Download Ohm`s Law and Resistance

Here are the digits represented by the
colored bands found on a resistor:
OHM’S LAW AND
RESISTANCE
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Resistance is one of the basic principles of
Ohm’s law, and can be found in virtually
any device used to conduct electricity.
Georg Simon Ohm was a German
physicist who conducted some very early
experiments in electricity. His discovery of
the relationship between current, voltage,
and resistance is the basic law of current
flow, and the formula that connects these
three measurements is named in his honor.
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Ohm’s law states this mathematical
formula:
Resistors are one of the basic building
blocks of electrical circuits. Resistance
occurs in all materials, but resistors are
discrete components manufactured to
create an exact amount of intended
resistance in a circuit. Resistors are made
of a mixture of clay and carbon, so they
are part conductor part insulator. Because
of this, they conduct electricity, but only
with a set amount of resistance added.
The value of the resistance is carefully
controlled. Most resistors have four color
bands. The first band reveals the first digit
of the value. The second band reveals the
second digit of the value. The third band
is used to multiply the value digits. The
fourth band tells the tolerance of the
accuracy of the total value. If no fourth
band is present, it is assumed that the
tolerance is plus or minus 20%.
Voltage is equal to resistance multiplied by
the current flow, or E=IR.
As with any algebraic formula, it is
possible to rearrange the terms in order to
solve the equation for a specific unit of
measurement. Two algebraic equivalents
of the formula would be:
I=E/R
R=E/I
A very handy magic triangle is available
that makes it easy to remember the
different permutations of this formula.
Cover the value to be determined with
your finger, and the relationship of the
other two are already in the proper form.
(Example: you need to know the amount
of current flowing in a circuit with 100Ω
of resistance and 100 volts of pressure.
Cover I, the symbol for current, and the
remaining two symbols, E and R, appear
in their correct relationship E/R.)
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It also possible to “mix and match”
prefixes to make the final answer come out
as units.
Ohms law and other formulae like it will
yield an accurate result if and only if all of
the units of measurement (such as Volts,
Amps, and Ohms) use the same multiplier
prefix within the same algebra problem.
Otherwise, your answer will be off by
some order of magnitude, or power of ten.
Most often, it is easiest just to convert any
readings you have into units, where no
prefix is required. But this could leave you
with a large number of 0s to keep track of.
On occasion, it may be more expedient to
maintain a prefix such as Mega, if all of
the measurements are given using that
prefix. If the latter method is used, the
answer to the problem will automatically
come out in the same prefix used for the
component parts.
For example:
E (in units) = I (in milliA) x R (in kiloΩ)
In this problem the prefixes on the right
hand side of the equation cancel each
other out since “milli” means 1/1000 and
Mega means 1000. 1/1000 x 1000 = 1.
These problems can also be worked with
-3
exponents using the form milli = 10 and
3
-3
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Mega = 10 . Again, 10 x 10 = 1, so the
end result would be an answer given in
units.
Commonly used prefixes:
For example:
#1
E (in volts) = I (in amps) x R (in ohms)
Mega
Kilo Units milli
X,000,000
X,000
M
K
E = 2A x 100Ω
m
μ
E = 200v
___________________________
#2
X
.00X
micro
.000,00X
millions
thousands
units
one thousandth
one millionth
200,000Ω is equal to 200kΩ or 0.2MΩ.
E (in Megavolts) = I (in MegaAmps)
x R (in MegaΩ)
0.002Ω is equal to 2m Ω.
E = 2MA x 100MΩ
3,300Ω can be written as either 3.3kΩ or
3k3Ω.
E = 200Mv
___________________________
You should try to write any amount using
the form and prefix that requires the
fewest 0s written on the page.
In the first problem, units were used
throughout, so the answer is simply given
in volts. In the second problem the Mega
prefix (M) is used for both amps and
ohms, so the answer will also be given
using the Mega prefix. Of course, these
are very unusual values that are unlikely to
occur in any sort of practical work.
