Basic Electrical Theory

Electricity got it's name from the electron; the negative subatomic particle that orbits the nucleus of an atom, which contains the positive proton and neutrally charged neutron. What makes each element on earth different from of all the other elements is the number and arrangement of these three basic atomic particles. Electrons (-), protons (+), and neutrons. (0) The electron is 1830 times smaller than a proton but has an equal, but opposite electrical charge. (Fig 1)	Fig 1
The number of electrons orbiting the nucleus of an atom determine its valence charge.  That is the number of free electrons available in it's outer shell. An element whose atoms contain lot's of free electrons is a good conductor of electricity, while an atom that has few valence electrons is considered a poor conductor, or insulator. (Fig 2)	Fig 2
A semiconductor is a material with an electrical conductivity that is intermediate between that of an insulator and a conductor.  Silicon and Germanium are the most commonly used semi-conductors. A PN junction  (Fig 3) allows current to flow in one direction making it perfect for use as a diode. A diode blocks DC current in one direction and allows it to pass in the opposite direction.     Figure 4 illustrates the effect of a diode (semi conductor) on an Alternating Current (AC) sine wave, creating a half-wave rectifier. Figure 5 shows how two diodes route current in opposite directions to form a full-wave rectifier.	Fig 3 Fig 4 Fig 5
When three pn junctions are formed within one case, we have a transistor. The three parts are the emitter, collector, and base.  They can be arranged as PNP's or NPN's. (depending on how their positive (P) and negative (N) ends are connected together.  (Fig. 6) To get electron or (hole) flow, the P and N semiconductor material must be doped with another element such as arsenic or germanium.	Fig 6
By controlling the electrical bias (signal) of the base you can control the current flow between the emitter and collector creating either an "off/on" switch or an amplifier.  ( Fig 7)	Fig 7
Ohms Law Basically we use Ohms Law to determine Voltage Drop. In other words, we as electricians need to know the voltage and currents draw on equipment in order to fuse it correctly and operate the equipment in the way it was intended to be used. We want to accomplish the task without causing fires or killing someone by electrocution. The human body is an excellent conductor of electricity and as little as 1/2 ampere is enough to kill you. Ohms Law tells us just how much current will flow through a circuit at a given voltage and resistance. Equipment has, or should have, a nameplate that gives the correct voltage to use and the expected current to flow in the device. Some nameplates even suggest the proper fuses to use. The three components of Ohms Law are Voltage (V or E), Resistance (Ohms or W), and Current I or A. The basic formula is in the voltage drop configuration: E=I x R (Fig 7) (Note:  Although this is the basic formula of all electric calculations you must use tables in the NEC for most of your calculations; especially motors.  If you try to use Ohms Law exclusively, none of your answers will turn out right) Ohms Law is something you must know but you must know how the NEC expects you to solve electrical calculations when selecting proper short-circuit and ground-fault protection of equipment such as motors and transformers.   As far as the test goes you will most likely be given the Voltage and the Wattage. For NEC purposes VA or Volt-Amps is the same as Watts. Power (P) in watts = I (current) x E (Voltage)  i.e.  P =I x E  746 Watts = 1 HP (Horsepower)	Cover Up The term You Want to solve for
Keep the Ohms Wheel handy, especially if you have problems transposing algebraic formulas, or if you've never taken an Algebra class.
Conductors themselves have resistance. The longer a conductor is the more resistance it has.  The bigger around(crossectional area) the conductor is, the less resistance it has.  Therefore we say that the length of a conductor is directly proportional to its resistance and inversely proportional to its cross-sectional area. If we double the length of a conductor we double its total resistance.  If we double the cross-sectional area we halve the resistance.  This is why we oversize conductors for long runs to reduce the Voltage Drop of the conductors.  We must keep the voltage drop 3% or less for branch circuits an 5% total for feeders plus branch circuits.
The two basic circuits we use are series and parallel. (Fig 10)
Total resistance in series is the sum of the resistances.	RT  =  R1   +  R2   +   R3
Total resistance in parallel is always less than the smallest resistor.  If the resistors are equal divide the resistance of one resistor by the number of resistors in the circuit.	1                  RT =             _______________             R1  +  R 2  +  R3
If you have three 30,000 ohm resistors in parallel the total resistance is 10,000 ohms.              W omega is the symbol for Ohms	RT  =( 30,000 W ) / 3 = 10,000W Divide one resistor by the number of resistors
If you parallel batteries you double the current. If you series batteries you double the voltage. Use distilled water in batteries and don't overfill the cells.  A normal charged cell should read around 2.3 volts.
