Basic Electrical Theory in a Nutshell

by electrician2.com
 


 
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
   
VOLTS   =
TOTAL VOLTAGE
TOTAL 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 
___________________
   + + + ......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:
 
POWER
 I2 x R

TO DETERMINE THE POWER CONSUMED BY AN INDIVIDUAL RESISTOR IN A PARALLEL CIRCUIT USE THIS FORMULA:
 
POWER
 E2
 R

TO DETERMINE THE TOTAL POWER CONSUMED BY AN INDIVIDUAL CIRCUIT USE THIS FORMULA:

POWER = E (TOTAL VOLTAGE)  x  I (TOTAL CURRENT)
 
 
 



RULES OF THUMB:




POWER IN ALTERNATING CURRENT CIRCUITS WHERE POWER FACTOR IS NOT 100 PERCENT

(True POWER) = E x I x POWER FACTOR (FOR SINGLE PHASE)

(True 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 VOLT-AMPERES.

Watt meters read True Power.

Apparent Power = VOLT-AMPERES = E x I (FOR SINGLE PHASE)

Apparent Power = VOLT-AMPERES = 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


Switch Hookup

4 Way

D to S, E to R, F to T, G to W

3 Way

A to Z, B to Y, C to X


Cable Tray Fill Example



 
 
Solution
 

For multiconductor cables rated 2,000 volts and where there are 4/0 and larger cables are installed with cables less than 4/0 in size refer to Section 392.22(A)(1)(c).

The sum of the cross sectional areas of all cables smaller than 4/0 shall not exceed the maximum allowable fill area resulting from the computation in Column 2 of Table 392.22(A)for the appropriate cable tray width.

In this table sd = the sum of the diameters of the cables 4/0 and larger.

Then

Sum of cross section of areas for smaller than 4/0 cables (SUM) <= X - 1.2 x sd

X determines the cable tray width from the Table 392.22(A).

X >= SUM + (1.2 x sd)

SUM = 6 x 3.14 x .5 x .5 sq inches

SUM = 4.71 sq. inches

sd = 3 x 2 inches

sd = 6 inches

X >= 4.71 + (1.2 x 6)

X >= 11.91

From Table 392.22(A) the next larger X is 14 and this converts to a 12.0 inch wide cable tray in column 1.

It should be noted that the 4/0 and larger cables shall be installed in a single layer.


 

 

 
Maximum Horsepower
for NEMA-Rated
Motor Starters
Single-Phase
Three-Phase
NEMA
Size
115
Volt
230
Volt
208/230
Volt
460/575
Volt
00
1/3 1 1.5 
0
1 2
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:

  1. Prevent accidental contact with live parts.
  2. Protect the control from harmful environmental conditions.
  3. 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 sleet-resistant.

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, CORROSION-RESISTANT

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.