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Current and resistance are inversely
proportional, as one goes up the other
goes down. A high resistance value will
lead to a low current flow. A low
resistance value will lead to a high current
flow. This presupposes that the voltage
remains constant. A higher voltage will
pass more current at a static resistance
value.
RESISTANCE IN SERIES:
A series of something generally means
connected along a line, or in a row, or in
an order of some sort. In electronics, series
resistance means that the resistors are
connected one after the other, and that
there is only one path for current to flow
through.
The behavior of series circuits are
governed by three specific laws that can be
used to determine the relationship
between volts, amps, and ohms within
that circuit.
Here is an example of resistance in series:
LAWS OF SERIES CIRCUITS
1)
Individual resistances add up to the
total circuit resistance.
2)
Current through the circuit is the same
at every point.
R1=100 Ω R2=200Ω R3=300Ω E=24v
3)
Individual voltages throughout the
circuit add up to the total voltage.
Note that the resistors are labeled R1, R2,
and R3. The numbers 1, 2, and 3 are
given as subscripts. Subscripts are very
common in electronics work. In this case,
the resistors are given identifiers on the
schematic, and the values are listed
separately.
Law # 1 was addressed on the previous
page as R1 + R2 + R3 = RT. Law # 2
should be somewhat intuitive, because it
seems self evident that the same number
of electrons should return to the power
source as the number that left it.
According to Rutherford’s atomic theory,
electrons are not being created or
destroyed, they are just being pushed
along through the circuit.
Resistances in series are seen by the circuit
as only one resistance, so it is necessary to
add the values together to get a total
resistance. In this example:
R1 + R2 + R3 = RT
Law # 3 requires a bit more explanation.
As it turns out, the voltage pressure is
shared
throughout
the
circuit,
proportional to the amount of resistance
at specific points in that circuit. In
keeping with that rule, voltage readings
taken at various points in a series circuit
will vary in accordance with the resistances
present at the particular point in the
circuit where the reading is taken.
100Ω + 200Ω + 300Ω = 600Ω
Use the RT value to find the current draw
on this circuit using ohm’s law:
I = E/R
or
or
I = 24v/600Ω
I = 0.04A
40mA
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The answer could be converted to
milliamps, but this would just confuse the
rest of the problem. It is best to wait until
the end.
STEP THREE:
Remember that the current (I) remains
constant throughout the entire circuit.
Ohm’s law in the configuration E = IR
can be used to determine the voltage drop
across any two nodes in the circuit.
R1 = 100Ω
R2 = 200Ω
R3 = 300Ω
E = 24v
Between A and B
The junction between each of the
components of this circuit is considered a
node. If this circuit were built, it would be
possible using a volt meter to take six
different voltage readings for this circuit
by measuring between these points:
E = IR or E = .04A x 100Ω or E = 4v
Between B and C
E = .04A x 200Ω or E = 8v
Between C and D
A/B B/C C/D A/D A/C B/D
E = .04A x 300Ω or E = 12v
It is also possible to determine the values
mathematically, using what we know
about Ohm’s law, and using the following
procedure.
The voltage between any other points can
be determined by adding together the
appropriate legs of the circuit.
STEP FOUR:
STEP ONE:
Add all of the voltages together to check
your work.
The individual voltages
should add up to the total voltage from
the power source, which is the third law of
series circuits.
Use the first law of series circuits to
determine RT for the circuit by adding
together the individual resistances. In the
earlier section, this was determined to be;
100Ω+200Ω+300Ω=600Ω
4v + 8v + 12v = 24volts, the answers we
had were correct.
STEP TWO:
Use Ohm’s law to determine the current
flow through the circuit. I = E/RT
The current flow is the same at every
point in a series circuit. This is the second
law of series circuits. Again, we have
already worked the current out to be:
I = E/R or I = 24v/600Ω or I = .04A
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Here is an example in which a meter is
used to reference the same concept:
As a second example, if you were to use a
very long power cord for tool with an
electric motor, it might not operate
properly. Quite often the motor might
stall or have trouble starting. This
problem comes about because the
resistance of the electric motor is in series
with the resistance present in the power
cord itself, and a voltage divider is created.
