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					                                      4.        RESISTANCE

Resistance refers to the property of a substance that impedes the flow of electric
current. Some substances resist current flow more than others. If a substance
offers very high resistance to current flow it is called an insulator. If its resistance
to current flow is very low, it is called a conductor. Resistivity refers to the ability
of substances to resist current flow. Good conductors have low resistivity and
insulators have high resistivity.

Resistance at the Molecular Level
Resistance to current flow occurs at the molecular level of substances. For
example, a metal conductor, such as copper, consists of atoms having free
electrons in their outer most shells. These free electrons ordinarily move
randomly from one atom to another. However, if a potential difference, also
called voltage, is applied across the conductor, such as with a battery, free
electrons flow from the negative to the positive terminals of the battery. Electric
current refers to the rate of flow of electric charge, which causes free electrons to
As electrons move through the conductor, some collide with atoms, other
electrons, or impurities in the metal. It is these collisions that cause resistance.
The molecular makeup of a substance determines the number of collisions, or
amount of resistance, to electron flow. Since the molecular makeup of copper
provides for extremely low resistivity, it is often used as a conductor in electric
As electrons collide with atoms and other particles, the energy provided by the
applied voltage is converted into heat. We make use of the energy generated by
resistance in the heating elements of toasters, incandescent lamps, and space

Most of the resistance in circuits is found in components that do specific work,
such as bulbs or heating elements, and in devises called resistors. Resistors are
devises that provide precise amounts of opposition or resistance to current flow.
Resistors are very common in electric circuits. They are used to provide specific
resistivity to limit current and to control voltage in a circuit.

Types of Resistors
Resistors come in a variety of values and types. The most common type is the
fixed resistor. Fixed resistors have single values of resistance, which remain
constant. There are also variable resistors that can be adjusted to vary or change
the amount of resistance in a circuit.
The value of resistance of resistors is given in ohms. Resistors can have values
from less than one ohm up to many millions of ohms.

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Fixed Resistors
The most common fixed resistor is the composition type. The resistance element
is made of graphite, or some other form of carbon, and alloy materials. These
resistors generally have resistance values that range from 0.1 Ω to 22 MΩ.
Another kind of fixed resistor is the wire wound type. The resistance element is
usually made of nickel-chromium wire wound on a ceramic rod. These resistors
generally have resistance values that range from 1 Ω to 100 kΩ.
Variable Resistors
Variable resistors are used to adjust the amount of resistance in a circuit. A
variable resistor consists of a sliding contact arm that makes contact with a
stationary resistance element. As the sliding arm moves across the element, its
point of contact on the element changes, effectively changing the length of the
element. The rating of a variable resistor is its resistance at its highest setting.
Variable resistors are also called rheostats or potentiometers. The resistance
elements of rheostats are usually wire wound. They are most often used to
control very high currents, such as in motors and lamps. Potentiometers
generally have composition elements. They are used as control devices in
radios, amplifiers, televisions, and electrical instruments.

Rating Tolerances
The actual resistance of a resistor may be greater or less than its indicated
rating. The possible range of variance from the indicated rating is called its
tolerance. Common tolerances for composition resistors are ±5, ±10, and ± 20
percent. Wire wound resistors usually have a tolerance of ±5 percent.
Resistor Rating Color Code
Composition resistors are color coded to indicate resistance values or ratings.
The color code consists of various color bands that indicate the resistance values
of resistors in ohms as well as the tolerance rating. The Resistor Rating Color
Code Table below is used to identify the resistance rating of resistors.
                  Color        1st Band        2nd Band             3rd Band      4th Band
                  Black            0               0                      1           1
                  Brown            1               1                     10
                   Red             2               2                    100
                  Orange           3               3                   1,000
                  Yellow           4               4                   10,000
                  Green            5               5                  100,000
                   Blue            6               6                 1,000,000
                  Violet           7               7                10,000,000
                   Gray            8               8               100,000,000
                  White            9               9              1,000,000,000
                   Gold                                                  0.1        5%
                  Silver                                                0.01       10%
                   None                                                            20%