Besides resistors, there are two other components that create resistance.  Inductors (coils, motors) and Capacitors. The resistance they create in Alternating Current (AC) circuits is called Inductive Reactance for coils and Capacitive Reactance for Capacitors.	Inductors (coils)     Capacitors
The formula for Capacitive Reactance is: Xc = 1/2p fc	Xc  is capacitive reactance in ohms f is frequency in hertz c is capacitance in farads
The formula for Inductive Reactance is: Xl = 2pfl	Xl     is inductive reactance in ohms      f      is frequency in hertz       l     is inductance in henrys
Henrys and Farads are usually expressed in ? henrys (micro henrys) or ? farads (micro farads) (See Orders of magnitude on the right)	Orders of Magnitude 1,000,000,000,000 +12 Tera 1,000,000,000 +9 Giga 1,000,000 +6 Mega 100,000 +5   10,000 +4   1000 +3 Kilo 100 +2   10 +1   1 0   .1 -1   .01 -2   .001 -3 mili .0001 -4   .00001 -5   .000001 -6 micro .000000001 -9 nano .000000000001 -12 pico
Total Resistance of an AC circuit is  expressed in Impedance or Z	The formula for total Impedance of an AC circuit is:
Reactance is called reactance because of the way Alternating Current reacts to coils and capacitors.  Both cause the current and voltage to go out of sync or out of phase; phase shift.  It's this out of phase condition between the applied voltage and the inductance or capacitance that creates the pf or power factor of an AC circuit.
It's easy to remember the effect of each of these reactive components by the phrase: ELI  the  ICE  man E, voltage in an inductor (L), leads the I current And I in a capacitor (C),   leads the E voltage
We can have RC circuits consisting of Resistors and Capacitors; RL circuits made up of Resistors and Inductors; and a combination of all three known as an RLC circuit.  The latter circuit will attain Resonance at the one frequency where the impedance of the coil equals the impedance of the capacitor. i.e.  where  Xc  =  Xl
Electro Magnetism When current passes through a conductor it sets up a magnetic field around the conductor.  This electro-magnetic effect is what makes generators, motors, and transformers work.
Motors and generators are both spinning magnetic fields; a generator has power applied to the armature; and a motor has power supplied to the stator or field. A transformer has no moving parts other than the Alternating Current itself. All three work on the principal of magnetic lines of force cut by electrical conductors. That is why motors are called induction motors.	D C Motor Generator Set
Transformers A transformer works on the principal of Induction.  The ratio of the transformer depends upon the turns ratio. If we have 1 turn in the primary of a transformer and four turns in the secondary we would have a 1 : 4 ratio.	(Iron Core x-frmr with ratio of 1 to 4)
Of course there would be hundreds of turns probably in each side of the transformer. There are transformers which have no core called air core transformers.   Others are iron core transformers because they use iron cores to wrap the wires around.	Iron Core Transformer
These iron cores become magnetized with each positive and negative cycle or hertz of the applied AC voltage. Therefore a 60 cycle AC signal would magnetize the coil 120 times (one for each positive and negative alternation.
Iron has a a resistance to being magnetized called Reluctance.  Reluctance causes hysteresis losses. The three primary losses of a transformer are copper resistance, eddy currents in the core, and hysteresis losses.
Efficiency is determined by dividing the  Output Power  by the Input Power of an electrical system. Transformers are one of the most efficient pieces of electrical equipment, generally 95% or better. [NOTE: Unless you are told otherwise on the exam.  Assume a power factor of Unity (no losses) and an efficiency of 100%]	Efficiency = Output / Input pf (power factor) = Watts / VARS The power factor of an AC electric power system is defined as the ratio of the real power (watts) to the apparent power (vars).
The one fact that will help you the most on the NEC exam is that the power on the primary of the transformer must be equal to the power on the secondary of that transformer. If I have a 4.8VA transformer it must be 4.8VA on the primary and the secondary.  (The exam assumes 100% efficiency)
So If we have  a 240 to 120 Volt 5KVA transformer our ratio is 2 : 1 so as the voltage is divided by a factor of 2 from primary to secondary; in order to maintain 5KVA our secondary current must double.	5,000/240 = 20.83A primary 5,000/120 = 41.66A secondary
Current and Voltage are inversely proportional to the turns ratio of the transformer.  This means as one goes up the other must go down.	The current is therefore inversely proportional from primary to secondary and vice versa to the voltage in a transformer; as one goes up the other goes down.
What I have shown you are engineering formulas.  The NEC Exam requires you use NEC Tables to solve the calculations on the test. My Online NEC Classroom will teach you How To calculate and design overcurrent protection and conductor size for the following : Motors Cooking Equipment Appliances Residential, Commercial, and Industrial Services Bonding and Grounding Conductors Conduit and Box Fill Mobile and Manufactured Homes RV and Mobile Home Parks Heating and Air Conditioning Special Equipment Ambient Temperature Corrections Emergency Systems Hospital Electrical systems Hazardous Locations	I teach you only what you need to know in order to pass the exam Cost is currently $49.95 Don't wait til the last year, last month, or last day to get your license. Do that and you'll most likely be looking for a new line of work! Add this page to your Favorites  Return to Wisconsin Master STUDENTS USE YOUR "BACK" BUTTON ON YOUR BROWSER TO RETURN TO THE TABLE OF CONTENTS