The voltage pressure is shared between the
cable and the tool. Any type of cable has a
certain resistance to the flow of electrons,
but a larger diameter conductor has less
resistance per foot. Also, a shorter cable
has less resistance than a longer one of the
same diameter because there are fewer feet
of it creating resistance. This problem
with the motor can be avoided by using a
larger gauge cable that is as short as
possible.
SOME PRACTICAL EXAMPLES
ACLs (aircraft landing lights) are
sometimes used for special effects lighting
on stage because they put out a tightly
focused beam of light. These lamps were
literally designed to be used on airplanes,
which traditionally use a voltage rated at
28.5v. If they were simply plugged into a
standard wall voltage of 120v, the
filaments would burn out immediately
because the voltage pressure would be far
too much for them to carry. A special
power supply could be used, but there is
an easier way around this problem.
Ohm’s law can be used to determine a
way to divide up the voltage in a series
circuit created by four of the lamps in
series. This will allow the lamps to be used
with a standard 120 volt source, however
it should be noted that if one of the lamps
burns out, all of them will go dark because
the completed circuit has been opened.
Electrons cannot move through an open
circuit.
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In this example, each resistor has its own
discrete path to the voltage source, and if
one of the pathways is opened, the other
will still operate. In a parallel circuit, the
voltage in each part of the circuit remains
constant, but the current varies in
accordance with where a reading is taken.
This is the opposite of the way a series
circuit operates.
In electronics work, voltage dividers are
often used to lower the voltage applied to
a specific part of a particular circuit. This
is especially true for circuits using
transistors that we will look at later.
Another case might involve an indicator
light that shows that the power is switched
on to a particular device. Adding a resistor
in series with the lamp will “share” the
voltage between the resistor and the lamp
so that the light runs on a smaller voltage.
Higher voltages make it much more likely
that a person can receive electrical shock,
so it is common to use a lower voltage for
control devices.
There are many different ways to organize
a parallel circuit. In the practical world,
most wiring is done in parallel so that the
voltage to any one part of the network is
the same as the voltage supplied to any
other part of it. Having a constant voltage
is very important because electrical devices
are designed to operate from a specific
pressure. It would be impractical to
change that voltage at will throughout the
electrical service.
RESISTANCES IN PARALLEL:
There is another way to place more than
one resistance into a circuit rather than in
series. Here is a standard type of parallel
circuit.
Although the wiring running between the
lights is arranged differently, these lamps
have the same electrical connection as the
lamps depicted in the previous schematic
drawing. No matter how convoluted the
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wiring in a lighting system may be, all of
the circuits involved are still in parallel,
and all of the outlets have the same 120v
service.
draws on a system to see if that total
amount exceeds the limitation set by the
circuit breaker.
HOW TO DETERMINE CURRENT FLOW
IN A PARALLEL CIRCUIT:
LAWS OF PARALLEL CIRCUITS
1)
Use Ohm’s law to determine the
current flow in each branch.
1)
The reciprocals of all the individual
resistances add up to the reciprocal of the total
circuit resistance. 1/RT = 1/R1 + 1/R2 + 1/R3 …
2)
Add the currents together to find
IT for the entire circuit.
2)
Voltage through the circuit is the same
at every point.
In this procedure, we will assume that
both the resistance and the voltage are
givens for any particular problem, since it
is I, the current, that is being determined.
Here is a drawing of a parallel circuit:
3)
Individual current draws throughout
the circuit add up to the total current draw. IT
= I 1 + I 2 + I 3…
Remember that the voltage in every part
of a parallel circuit is the same. As a result,
Ohm’s Law is most often used in a parallel
circuit to determine what the total current
draw for the entire network will be.