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Composition resistors generally have four color bands. The color code is read as
First, look up the number values of the first two bands on the table and combine
the two numbers.
Then multiply this two digit number by the value of the 3rd band, the multiplier
The resulting number is the resistance value of the resistor in ohms.
The fourth band is the tolerance band. If the 4th band is gold, the resistor is
guaranteed to be within 5% of the rated value. If the 4th band is silver, it is
guaranteed to be within 10%. If there is no 4th band, the resistor is guaranteed to
be within 20% of the rated value.

    For example, the color code of the above resistor in Figure 2 is read as follows:
        The 1st band is brown. The first band is always the band closest to the end of the resistor. From
         the table you can see that the number value of brown in the 1st band column is 1.
        The 2nd band is black. The number value of black in the 2nd band column is 0.
        Combining the two numbers gives you 10.
        The 3rd band is red. This is the multiplier band. The multiplier value of red is 100.
        Multiplying the combined digit of 10 by the multiplier gives us 1,000.

    Therefore, the above resister is rated at 1,000 ohms, which can be written as 1 kΩ. The 4th, or
    tolerance, band of the resister is silver. Therefore, the resistor is guaranteed to have a resistance value
    within 10% of 1kΩ.

Resistors in Series Circuits
A series circuit is a circuit in which the current has only one path. In a series
circuit, all of the current passes through each of the components in the circuit.
The circuit below in Figure 3 has three resistors is series. The current from the
battery flows through each of the resistors.

Since the current passes through each resistor in the circuit, the total resistance
encountered by the current is cumulative. The same amount of resistance would
exist in a circuit with a single resistor equal to the sum of the three resistors.

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Such a resistance is called the equivalent or total resistance of the circuit. The
equivalent resistance of a series circuit is the sum of all the resistances in the
circuit. Therefore, to calculate the total resistance of a series circuit, use the
following formula:

                                              RT = R 1 + R 2 + R 3 . . .

where RT is the total or equivalent resistance in the circuit, and R1 through R3 . . .
are the resistance ratings of the individual resistors or components in the circuit.
Using this formula, the total or equivalent resistance of the series circuit in Figure
3 can be calculated as follows:

                                            RT = 2.5 + 1 + 3 = 6.5 kΩ

Resistors in Parallel Circuits
A parallel circuit is a circuit in which components are arranged so that the path
for the current is divided. The circuit below in Figure 4 has three resistors in

Placing the resistors in parallel always decreases the total or equivalent
resistance of the circuit. This is true because connecting resistors in parallel is
equivalent to placing them side by side, increasing the total area available for the
flow of current and thereby, reducing resistance. To calculate the total resistance
of a parallel circuit, use the following formula:

                                        RT = 1 ÷ (1/R1 + 1/R2 + 1/R3 . . .)

where RT is the total resistance in the circuit, and R1 through R3 . . . are the
resistance ratings of the individual resistors or components in the circuit.
Using this formula, the total or equivalent resistance of the above parallel circuit
can be calculated as follows:

                                        RT = 1 ÷ (1/1 + 1/2.5 + 1/3)
                                         RT = 1 ÷ (1 + 0.4 + 0.33)
                                              RT = 1 ÷ 1.73
                                              RT = 0.58 kΩ

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Resistors in Compound Circuits
Circuits often consist of combinations of series and parallel circuits. These
circuits are called compound circuits. The circuit in Figure 5 below is a compound

To calculate the total resistance of a compound circuit, first isolate and simplify
all branches of the circuit to their equivalent resistances.

