Journeyman Electrician: Electrical Theory 101

Conductive Materials and Insulators
Electrically conductive materials have atomic structures that provide free electrons for charge to flow easily when an external voltage is applied.  Most metals fall into this category including those most commonly used in wires and other conductors: copper, silver, gold, and aluminum.
Materials that conduct poorly are known as nonconductors, insulators, or dielectrics.  In these materials loose electrons are scarce, which prevents the free flow of electrical charge.  Commonly used materials for insulators are PVC and various other rubber, plastic, and ceramic materials.
Insulators can breakdown under high electrical potential and become conductive. The voltage at which this occurs is known as the dielectric strength of the materials.

Ways That Electric Current Can Be Produced
There are six ways to cause electrons to move and produce electrical potential and current. They are:
- The motion of a magnet relative to a conductor such as in an electric generator.
- Chemical reaction that transfers electrons through an external circuit, as from a battery.
- Light striking the sensitive semiconductor material of a photocell.
- Heat acting on a junction of dissimilar metals in a thermocouple.
- Pressure acting on a piezoelectric crystal.
- Friction of rubbing some materials together can produce static electricity, but normally this doesn’t result in any sustained current.

Simple Battery Cell
A galvanic (or voltaic) cell consists of a container with electrolyte solution and two dissimilar electrodes to and from which the current flows.  Chemical reaction of the electrolyte on the electrodes develops positive and negative charges on the electrodes.  When they are connected in an external circuit, electrons are transferred through the circuit resulting in an electric current.
The voltage produced per cell is constant for any specific set of materials, so batteries with higher voltage outputs have multiple cells connected in series.  The physical size of the battery determines its current capability and energy capacity. The surface area of the electrodes determines the maximum current, and the electrode size and quantity of electrolyte determine the overall energy capacity of the battery.

Different Types of Batteries
The two classes of batteries are primary and secondary. 
Primary batteries require no charging, while secondary batteries are designed for many cycles of charging and discharging.  Flashlights use primary batteries while the storage battery in a car is a secondary battery.
There are also two classifications of batteries based on the form of their electrolyte.  Dry cells contain electrolyte that is a semi-solid gel while wet cell electrolyte is liquid.
Battery capacity is measured in ampere-hours, which is simply the length of time that a specific current can be sustained multiplied by this current.
In secondary batteries, the specific gravity of the electrolyte is affected by how fully charged the battery is and this can be measured with a hydrometer.
Gasses can form at the electrodes of a secondary battery if it is overcharged.  In a lead-acid car battery, these gasses are hydrogen and oxygen and an explosion can result if a spark is introduced.

AC Versus DC
DC power is usually at a very low voltage, mostly due to the difficulty in developing or converting it to higher voltages.  At lower voltages, the transmission of power requires higher currents, which mean greater losses.  The power loss due to line resistance is proportional to the square of the current, so to reduce these losses power is always delivered at the highest voltage that is practical.  With AC power, voltages are easily changed with transformers that also have very little loss.  Once the power is delivered, the AC voltage can be regulated easily.  With DC, the most common method of reducing the voltage is with resistive dividers, which waste even more power.

DC is used only for low voltage applications or where portability requires the use of batteries.

Purpose and Construction of Transformers
Transformers are used to change the level of the AC line voltage, current, or impedance.  They are constructed with two or more coils of wire in close proximity, so that the magnetic fields of the coils are coupled and transfer the electrical energy.
The turns ratio (N) is the ratio of the number of turns or loops in the coil of the transformer secondary to the number of turns in its primary.

The turns ratio defines the input and output parameters as shown:
Voltage:   
Current:   
Impedance:   

An autotransformer has only one winding that is shared by the primary and secondary with separate taps for each.

Operating Conditions for Transformers and Motors
The usual conditions under which a transformer can carry its rated load are as follows:
1. The secondary voltage must not be over 105% of the rated value.
2. It must be operated at its rated frequency.
3. The average temperature must not be over 40 degrees C.

The ratings of the transformer are the limits of its use in voltage, current, and power.  The most important point in watching transformer performance is its temperature.
The maximum ambient temperature for a motor to operate is 40 degrees C (104 degrees F) unless otherwise designated.  The service factor on the motor nameplate tells whether a motor is allowed to develop more than its rated horsepower without causing damage to its insulation.
Motor bearings must be kept lubricated.  Sleeve bearings are usually lubricated with oil.

