Download Resistance and Ohm`s Law

EE301 Lesson 2:
Resistance (Chapter 3) and
Ohms Law (Chapter 4)
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Learning Objectives
• Describe the concept of resistance.
• Use Ohm’s law to calculate current, voltage, and
resistance values in a circuit.
• Discuss the difference between an open circuit and a
short circuit.
• Given a color code table, determine the value and
tolerance of fixed resistors using their color codes.
• Demonstrate how to measure current, voltage, and
resistance in a circuit.
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Resistance of Conductors
• Resistance is the opposition to charge movement.
• As electrons move through a material, they constantly
collide with atoms in the material and with other
electrons.
• These collisions cause some of the energy carried by
the charge to be released as heat.
• So resistance is dependent on several factors:
−
−
−
−
type of material
length of the conductor
cross-sectional area
temperature
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Resistance of Conductors
• Type of material:
• Atomic differences of materials
cause variations in how electron
collisions affect resistance.
• Differences produce resistivity.
• Resistance is directly proportional
to the resistivity. The higher the
resistivity, the greater is the
resistance of the conductor.
• Resistivity is represented by the
symbol  (Greek letter rho).
• Units of : Ohms * meters (Ω∙m).
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Resistance of Conductors
• Length of conductor:
• Resistance is directly proportional to the conductors length. The
longer the conductor, the greater the resistance.
• If you double the length of the wire, the resistance will double.
•  = length
• Measured in meters or feet.
• Cross-sectional area:
• Resistance is inversely proportional to cross-sectional area of the
conductor. The greater the area of the conductor, the less resistance.
• If cross-sectional area is doubled, resistance will be one half as much.
• A =Cross-sectional area, in m2.
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Resistance of Conductors
• Temperature:
• For most conductors, a temperature increase causes an increase in
resistance.
• Increase is relatively linear.
• However, not that for semiconductors and insulators, an increase in
temperature results in decrease in resistance.
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Resistance of Conductors
• Resistance of a conductor at a given temperature can be
expressed mathematically:
R

[ohms, ]
A
where
  resistivity, in ohm-meters (  m)
 length, in meters (m)
A(CM)
A  cross-sectional area (m 2 )
1x10-3 inches = 1 mil
ACM = (diametermils)2
&
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Example Problem 1
• You need to measure length of this copper coil but don’t
want to unroll it. Resistance measured is 103.7 Ohms.
Diameter is 0.01 inches. Find the length.
Knowns :
R  103.7 
copper  10.37CM   / ft
R=
ρl
, where A CM = (d mils ) 2
A
d mils =
1in 1000mil
*
=10mil
100
1in
A CM = (10 mil) 2 = 100 CM
103.7 Ω=
(10.37 CM-Ω/ft)l
100 CM