The following steps are helpful:
        Calculate the equivalent resistances of resistors in parallel.
        Calculate the equivalent resistances of resistors in series.
        By repeating steps 1 and 2, as needed, the circuit can be simplified to an equivalent
         series circuit.
        Simply add the equivalent resistances of the simplified equivalent series circuit to find the
         total resistance of the compound circuit.
        Using these steps, the total or equivalent resistance of the above parallel circuit can be
         calculated as follows:

First calculate the equivalent resistance of the two resistors in parallel:

                                               RT = 1 ÷ (1/2 + 1/4)
                                              RT = 1 ÷ (0.50 + 0.25)
                                                  RT = 1 ÷ 0.75
                                                  RT = 1.33 kΩ

At this point the circuit has been simplified to an equivalent series circuit

Therefore, the total resistance of the compound circuit can be calculated as
                                                   RT = 1.33 + 3
                                                   RT = 4.33 kΩ

Electric Power and Resistors
Even though electrons are very small, it takes energy to move them through a
conductor. The energy available to move electrons is referred to as difference in
potential, or voltage. Voltage is most often provided by a battery or generator.
Voltage represents the work involved in the transfer of electric charge from one

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point to another. The higher the voltage, the more energy the current carries and
the more work it can do.
In electric applications, voltage is often converted to other forms of energy to do
work, such as heating, lighting, or motion. As noted earlier, we often make use of
resistance to convert electric energy to heat or light.
The rate at which electricity does work or provides energy is referred to as
electric power. The unit of electric power is the watt. One watt of power is
delivered when a current of one ampere flows through a circuit whose voltage is
one volt. Electric power can be calculated using the following formula:

where P is power in watts, I is current in amperes, and E is energy (applied
voltage) in volts.
The wattage ratings of resistors indicate operating limits. The product of applied
voltage and current through a resistor must not exceed its wattage rating. When
current passes through a resistor, electric energy is converted to heat, which
raises the temperature of the resistor. If the temperature becomes too high, the
resistor may be damaged. The above electric power formula can be used to
determine the maximum safe power consumption and appropriate wattage rating
of a resistor to use for an application.

Power Ratings of Resistors
The power rating of resistors is specified in watts. Composition type resistors
have wattage ratings from 1/16 to 2 watts. Wire wound resistors have ratings
from 3 watts to hundreds of watts. The size of the resistor is usually a good
indicator of its power rating. Generally, the physical size of a resistor increases
as the power rating increases.

Effect of Temperature on Resistivity
The resistivity of most materials changes with temperature. For most materials,
resistance increases as the temperature of the material increases. This occurs at
the molecular level. As electrons move through the material, some collide with
atoms, other electrons, or impurities. It is these collisions that cause resistance.
Heat causes molecules of the material to vibrate. These vibrations effectively
increase the areas of possible collisions, thereby increasing resistance to current
Most conductors increase in resistivity as temperature increases. Carbon
however, decreases in resistivity as temperature increases. This is also generally
true for semiconductors, such as germanium and silicon. The resistivity of
constantan is not affected by changes in temperature. For this reason,
constantan is often used for precision wire-wound resistors with very low

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Resistance and Superconductivity
For most conductors, resistivity decreases as temperature decreases. For some
materials, like mercury and aluminum, resistivity falls to zero at extremely low
temperatures. Near absolute zero, -273°C, these materials are capable of
carrying current without any resistance at all. These materials are called
superconductors. The benefit of superconductors is that they can carry large
quantities of current without any loss of energy to heat.

Superconducting materials are currently used in particle accelerators and other
applications that require powerful electromagnets. Magnetic resonance imaging
technology (MRI), powered with the use of superconductors, has revolutionized
materials science and medicine. Superconductivity would be especially useful for
the transmission of electric power. Currently, about 15 percent of electric power
passing through copper transmission lines is lost as a result of resistance.
Unfortunately, it is very costly to cool superconductors to the critical temperatures
required. Refrigeration units using liquid helium or liquid nitrogen are currently
necessary to cool superconducting materials. However, progress is being made
to increase temperatures required for superconductivity. Materials have already
been developed that become superconducting at -175°C.

