Series Direct Current Circuit Rules
Rule #1: 
The same current flows through each
part of a series circuit. 


Rule #2: 
Total Resistance of a series circuit
is equal to the sum of the individual resistances. 


Rule #3: 
The total voltage across a series
circuit is equal to the sum of the individual voltage drops. 


Rule #4: 
The voltage drop across a resistor
in a series circuit is proportional to the size of the resistor. 


Rule #5: 
The total power dissipated in a
series circuit is equal to the sum of the individual power dissapations. 
SUMMARY OF OHMS LAW
FORMULAS
AMPERES = 
VOLTS
RESISTANCE 


RESISTANCE = 
VOLTS
AMPERES 


VOLTS = 
AMPERES x RESISTANCE 


Parallel Direct Current
Circuit Rules
Rule #1: 
The same voltage exists across each
branch of a parallel circuit and is equal to the source voltage. 


Rule #2: 
The current through a branch of a
parallel network is inversely proportional to the amount of resistance
of the branch. 


Rule #3: 
The total current of a parallel
circuit is equal to the sum of the currents of the individual branches
of the circuit. 


Rule #4: 
The total resistance of a parallel
circuit is equal to the reciprocal of the sum of the reciprocals of the
individual resistances of the circuit. 


Rule #5: 
The total power dissipated in a
parallel circuit is equal to the sum of the individual power
dissapations. 
SUMMARY OF PARALLEL CIRCUIT
RULES
TOTAL VOLTAGE = 
E(1) = E(2) = E(3)
...etc. 


_{ TOTAL
RESISTANCE = } 
VOLTS
AMPERES 




_{TO DETERMINE
THE TOTAL RESISTANCE IN A PARALLEL CIRCUIT WHEN THE TOTAL CURRENT AND TOTAL
VOLTAGE ARE UNKNOWN USE EITHER OF THE FOLLOWING FORMULAS:}
RT
= 
1
___________________
1 + 1
+ 1 + ......etc
R1 R2
R3 


FOR TWO RESISTORS IN
PARALLEL USE THIS FORMULA CALLED THE "PRODUCT OVER THE SUM" 



_{ RT
= } 
R(1) * R(2)
R(1) + R(2) 


_{POWER IN SINGLE
PHASE RESISTIVE CIRCUITS}
_{WHERE POWER
FACTOR IS 100 PERCENT}
_{(THESE
FORMULAS ARE COMMONLY USED TO SOLVE MOST CIRCUIT POWER PROBLEMS ON TESTS)}
_{TO DETERMINE THE
POWER CONSUMED BY AN INDIVIDUAL RESISTOR IN A SERIES CIRCUIT USE THIS
FORMULA:}
_{TO DETERMINE THE
POWER CONSUMED BY AN INDIVIDUAL RESISTOR IN A PARALLEL CIRCUIT USE THIS
FORMULA:}
_{TO DETERMINE THE
TOTAL POWER CONSUMED BY AN INDIVIDUAL CIRCUIT USE THIS FORMULA:}
POWER
=
E (TOTAL VOLTAGE) x I (TOTAL CURRENT)
_{RULES OF THUMB:}
 _{THE TOTAL
RESISTANCE OF RESISTORS IN PARALLEL IS ALWAYS LESS THAN THE VALUE OF ANY
ONE RESISTOR.}
 _{THE TOTAL
RESISTANCE OF PARALLEL RESISTORS THAT ARE ALL THE SAME VALUE IS THAT VALUE
DIVIDED BY THE NUMBER OF RESISTORS.}
 _{ALWAYS USE THE
PRODUCT OVER SUM RULE TO BREAK DOWN TWO PARALLEL RESISTORS INTO ONE
RESISTOR. THIS IS MUCH EASIER THAN TRYING TO SOLVE LARGE ALGEBRAIC
EXPRESSIONS.}
 _{746 WATTS IS EQUAL
TO ONE HORSEPOWER}
 _{EFFICIENCY IS
EQUAL TO OUTPUT DIVIDED BY INPUT}
 _{IN INDUCTIVE
CIRCUITS CURRENT LAGS VOLTAGE.}
 _{IN CAPACITIVE
CIRCUITS CURRENT LEADS VOLTAGE.}
 _{POWER FACTOR IS A
MEASURE OF HOW FAR CURRENT LEADS OR LAGS VOLTAGE.}
_{POWER IN ALTERNATING CURRENT
CIRCUITS WHERE POWER FACTOR IS NOT 100 PERCENT}
_{
POWER = E x I x POWER FACTOR
(FOR
SINGLE PHASE)}
_{
POWER = E x I x 1.732 X POWER FACTOR
(FOR
THREE PHASE)}
_{
THIS POWER IS ALSO CALLED TRUE POWER OR REAL POWER AS OPPOSED TO APPARENT
POWER FOUND BY CALCULATING VOLTAMPERES.}
_{
VOLTAMPERES = E x I (FOR
SINGLE PHASE)}
_{
VOLTAMPERES = E x I x 1.732
(FOR
THREE PHASE)}
_{
IT CAN READILY BE DETERMINED BY ALGEBRA THAT}
POWER FACTOR =