Generators
The most common source of electrical power is the generator.  AC generators are also known as alternators, because they produce alternating current.  There are any number of mechanical energy sources that can be used to drive a generator from water and wind to coal-fired steam.
In a generator, power is generated from the relative motion between a conductor and a magnetic field.  This motion forces the electrons in the conductor to flow, which produces electric current and develops a voltage.
The stationary part of a generator is known as the stator and the moving portion is the rotor.  These contain the field windings, which set up the magnetic field, and the armature windings where the output is produced.  Depending on the type of generator, the armature or the field windings may be stationary or moving.

DC Generator
A DC generator is a device for producing direct current (DC) power.  Its output voltage is actually a sinusoid that has been rectified
(converted to DC).  A number of coils are rotated within a magnetic field, and their corresponding alternating current outputs are delivered from a commutator through brushes that pick up the current with the proper phase.  Normally, there is a rectifier circuit to produce a relatively constant DC output.  In a DC generator, the rotor is the armature and the stator contains the field coils.
There are several limitations in DC generator design.  Since contact with the moving armature is required, brushes produce noise and eventually will wear out. Even the use of a large number of coils produces a DC output with significant ripple.  The torque required to turn the armature of a DC generator is usually fairly high.
The commutator of a generator should be cleaned with fine sandpaper.

AC Generator
An AC generator is a device for producing alternating current (AC) power.  It operates much like the DC generator, but in AC generators the rotor contains the field coils and the stator is the armature. 
In this way, the higher voltage and current connections to the induction coils are not required to be made through slip rings or brushes.  Unlike DC generators no commutator is required since the AC output is what is desired, but slip rings are still needed to connect to the rotating armature, which contains the field coils.  Multi-phase alternators are built with multiple coils, one for each phase.
As conductors in the armature rotate through the magnetic flux established by the field coils, AC current is generated.  One rotation of the armature results in one electrical cycle or 360 degrees of phase.  Each cycle per second is defined as 1 Hertz (abbreviated Hz.), and most AC generators operate at 60 Hz.

Ohm’s Law
Ohm’s Law is the relationship of voltage, electric current, and resistance.  It is simply stated as E = IR.
Manipulating the equation results in the following set of relations:
E = IR
I = E/R
R = E/I

The Ohm’s Law triangle is a simple way to remember the various forms of the equation.  If you cover the unknown, you are left with the formula to calculate that value.


The units that must always be used for the Ohm’s Law equations are volts, ohms, and amperes.

Power in Electric Circuits
Power is the rate of energy consumption and is the product of voltage and current:
P = I . V.

Substituting variables from Ohm’s Law results in the following set of relations:




To be consistent with the other units, power must be expressed in watts.  In motors, horsepower is commonly used for power and one horsepower equals 746 Watts.
The Ohm’s Law circle incorporates the power equations above and contains all the formulas relating resistance, current, voltage, and power.  An unknown in the inner circle and its defining equations are in each quadrant. Using the circle, you can find the appropriate formula to define any of these quantities when you know any two of the others.


A circuit is an electrical network containing a voltage source and a load connected in a circular path with conductors such that current can flow. A complete circular path from the source through the load and back to the source must exist for current to flow.
Series circuits are those with elements connected sequentially in the same path. The elements share the same current and divide the voltage.
Parallel circuits have their circuit elements in separate branches. They share the same voltage but divide the current. In a series circuit, if the electrical path through any element breaks and is open no current flows. With parallel connections if one path opens the rest continue to conduct.
A very high (near infinite) resistance is known as an open circuit, a very low resistance (near zero) is a short circuit. In an open circuit no current flows; in a short circuit a very high amount of current flows because the load is bypassed by a very low resistance path.
A jumper is a short length of conductor used to bypass a break in a circuit or to make a connection between terminals.
A poor or corroded electrical connection increases the resistance at this point and converts some of the voltage and current that should be applied to the load to heat.

Kirchhoff’s Two Laws
Kirchhoff’s current law applies to currents in parallel branches of a circuit.  It states that at any junction, the sum of the currents must be zero or the sum of all currents flowing in must equal the sum of those leaving.
Kirchhoff’s voltage law states that the sum of the changes in potential encountered in making a complete loop around a circuit is zero. 
Another way to state this is that the sum of the voltage sources must equal the sum of the voltage drops.
Kirchhoff’s laws simplify the analysis of circuits by permitting examination of individual circuit branches and series elements. 
Implied in the laws is the fact that parallel branches of circuits all have the same voltage across them, and those series circuit elements all have the same current flowing through them.

How Resistance Values Combine in Series
Resistors in series behave the same as a single resistor with a value that is the sum of the individual resistor values.  In the equivalent circuits shown below R = R1 + R2.


In either case the current I is exactly the same and equals V/R or V/(R1 + R2), and the total power consumed is also identical and equals I x V.