Scientists are working diligently to develop room-temperature superconductors.
Such superconductors would greatly reduce the cost of electric power production
and transmission. Electric motors could be made that are much smaller and
powerful. Computers could be made even smaller and faster. Other amazing
applications, such as magnet-levitated trains and launching of spacecraft, would
become much more feasible.


If we neglect for the time being the effect of temperature (which will be
considered at this stage), we find that:

                                                    R = P l/a

                             Where: R = resistance
                             p = ("rho"). Resistivity or specific resistance
                              I = length of conductor
                             a = CSA of conductor

This means, in effect that the resistance of a conductor of a given material
increases in proportion to its length and is inversely proportional to its CSA

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This is nothing else but the resistance of a unit conductor made from a particular
material, that is a conductor with a cross-sectional area (CSA) of one square
meter (1m2) and a length of one meter (1m)
Resistivity is thus the resistance between the opposite faces of a cube from a
particular material, having sides of one unit length and this was previously known
as the specific resistance
E.g. Resistivity of annealed copper at 20°C is approx 1.725 x 10-8 Om

Resistivity of common materials

                                                            Resistivity (Ωm)
       Materials                                                                Usage
                                                                at 20°C

                       SILVER                                     1.64 X 10-8       Conductor

                      COPPER                                      1.72 X 10-8            "

                     ALUMINUM                                     2.8 X 10-8             "

                        GOLD                                      2.45 X 10-8            "

                      CARBON                                       4 X 10-5       Semi conductor

                    GERMANIUM                                     47 X 10-2              "

                       SILICON                                    6.4 X 102              "

                       PAPER                                         1010            Insulator

                        MICA                                       5 X 1011              "

                       GLASS                                         1012                "

                       TEFLON                                      3 X 1012              "

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The increase in resistance is almost directly proportional to the increase in

                                              RT = R0 (1 +  t)

                                                 RT = Increased resistance in ohms
                                                 R0 = Resistance at initial temperature in ohms
                                                   = Temperature coefficient (no unit)
                                                 t = Temperature change in degrees Celsius

Note: This equation is still valid with reasonable accuracy when R0 is the
measured resistance at a temperature other than 00C

Temperature Coefficient

                              Substance                     Temp Coeff.
                              Aluminum                      0.0039
                              Brass                         0.0015
                              Copper                        0.0043
                              Iron                          0.0056
                              Silver                        0.0039
                              Tungsten                      0.0058

Q:     If a copper wire has a resistance of 60Ω at 200C, what will its resistance
be at 1200C?

A:       Data:
         R0 = 60Ω
         T = 1200C – 200C = 1000C
          = 0.0043
         RT =?

RT = R0 (1 +  t)
         = 60 (1 + 0.0043 x 100)
         = 60 (1 + 0.43)
         = 60 x 1.43
         = 86Ω

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1.       State the factors affecting the resistances of materials

2.       Explain the concept of resistivity. Use illustrations.

3.       What is the resistance of a strip of copper, the length of which is 2m and
         the CSA of which is 2m2

4.       A battery positive cable (copper), connecting to the starter motor main
         terminal is 60cm long and a diameter of 12mm. Determine its resistance.

5.       Explain the effects of temperature on resistance

6.       If a copper wire had a resistance of 60Ω at 200C, what would its resistance
         be at 800C?

7.       If an Aluminum wire had a resistance of 40Ω at 300C what would its
         resistance be at 600C?

8.       Determine the resistance of the following with temperature at 120 0C
         (a) 20 ohms Aluminum at initial temperature of 350C
         (b) 16 ohms at 150C of a Silver Bar
         (c) Brass Bar at 300C having resistance of 10 ohms

9.       The battery cable above (no.4) is being subjected to heat after 5 seconds,
         thus increasing its temperature to 500C and further increases to 580C at 6
         seconds. What is its resistance after 5 seconds and at 6 seconds if the
         temperature was constant at 200C for the 1st 5 seconds?

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