TRUE
POWER
APPARENT POWER 
_{
MOTOR APPLICATION FORMULAS}
HORSEPOWER =
(for three phase motors)

1.732 x VOLTS x AMPERES x EFFICIENCY x power factor
746 
THREE PHASE AMPERES =
(for three phase motors)

746 x HORSEPOWER
1.732 x VOLTS x EFFICIENCY x
POWER FACTOR 
SYNCHRONOUS RPM =

HERTZ x 120
NUMBER OF POLES 
_{
MOTOR MARKINGS AND CONNECTIONS}
_{
CONNECTIONS FOR NINE LEAD}
_{
THREE PHASE MOTORS}
_{
THREE PHASE STAR OR Y}
STAR CONNECTED
Voltage

Line 1

Line 2

Line 3

Together

Low

1 & 7

2 & 8

3 & 9

4 & 5 & 6

High

1

2

3

4 & 7, 5 & 8, 6 & 9

_{
THREE PHASE DELTA}
DELTA CONNECTED
Voltage

Line 1

Line 2

Line 3

Together

Low

1 & 6 & 7

2 & 4 & 8

3 & 5 & 9

NONE

High

1

2

3

4 & 7, 5 & 8, 6 & 9

_{
DELTA WYE HOOKUP FOR TRANSFORMER}
_{
MOTOR CONTROLLER WITH THREE}
_{
START STOP STATIONS}
_{
(HOLDING CONTACTS NOT SHOWN)}
_{
TRANSFORMER TURNS RATIO}
Ep _{= } Tp
Es Ts
Where
Ep is primary voltage
Es is secondary voltage
Tp is number of turns in primary
Ts is number of turns in secondary
Delta and Wye Circuit Equations 
Typical 3Phase Wiring Diagrams and Equations
for Resistive Heaters
Definitions
For Both Wye and Delta
(Balanced Loads)
V_{P} = Phase Voltage
V_{L} = Line Voltage
I_{P} = Phase Current
I_{L} = Line Current
R = R1 = R2 = R3 = Resistance of each branch
W = Wattage
Wye and Delta Equivalent
W_{DELTA} = 3 W_{WYE}
Open 3Phase Circuit Formulas:
Open Delta Watts = ^{2}/_{3} W_{DELTA}
Open Wye Watts = ^{1}/_{2} W_{WYE}
Open 4wire Wye Watts = ^{2}/_{3} W_{WYE}

3Phase Wye
(Balanced Load)


3Phase Open Wye
(No Neutral)

I_{P} = I _{L}
V_{P} = V_{L}/1.73
W_{WYE} = V_{L}^{2} /R = 3 (V_{P}^{2})
/R
W_{WYE} = 1.73V_{L}I_{L} 

I_{PO} = I _{LO}
V_{PO} = V_{L}/2
W_{OWYE} = ^{1}/_{2} ( V_{L} /R)
W_{OWYE} = 2 (V_{PO2}/R)
W_{OWYE} = V_{L}I_{LO}


3Phase Delta
(Balanced Load)
I_{P} = I _{L}/1.73
V_{P} = V_{L}
W_{DELTA} = 3(V_{L}^{2})/R
W_{DELTA} = 1.73V_{L}I_{L}


3Phase Open Delta
.
V_{P} = V_{L}
I_{PO1} = I _{PO3} = I _{LO2}
I_{LO3} = 1.73 I _{PO1}
W_{ODELTA} = 2(V_{L}^{2}/R )


Fractional/Decimal/Millimeter
Conversion 
Fraction Decimal Millimeter 
Fraction Decimal Millimeter 
MM Inch 
1/64  .015625  0.397
1/32  .03125  0.794
3/64  .046875  1.191
1/16  .0625  1.588
5/64  .078125  1.984
3/32  .09375  2.381
7/64  .109375  2.778
1/8  .125  3.175
9/64  .140625  3.572
5/32  .15625  3.969
11/64  .171875  4.366
3/16  .1875  4.762
13/64  .203125  5.129
7/32  .21875  5.556
15/64  .234375  5.953
1/4  .25  6.350
17/64  .265625  6.747
9/32  .28125  7.144
19/64  .296875  7.541
5/16  .3125  7.938
21/64  .328125  8.334
11/32  .34375  8.731
23/64  .359375  9.128
3/8  .375  9.525
25/64  .390625  9.921
13/32  .40625  10.319
27/64  .421875  10.716
7/16  .4375  11.112
29/64  .453125  11.509
15/32  .46875  11.906
31/64  .484375  12.303
1/2  .5  .12.700 
33/64  .515625  13.097
17/32  .53125  13.494
35/64  .546875  13.891
9/16  .5625  14.288
37/64  .578125  14.684
19/32  .59375  15.081
39/64  .609375  15.478
5/8  .625  15.875
41/64  .640625  16.272
21/32  .65625  16.669
43/64  .671875  17.066
11/16  .6875  17.462
45/64  .703125  17.859
23/32  .71875  18.256
47/64  .734375  18.653
3/4  .75  19.050
49/64  .765625  19.447
25/32  .78125  19.844
51/64  .796875  20.241
13/16  .8125  20.638
53/64  .828125  21.034
27/32  .84375  21.431
55/64  .859375  21.828
7/8  .875  22.225
57/64  .890625  22.622
29/32  .90625  23.019
59/64  .921875  23.416
15/16  .9375  23.812
61/64  .953125  24.209
31/32  .96875  24.606
63/64  .984375  25.003
1  1.  25.400 
1  .039 2 
.0790
3  .1181
4  .1575
5  .1969
6  .2362
7  .2756
8  .3150
9  .3543
10  .3937
11  .4331
12  .4724
13  .5119
14  .5519
15  .5906
16  .6300
17  .6693
18  .7087
19  .7480
20  .7874
21  .8268
22  .8661
23  .9055
24  .9449
25  .9843 
Maximum Horsepower
for NEMARated
Motor Starters



