Electrical Theory



          Atoms are all part of matter.  An atom which has a nucleus being the center contains electrons which encircle the nucleus.  Electrons move from one atom to another.  If a force or voltage is applied to the ends of the matter, they put pressure on the electrons in a specific direction in which an electrical current is established.  The measurement of this electrical current is known as amperage (I = E/R).  The conductivity or atomic structure of certain metals vary and allow electrons to move from one atom to another more freely.  Silver allows the highest conductivity.  Too expensive to manufacture and use we normally use copper and aluminum.  If 6,250,000,000,000,000,000 electrons are equal to 1 coulomb which flows at a rate within 1 second this will generate 1 amp.



          We call the force that is applied to the electrons, electromotive force which is also known as emf.  A generator produces electromechanical force while a battery will produce electromotive force through a chemical reaction.  The voltage force induced is the measurement of energy such as 1 volt required to move 1 coulomb, or 1 amp from one end of the conductor to the other depending on resistance and other factors(if R= 1 ohm).  Depending on the conductivity or conductor properties of the material used will allow the electrons to move more freely and ultimately result in a specific size of wire in which we should use. The force required to move these electrons (current) from one end to the other requires a certain amount of voltage considering the amount of resistance (E = I x R).  High Voltage is like an arc that jumps in a bad switch or loose splice.  The pressure can cross boundaries and is an example of voltage force.




          The opposition to current flow is known as resistance (R = E/I).  Resistance is a fixed value.  Conductor properties such as silver, copper, aluminum, gold all contain a fixed specific resistance which will affect the ease or conductance of electrons to move freely.  When any of these materials are used and manufactured to develop a wire we determine that the unit of resistance is expressed in Ohms for every circular mil foot.  In the length of one foot of a circular wire whose diameter measures 1mil there will be a specific resistance which will affect the ease in which current will flow.  This effect is known as Resistance measured in Ohms.  If the length of circuit doubles then the resistance should also double.  Resistance will always be a fixed value.  In order to change the resistance we have to change the length of wire (length of circuit), change the size of wire (circular mils), change the conductor property of the conductor (copper to aluminum) or change the temperature in which the conductor is subjected to. 




          A way to describe the potential difference in voltage between two points is referred to as voltage drop.  The voltage seen across a resistor or also known as a load will vary depending on variable factors.  The (Vd =I x R) voltage drop across the load is reflected in volts and depends on the current being used by the load, its fixed internal resistance and how the load is connected to the circuit.  In real life situations most circuits we install are paralleled circuits.  Voltage drop at each receptacle outlet should be 120v and each lighting outlet may be 120v or 277v.  However there is a voltage drop due to the length of the circuit.  (Voltage drop) = (to the load of the equipment to be used) x (the total resistance of the wires considering the length of the circuit) OR (Line voltage - Load voltage).  Certain provisions require that the branch circuit voltage drop should not exceed 3% (total of 5%) if the feeder voltage drop is 2%.  In this case after determining voltage drop divide it by the source voltage and multiply by 100%.  If this value is more than the permissible voltage drop of 2 % then a larger wire is needed.




          Electrical circuits transmit energy where as transformer transfer energy.  Energy is represented by joules.  However Power is the rate that energy is used.  If 1 joule of energy is used in 1 second then the rate at which it is used is 1 watt (w).  One joule per second or one joule should be equal to 1 watt per second.  Wattage depends on various factors.

In order to use this energy we refer to it by power.  Power is the product of voltage and current (P = E x I).  The required energy to produce electrical energy is defined as watts.  If there is a cost to use Power from the utility company and there is a loss of power due to heat from an incandescent bulb, inefficient installation or equipment, then power losses should be kept to a minimum.  Power loss is a measurement represented by I x I x R. 




          Series circuits are almost never used in electrical installations.  The series circuit is a circuit where the voltage and current never meet a splice point where there are multiple connections or paths.  There is only one path for voltage and current as it makes its way back to its source.  Current (I) remains constant as Voltage (v) loses pressure or force passing through resistance as it makes its way down the circuit.  Voltage Drop appears at every resistor with a different voltage drop value depending upon the resistors value.  (Remember Vd = I x Resistor 1 or V1 = It x R1).  The sum of the voltage drops throughout the series circuit is equal to the source voltage or total voltage (Et = V1 + V2 + V3 + etc……. ). 



                   Et = V1 + V2 + V3 + etc…….

                   It = I1 = I2 = I3 = etc……..

                   Rt = R1 + R2 + R3 + etc…….

                    Pt = Pr1 + Pr2 + Pr3 + etc…..