How Resistance Values Combine in Parallel
Two resistors in parallel behave the same as a single resistor with a value as follows:


For parallel resistors with equal values, simply divide the single resistor value by the number of resistors.  For the two resistors above, if R1 = R2 then R = R1/2 = R2/2
 

For unequal parallel resistors, the equivalent resistance is the product of the values divided by the sum:

With parallel resistors, the combination of resistors always has a resistance lower than the lowest valued single resistor.
Series/parallel combinations of resistors can be converted to a single value by stepwise application of series and parallel conversions.

RMS Values
RMS, or root-mean-square, values are a very useful way of expressing AC waveform voltages and currents.  The RMS value is also known as the effective value, because it is the value to use in steady-state calculations.  The RMS value of a waveform can be thought of as the equivalent DC value.
For the sinewave, the RMS value is the peak value times ½ the square root of 2, or approximately .707 of the peak.
The peak instantaneous value is then 1.4 times the RMS value. A single-phase 120 VRMS source will have a peak potential difference between the two conductors of 120 x 1.4 = 168 V peak-to-peak. 

The peak potential difference between the two 2-phase 120/240 lines used in residences is twice this value, 336 Volts!

Impedance
The impedance of a load is composed of the resistance as well as the contributions of capacitance and inductance, which is known as reactance.  The reactance may introduce an out of phase component to the impedance, and cause the applied voltage and resulting current to be out of phase with each other.  Like resistance, reactance and impedance are measured in ohms and their symbols are X and Z.

The value of impedance is



How Reactance Affects Ac Circuit Performance
All conductors and load components contain some inductance and capacitance as well as resistance.  A significant amount of inductance is present in loads that do physical work like motors and solenoids, because they are designed to produce magnetic fields.  This is especially true if the motors are operated at less than their full load.  Fluorescent lights, on the other hand, are by nature capacitive.  Resistive loads like incandescent lights and heaters cause no appreciable phase shift.

Inductive and capacitive loads cause the phase of the current to lead or lag the voltage, and the power factor shifts away from the ideal value of 1.  The useful real power dissipation is reduced while the apparent power is increased thereby reducing efficiency.  This can be corrected with the use of external capacitors in the case of inductive loads, or with an inductive ballast in a fluorescent light circuit.
Real power is the average in-phase power, that which is dissipated in the resistive elements of a circuit. It is the product of the RMS voltage, the RMS current, and the cosine of the phase angle between the voltage and current.
Reactive power is the out of phase component. It is the product of the RMS voltage and current and the sine of the phase angle between them. It is important because it contributes to the overall apparent power.
Apparent power is the product of the RMS values of the circuit voltage and current without considering phase.
Real power is measured in watts, reactive power in vars, and apparent power in volt-amperes. Vars and volt-amperes are more or less equivalent units to watts that are used to distinguish them from real power.

Power Factor
AC electrical systems have inductive and capacitive loads that create a non-resistive impedance called reactance. This reactance results in reactive power within the system that does no useful work and results in the voltage and current being out of phase with each other. Reactive power is measured in volt-amps and does not transfer any net power to the load but is necessary for the delivery of real power. Real power is the power that is paid for at the meter, measured in kW, and is used by equipment for useful work. The total power that must be supplied by the utility is the apparent power, measured in volt-amps.

The apparent, real, and reactive powers can be added vectorially to be represented by a power triangle:


The cosine of the angle, θ, which is the phase angle between the voltage and current, is the ratio of the real power to the apparent power and is called the power factor.

The calculation of power may be carried out as for any Pythagorean triangle:



“Eli the Ice Man”
The saying “ELI the ICE man” is a convenient way to remember that in inductors (L) the voltage (E) leads the current (I).  E comes before I when there is an L. The phase of the voltage through the inductor is such that its sinusoidal peaks and valleys occur prior to those of the current during each cycle.
In a capacitor (C), the current (I) leads the voltage (E). 
I comes before E when there is a C.  The phase of the current through the capacitor is such that its peaks and valleys occur prior to those of the applied voltage for each cycle.

Harmonics
Harmonics are distortion in the current waveform that contains higher frequency components, which are at multiples of the power line frequency (60 Hertz). Harmonics are produced by nonlinear loads such as computers and other electronics.  Linear loads are such devices as heaters, motors, and lighting.
Harmonics are significant because these unwanted currents from each line are summed together in the neutral conductor of the power system.  Harmonic currents may be large enough to cause an overcurrent condition in the neutral conductors; a situation made worse because for safety reasons neutral conductors never have overcurrent protection.  Third harmonics and higher multiples of them are particularly damaging since in three phase systems they are in phase for each leg and add directly in the neutral conductors.
The skin effect makes heat generated from harmonics, worse because at the higher frequencies the skin effect is more pronounced.  This increases the effective resistance they see which increases the heating effect.
Cords sometimes have larger neutral wires to deal with higher harmonic currents, especially for computers and other nonlinear loads.

