e 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%.








Here are the digits represented by the
colored bands found on a resistor:


Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9


Ohms law states this mathematical
formula:

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 100
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.)

1 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:

#1

E (in volts) = I (in amps) x R (in ohms)

E = 2A x 100

E = 200v
___________________________

#2

E (in Megavolts) = I (in MegaAmps)
x R (in Mega)

E = 2MA x 100M

E = 200Mv
___________________________


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.

It also possible to mix and match
prefixes to make the final answer come out
as units.

For example:

E (in units) = I (in milliA)

x

R (in kilo)

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
exponents using the form milli = 10
-3
and
Mega = 10
3
. Again, 10
-3
x 10
3
= 1, so the
end result would be an answer given in
units.

Commonly used prefixes:

Mega Kilo Units milli micro

X,000,000 X,000 X .00X .000,00X

M millions
K thousands
units
m one
thousandth
one
millionth

200,000 is equal to 200k or 0.2M.

0.002 is equal to 2m .

3,300 can be written as either 3.3k or
3k3.

You should try to write any amount using
the form and prefix that requires the
fewest 0s written on the page.









2 R
ESISTANCE IN
S
ERIES:


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.

Here is an example of resistance in series:




R
1
=100 R
2
=200 R
3
=300 E=24v

Note that the resistors are labeled R
1
, R
2
,
and R
3
. 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.

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:

R
1
+ R
2
+ R
3
= R
T


100 + 200 + 300 = 600

Use the R
T
value to find the current draw
on this circuit using ohms law:

I = E/R
I

=

24v/600
or
I = 0.04A
or

40mA

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.

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.

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.

3)
Individual voltages throughout the
circuit add up to the total voltage.

Law # 1 was addressed on the previous
page as R
1
+ R
2
+ R
3
= R
T
. 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 Rutherfords atomic theory,
electrons are not being created or
destroyed, they are just being pushed
along through the circuit.

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.

3



R
1
= 100

R
2
= 200

R
3
= 300

E = 24v

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:


A/B B/C C/D A/D A/C B/D

It is also possible to determine the values
mathematically, using what we know
about Ohms law, and using the following
procedure.

STEP ONE:

Use the first law of series circuits to
determine R
T
for the circuit by adding
together the individual resistances. In the
earlier section, this was determined to be;

100+200+300=600

STEP TWO:

Use Ohms law to determine the current
flow through the circuit. I = E/R
T

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/600 or I = .04A

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.
Ohms law in the configuration E = IR
can be used to determine the voltage drop
across any two nodes in the circuit.

Between A and B

E = IR or E = .04A x 100 or E = 4v

Between B and C

E = .04A x 200 or E = 8v

Between C and D

E = .04A x 300 or E = 12v

The voltage between any other points can
be determined by adding together the
appropriate legs of the circuit.

STEP FOUR:

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.

4v + 8v + 12v = 24volts, the answers we
had were correct.











4 Here is an example in which a meter is
used to reference the same concept:



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