SinglePhase

ThreePhase

NEMA
Size

115
Volt 
230
Volt 
208/230
Volt 
460/575
Volt 
00

1/3 
1 
1.5 
2 
0

1 
2 
3 
5 
1

2 
3 
7.5 
10 
2

3 
7.5 
10/15 
25 
3


25/30 
50 
4

40/50 
100 
5

75/100 
200 


NEMA RATING FOR ENCLOSURES
NEMA and other organizations have
established standards of enclosure construction for control equipment. In
general, equipment would be enclosed for one or more of the following
reasons:
 Prevent accidental contact with live
parts.
 Protect the control from harmful
environmental conditions.
 Prevent explosion or fires which might
result from the electrical arc caused by the control.
Common types of enclosures per NEMA
classification numbers are:
NEMA I  GENERAL PURPOSE
The general purpose enclosure is intended
primarily to prevent accidental contact with the enclosed apparatus. It is
suitable for general purpose applications indoors where it is not exposed to
unusual service conditions. A NEMA I enclosure serves as protection against
dust and light indirect splashing, but is not dusttight.
NEMA 3  DUSTTIGHT, RAINTIGHT
This enclosure is intended to provide
suitable protection against specified weather hazards. A NEMA 3 enclosure is
suitable for application outdoors, on ship docks, canal and construction
work, and for application in subways and tunnels. It is also
sleetresistant.
NEMA 3R  RAINPROOF, SLEET RESISTANT
This enclosure protects against interference
in operation of the contained equipment due to rain, and resists damage from
exposure to sleet. It is designed with conduit hubs and external mounting,
as well as drainage provisions.
NEMA 4  WATERTIGHT
A watertight enclosure is designed to meet
the hose test described in the following note: "Enclosures shall be tested
by subjection to a stream of water. A hose with a one inch nozzle shall be
used and shall deliver at least 65 gallons per minute. The water shall be
directed on the enclosure from a distance of not less than 10 feet and for a
period of five minutes. During this period it may be directed in any one or
more directions as desired. There shall be no leakage of water into the
enclosure under these conditions."
A NEMA 4 enclosure is suitable for
applications outdoors on ship docks and in dairies, breweries, etc.
NEMA 4X  WATERTIGHT, CORROSIONRESISTANT
These enclosures are generally constructed
along the lines of NEMA 4 enclosures except they are made of a material that
is highly resistant to corrosion. For this reason, they are ideal in
applications such as paper mills, meat packing, fertilizer and chemical
plants where contaminants would ordinarily destroy a steel enclosure over a
period of time.
NEMA 7  HAZARDOUS LOCATIONS  CLASS I
These enclosures are designed to meet the
application requirements of the National Electrical Code for Class I
hazardous locations. In this type of equipment, the circuit interruption
occurs in air.
"Class I locations are those in which
flammable gases or vapors are or may be present in the air in quantities
sufficient to produce explosive or ignitable mixtures."
NEMA 9 HAZARDOUS LOCATIONS  CLASS II
These enclosures are designed to meet the
application requirements of the National Electrical Code for Class II
hazardous locations.
"Class II locations are those which are
hazardous because of the presence of combustible dust."
The letter or letters following the type
number indicates the particular group or groups of hazardous locations (as
defined in the National Electrical Code) for which the enclosure is
designed. The designation is incomplete without a suffix letter or letters.
NEMA 12  INDUSTRIAL USE
The NEMA 12 enclosure is designed for use in
those industries where it is desired to exclude such materials as dust,
lint, fibers and flyings, oil see page or coolant see page. There are no
conduit openings or knockouts in the enclosure, and mounting is by means of
flanges or mounting feet.
NEMA 13  OILTIGHT, DUSTTIGHT
NEMA 13 enclosures are generally of cast
construction, gasketed to permit use in the same environments as NEMA 12
devices. The essential difference is that, due to its cast housing, a
conduit entry is provided as an integral part of the NEMA 13 enclosure, and
mounting is by means of blind holes, rather than mounting brackets.