Theatre lighting systems (like all others)
are protected by either fuses or circuit
breakers which will disconnect the flow of
electricity if too much demand is placed
on that system. The purpose is to protect
the component parts from damage from
overloading. If too many electrons pass
through the wiring inside the wall, or
through a jumper, the wire will overheat
just like the filament inside a light bulb.
However, the filament is housed inside a
vacuum, and the entire lamp is
constructed to withstand such overheating.
Wiring is not intended to withstand that
sort of extreme use, and will likely cause a
fire if too great a load is place on it.
Circuit breakers have a current limit
stamped on the switch so that users know
in advance how much current can be
drawn through them. This maximum
allowable value is determined by engineers
to limit the current to an amount safe for
all the components in the system. It is
often necessary to add up all of the current
Use the magic triangle to find the correct
formula for finding the current value of
the entire circuit. The formula is I = E/R,
the voltage divided by the resistance. The
voltage is 120v. But what should the total
resistance be? In series circuits RT was
discovered by adding together all of the
individual resistances because the current
must flow through each one of them to
complete the circuit. But in examining the
drawing it is apparent that the current will
be split between two branches of the
circuit. Splitting the current has the effect
of lessening the resistance against it
because the pathway has in effect become
“wider”.
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Notice that adding lamps to the system
causes the current draw to go up. It seems
intuitive that the more lights in a circuit
the more power will be consumed. Also,
the lower the resistance of each lamp, the
more power will be consumed.
Referring back to the first law of parallel
circuits we see that it states:
The reciprocals of all the individual
resistances add up to the reciprocal of the
total circuit resistance. 1/RT = 1/R1 + 1/R2
+ 1/R3 …
Most of the time, we do not know the
resistance of a particular stage lamp,
although it could easily be determined
with a VOM. Instead, the power rating is
given. Power ratings are stated in Watts.
So in determining RT for the parallel
circuit shown, it is apparent that:
1/RT = 1/6 + 1/8
or
1/ RT = .167 + .125 or
1/ RT = .292
R T = 3.42Ω
P is the symbol used for mathematical
computations using power.
Continuing on, the formula I = E/R is
used to determine the total current used in
the circuit:
W is the symbol used to express an
amount of power. Example: P=100W.
I = 120v/3.42Ω
I = 35A
HOW TO DETERMINE POWER USAGE
IN WATTS:
There is an alternative method to using
the reciprocals, that determines the value
of I one branch at a time. If instead of
two lamps in this circuit, there were only
the first one with its 6Ω resistance, the
current would be determined as follows:
Another of Ohm’s formula’s is used to
determine wattage, and is often used in
conjunction with the formula E = IR that
we have been using so far. This formula is
called the Pie Formula for obvious reasons.
P = IE
I = 120v/6Ω
I = 20A
The same sort of magic triangle that was
used previously will work for this formula
as well:
Solving for the 8Ω resistance we see:
I = 120v/8Ω
I = 15A
The 20A and the 15A can be added
together for a sum of 35A, the same
answer as with the first method.
Determining the individual currents in a
system, and adding them together to get a
figure for the entire system is another way
to solve for IT.
The following derivations are possible:
P = IE
I = P/E
E = P/I
I T = I 1 + I 2 + I 3…
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Suppose that the following schematic is
given, and that the problem is to find the
total current draw:
TERMS USED IN THIS CHAPTER
Aircraft Landing Lights
Color Band
Laws of Parallel Circuits
Laws of Series Circuits
Magic Triangle
Ohm’s Law
Open Circuit
Order of Magnitude
We are seeking the value of I, and
covering that symbol on the magic
triangle gives the formula:
Parallel
I = P/E
Resistance
First the total power consumed by the
circuit must be determined.
Resistor
P T = P 1 + P 2 + P 3…
Subscript
Pie Formula
Power
Series
PT = 500W + 1000W
PT = 1500W
Solving:
I = P/E
I = 1500W/120v
I = 12.5A
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