently used.
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American Wire Gauge
• Diameters are measured in thousands
of an inch, or mils.
• The unit of cross-sectional area used is
circular mils:
1 CM 

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sq mil
• If the diameter of the wire is in mils,
then the area in circular mils is:
2
ACM  d mil
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AWG
• The following table applies to bare
copper wire only:
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AWG II
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Types of Resistors
• There exist different types of resistors,
created for different applications.
• The primary function of resistors is to
limit current, divide voltage, and
dissipate power.
• Resistors are either fixed or variable.
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Fixed Value Resistors
• The two most common types of fixed
resistors are wirewound and composition.
• Wirewound resistors are used when it is
necessary to dissipate a lot of heat.
• Wirewound resistors use the diameter and
length of the wire to determine resistance.
• Composition resistors use a mixture of
conducting and non-conducting materials to
vary the resistance.
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Variable Resistors
• There are two main types of
variable resistors:
potentiometers and rheostats.
• The potentiometer, or pot for
short is a three terminal
device with a sliding contact.
• By sliding the contact along
the resistive element, the
resistance between the fixed
terminals and the wiper
varies.
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Rheostats
• A rheostat is a two or three
terminal device used to control
the amount of current within a
circuit.
• As the rheostat is adjusted for
more resistance, less current
flows.
• The same variable resistor can
be used either as a pot or a
rheostat.
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Linearity
• Not all materials obey Ohm’s
Law.
• Resistors that do are called
linear resistors because their
current voltage relationship is
always linearly proportional.
• Diodes and light bulbs are
examples of non-linear
elements.
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Resistor Color Codes
• Only very large resistors are big enough to
have their resistance printed on them.
• The commonly used resistors however are
too small to print on.
• Instead they use a series of colored bands to
indicate the values.
• The first three bands (A,B,C) indicate the
resistance value.
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Color Codes
• Within these first
three, A is the first
significant figure and
B is the second
significant figure.
• C is the power of 10
multiplied against AB.
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Color Codes II
• The fourth band (D) indicates the
tolerance of the resistance; how far
from the stated value it may be.
• If it is not present, then a tolerance of
20% is assumed.
• If a fifth band is present (E), it indicates
reliability; how many components may
change their value after working for
1,000 hours.
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Color Codes III
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Standard Resistor Values
• Contrary to what one might expect,
resistors do not come in all possible
values.
• Rather, a series of agreed upon
standard values are available at
reasonable cost.
• Often these values can be used in a
circuit design with minor changes to
parameters, or combinations may be
made.
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Standard Values
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Measurement
• The three basic parameters that one may
wish to measure in a circuit are voltage ,V,
current, I, and resistance, R.
• The corresponding meters that can
measures these parameters are the
voltmeter, ammeter, and ohmmeter
respectively.
• It is common these days to have a single
meter that serves all three functions, called a
multimeter.
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Digital vs. Analog
• Multimeters come in two types: digital and
analog.
• The digital meter converts the measured
value to a digitized number and shows the
value on a display.
• The analog meter uses display the consists
of a needle that moves across a calibrated
meter.
• The needle points to the measured value.
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Digital vs. Analog II
• Below are examples of both types of
meter
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Voltmeter
• To measure voltage, the
voltmeter/multimeter is connected
across the element to be measured.
• This configuration is referred to as a
parallel connection.
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Ammeter
• To measure current, the ammeter/multimeter
is connected in series with the element.
• This means that the circuit must be “broken”
in order to insert the meter.
• For a positive reading, current must enter the
terminal marked as positive (+).
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Ohmmeter
• To measure resistance, the
ohmmeter/multimeter must be connected
across the element of interest.
• If this element is still connected within a
circuit, the measured resistance may
include other elements in the circuit.
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Ohmmeter II
• The ohmmeter may also be used to
check for open and short circuits.
• If there is a break in the circuit then the
resistance will appear as being very
large, off the scale of the meter.
• If there is a short, then the meter will
read nearly zero ohms.
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Best Practices
• When working the any meter, it is best
to follow these rules:
1.If possible, turn the circuit off before
connecting the meter.
2.To avoid damaging the meter, set the
range to the highest value first and turn
it down as needed.
3.When measuring DC current or voltage
observe proper polarity.
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Best Practices II
• When using a multimeter, make sure
you set the meter in the correct mode
(ac, dc, V, A, Ω), including moving the
test leads to the appropriate jacks.
• When the measurement is completed,
turn off the meter to avoid draining the
meter’s internal battery.
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Safety
• When working on circuits, the possibility of
electric shock is always present.
• The shock comes from current passing
through your body.
• Depending on the amount of current, the
effects can range from a tingling feeling to
death.
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