Current That Flows in a Neutral Conductor
Neutral currents are equal to the difference in current in the individual circuits. With balanced loads, no current will flow in the neutral conductor.
Do not confuse the neutral conductor in a multi-wire system with the white (neutral) wire in a common single-phase 2-wire circuit.  The white wire always carries the full current from the load.
A loose neutral can cause strange things to happen because loads may receive incorrect voltage.  This is why there is never a fuse or breaker on a neutral line, and you must never depend on the structure of a load device for continuity of a neutral connection.

K-Factor
A transformer’s K-factor is the multiple of the rated current that the transformer can handle in its neutral line.  Transformers that are specially designed for this purpose are known as K-factor transformers.
K-factor transformers are constructed to reduce the effects of increased neutral currents from harmonic distortion.  Nonlinear loads generate higher harmonic currents that could cause transformers and system neutrals to overheat and cause damage.  K-factor transformers don’t get rid of harmonics, they are just rated to handle them.
Standard values of K-factors are K-1, 4, 9, 13, 20, 30, and 40.  The latter can safely dissipate 40 times the harmonic current of a standard (K-1) transformer.

Line Voltage Drop
Voltage drop is another consideration in sizing wires (aside from ampacity).  The electrical code requirements limit the drop to 3% on branch circuits and 5% overall (from the main panel).  The voltage drop is equal to the IR drop in the wires; that is, the voltage that is robbed from the load. = IRline.
Voltage drop is important because it robs power from the load and wastes energy.  The cost of voltage drops is equal to the product of the power loss, the running time, and the cost of power per unit of time.  Over long periods of time, these costs can add up.
Controlling voltage drops can only be accomplished by limiting the length of wires to the load (which is sometimes impossible) and increasing the wire size to reduce resistance.
If conduit needs to be rerouted, an increase in the wire size might be required to compensate for the additional voltage drop of the longer run.

The voltage drop Vd = IRc, where Rc is the conductor resistance taken from tables or calculated from the wire diameter in circular mils and the resistivity of the material.  Note that wires of the same size may have different resistances depending on their type (stranded, solid, coated/uncoated, aluminum, etc.).  From the tables, Vd = k x length / area (circ.mils) where the k-factor is given in circular-mil-feet.

The one-way voltage drop must be multiplied by 2 for the 2-way resistance in a single-phase circuit. For 3 phase systems this factor is 1.732.
The resistance determined from the tables is valid for only one temperature.  The tables provide values for different temperatures, but typically the resistance increases 5% (1.05) for each additional 15 degrees Celsius.

Skin Effect and Resistance
In AC systems, the electric current tends to concentrate near the surface of conductors rather than being uniformly distributed throughout the conductor cross-section.  This increases the effective resistance of the wires.  For this reason, tables are provided for both DC and AC resistance of conductors.

Voltage (symbol V or E) is the potential for doing work in an electrical circuit.

Current (I) is the rate of flow of electrical charge through a conductor, basically the number of electrons passing per second. It is the result of electrons in motion. The current direction is opposite to the physical flow of electrons. This is because electrons are negatively charged and current is the transfer of positive charge. Electric current is evident from the effects it produces: heat, magnetism, and electric shock.

Resistance (R) is the tendency of loads or wires to oppose the flow of current. The resistance of a load or wire is determined by the dimensions of the component and the resistivity of the material. As the length increases the resistance goes up and as the cross-sectional area increases and there are more microscopic paths for the current to flow, the resistance goes down. Variable resistors are called potentiometers or rheostats.

Conductance is the inverse of resistance (1/R), and it is useful in series circuits because conductances add directly instead of inversely like resistances.

Inductance is the tendency of circuit elements to resist changes in current as they build and collapse a magnetic field. In doing this an inductor may develop large voltages when its magnetic field collapses.

For this reason, the coil of a relay may have a diode to conduct away current and prevent the large reverse voltage that would develop when the relay is deenergized. Inductors are usually constructed by winding wire into loops, which concentrates the magnetic field and increases the inductance.

Electrical charge is measured in Coulombs. One Coulomb is the charge that is transferred by the flow of one Ampere of current for one second, and it is equal to a very large number of electrons (about 20,000,000,000,000,000,000).
Capacitance is the tendency of circuit elements to resist changes in voltage as the electric field builds and recedes.  Current through a capacitor initially is at a maximum, limited only by the resistance in the circuit. Capacitors can be used to prevent arcing in movable contacts.