1x10-3 inches = 1 mil = 1/1000 inch
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103.7 Ω * 100 CM
(10.37 CM-Ω/ft)
&
ACM = (diametermils)2
 1000 ft
Fixed Resistors
• Used to provide control of electrical circuits.
• Produced in various shapes and sizes.
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Variable Resistors
• Variable resistors (VAR) have an adjustable value of
resistance and have two principle functions:
1. Potentiometers are used to adjust voltage.
2. Rheostats are used to adjust current.
− VARs are used to adjust volume, set level of lighting,
adjust temperature,…
a
a
Rab
Rab
b
b
Rbc
Rbc
c
c
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Resistor color coding
Resistors usually have 4, 5 or 6 color bands.
4 color bands:
5 color bands:
Band 1: First Digit
Band 1: First Digit
Band 2: Second Digit
Band 2: Second Digit
Band 3: Multiplier (10X)
Band 3: Third Digit
Band 4: Tolerance
Band 4: Multiplier (10X)
Band 5: Tolerance
gray
Sometimes a 5th or 6th band is added (Reliability) to meet MILSPEC
requirements.
NOTE: That for a 4-band
resistor, if the 4th band is not
present, it is assumed that the
resistor has a tolerance of ± 20%
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Resistor color coding
Yellow = 4
Purple = 7
Orange = 3=>103
Red = 2%
Read left
To right
47*103 = 47k Ω ±2%
MULTIPLIER (i.e)
4 = 104
5 = 105
IF THIRD BAND
gray
2nd Digit
1st Digit
3rd Digit
Multiplier
Tolerance
Green = 5
Blue = 6
Black = 0
Red = 2 =>102
Brown = 1%
560*102 = 56kΩ ±1%
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Example Problem 2
Determine the resistance of a carbon resistors having the color
codes shown in the figure below.
Make sure you identify that this is a
4-band resistor
Make sure you identify that this is a
5-band resistor
Brown = 1
10 * 101 = 100 Ω
Black = 0
Brown = 101
Gold = ± 5% tolerance => ± 5 Ω
R = 100 Ω ± 5%
Green = 5
564 x 105 = 56.4 MΩ
Blue = 6
Yellow = 4
Green = 105
Silver = ± 10% tolerance => ± 5.64MΩ
R = 56.4 MΩ ± 10%
gray
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Ohm’s Law
• Every conversion of energy from
one form to another can be related
to this equation.
• In electric circuits, the effect we are
trying to establish is the flow of
charge, or current.
• The potential difference, or voltage,
between two points is the cause
(“pressure”), and the opposition is
the resistance encountered.
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Ohm’s Law
• Georg Ohm discovered experimentally that voltage
and current in a wire were linearly related to each
other by a constant (Resistance)
E  IR [volts, V]
where,
E is voltage in volts
R is resistance in ohms
I is current in amperes
Plotting Ohm’s Law
• Current in a resistive circuit:
− Directly proportional to its applied voltage.
− Inversely proportional to its resistance.
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Ohm’s Law
• Two different symbols are commonly used to represent
voltage.
− E for sources.
− V for loads (such as the voltage drop across a resistor).
• When using Ohm’s Law be careful that you use the
voltage across the load (in the above that would be the
voltage across the resistor (R).
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Ohm’s Law
• In summary, therefore, the absence of an applied “pressure”
such as voltage in an electric circuit will result in no reaction
in the system and no current in the electric circuit.
• Current is a reaction to the applied voltage and not the factor
that gets the system in motion.
• EXAMPLE: The greater the pressure in a hose, the greater is
the rate of water flow through the hose, just as applying a
higher voltage to the same circuit results in a higher current.
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Example Problem 3
Determine the current provided by the source in the system
below.
I
E  IR [volts, V]
Rearrange the equation =>
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E
I
[amperes, A]
R
100V
I
= 2 [amperes, A]
50
Open Circuits
• Current can only exist where there is a conductive
path.
• When the current is zero, the circuit will have an
infinite resistance (remember Ohm’s Law).
• This is called an open circuit.
E E
R   
I 0
E E
I    0A
R 
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Short Circuits
• Short circuits occur when a very low (or near zero) resistance
is placed across a circuit.
• Since resistance is near zero, all current will bypass the rest of
circuit and go through the short (again, recall Ohm’s Law).
• With zero resistance, current draw will approach the limits of
the power source (infinite current), frequently causing damage
to wiring or the power source.
E E
I    A
R 0
E E
R  0
I 
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Measuring Voltage
• Voltage and current is measured using voltmeters and
ammeters, or a Digital Multi-Meter (DMM).
• Measure voltage by placing the voltmeter leads across the
component whose voltage you wish to measure.
• Polarity can be determined by probe placement.
“Auto-polarity”
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Meter Symbol: Voltmeter
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Current Representation
• The current depicted in the following circuits is
identical.
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Measuring Current
• The current that you wish to measure must pass
through the meter.
• Be careful that the meter’s maximum current rating is
not exceeded!
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Meter Symbol: Ammeter
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Voltage Polarity and
Current Direction
• For the voltage across a resistor, always place the plus sign at
the tail of the current reference arrow.
• To ensure the correct voltage sign on the DMM, place the red
lead where you think the “+” sign should be.
• For correct current polarity, the current should enter the red
lead of the DMM.
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Measuring Resistance
• An ohmmeter is a device used to measure the
resistance of a component.
• Resistance cannot be measured when voltage is
supplied to the circuit.
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Measuring Component
Resistance
• You must isolate the component that
you are measuring from the circuit!
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Measuring Total
Resistance
• You must remove the power source
prior to measuring total resistance!
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QUESTIONS?
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