          Parallel circuits are more commonly used and installed in residential commercial and industrial applications.  In a parallel circuit there are multiple paths for current to flow.  Current distributes among the parallel paths as voltage distributes evenly.  An example of this would be the 120 volt receptacles in your home.  Each have 120v at their outlet point but depending on what resistive load you plug in will determine the amperage taken from the available 15a or 20a circuit.  We all should know what happens when too many loads are connected.  All the loads plugged in add together.  If all loads added together equal 15a or 20a or more than the circuit should trip. 




                   Pt = Pr1 + Pr2 + Pr3 + etc……

                   Et = V1 = V2 = V3 = etc……..

                   It = I1 + I2 + I3 + etc……..



Rt = R1 x R2  

                    R1 + R2


1   =   1   +   1   +   1  + etc……

Rt       R1      R2       R3


Rt  = value of 1 resistor (only use for resistors of equal value)

                         # of resistors






Xl = Inductive reactance = 2(3.14)fL = ohms


L =  Inductance =     Xl        = Henrys








Xc = Capacitive Reactance =       1       = ohms


C = Capacitance =           1        = Farads






Impedance= Total opposition to current flow

Zt  =  (R² +  (Xl – Xc )² )  =  ohms


It = Et       Et = It x Zt        Et= Volts = Amps x Ohms=I x R




          Alternating Current (AC) considers the varying affects of voltages and current through the pattern of a sign wave.  Inductance and capacitance affect the power factor which plays a part in determining the true power seen in the circuit.  The True power (Power@ the Load) = Apparent Power (Power @ the Line) x Power Factor (PF).


                                       Single Phase             Three Phase

(P = E x I x PF)         (P = 1.73 x E x I x PF)



Direct Current (DC) does not follow the pattern or varying factors as AC circuits.  The Direct Current is a straight line when seen through an oscilloscope.  Inductance and capacitance doesn’t play a role in a DC circuit therefore there is no power factor nor angle to displace waveforms.

                                                (P = E x I)





A complete circle is 360 degrees representing one cycle.  60 cycles per second means that a sine wave that is represented on a horizontal axis or frozen in time on an oscilloscope will complete 60 (360 degree circles) in one second.  The 60 cycles per second represents the frequency measured in Hertz (HZ).  So how long does it take to complete one cycle or the period for each cycle?  Simply divide the frequency by one such as 1/60 (1/F=Time).  The period or time that it takes to complete one cycle is .016666 seconds.  For 2 cycles, 2/60 = .033333 seconds.  For 3 cycles, 3/60 = .05 seconds.


The root means squared or RMS is also known as the effective value.  The values that we read either on our volt meter or amp meter are RMS values.  When we read a voltmeter we may see a reading of 120 volts.  This value on our meter is the RMS value or effective voltage.  But what value does the voltage peak?  The Peak voltage is determined by multiplying the RMS value x the square root of 2.  Therefore 120 v x 1.414 = 169v.  Use the formulas and play around with the numbers.

E rms=E peak / 1.414         OR        E rms = E peak x .707


I rms = I peak / 1.414        OR       I rms = I peak x .707


When looking at phase relationships and which phase leads or lags in an inductive or capacitive remember ELI the ICE man.


ELI = voltage leads the current in an inductive circuit.


ICE = current leads the voltage in a capacitive circuit.


          In AC circuits depending if the circuit is inductive or capacitive will reflect on the true power.  True power = apparent Power x PF.  Analyzing through vector analysis will result in PF = W / VA = true/apparent (P = E x I x PF).  The cosine of the phase angle between the current and voltage also explains the relationship of current to voltage (P = E x I x cosine angle).





          Transformers transfer power.  Transformers are rated in kva.  They are referred as to either step up or step down the voltage only.  Yes they do step up current or step down current but we always refer to the voltage.  A transformer has two windings wrapped around an Iron Core.  The Input Power or Line connection is attached to the primary winding and the load is connected to the secondary winding.  No Electrical connections are between the two windings.  The principal in transferring Power or Energy is done through mutual inductance (through the iron core). 

The number of turns or ratio of turns on the primary winding to secondary winding will affect the voltage output.  If the secondary winding has twice as many turns than the primary winding (1:2 ratio) than the secondary will have twice the voltage and represent a step up transformer while cutting the current on the secondary by half (neglecting Efficiency).  Efficiency = Output of the transformer / Input.  The kva transformers output would still be represented by kva until a load having a power factor is introduced in which the kva would now become watts due to additional losses from the loads PF.

Keywords: Current, Voltage, Power, Transformer ratios

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