Electrical Theory

Competency 2.0 is the physics underneath everything else: what the atom is and why its electrons matter, magnetism and its link to electricity, what electricity is used for, how motors and generators work, current, voltage and resistance, resistive materials, capacitors and inductors, reactance and impedance, voltage sources and AC values, Ohm's law and power. This page follows ETA's list in order, with section 15 as job practice. The Atomic Structure, Ohm's Law, Capacitors and Inductors lessons in the Study Hub teach several of these topics step by step; this page links to them rather than repeating them.

The atom and electric charge

Competency 2.1 asks you to describe atomic structure, the parts of the atom, their charges and why they matter in electronics. NEETS: an atom has a heavy nucleus of protons, which are positive, and neutrons, which have no charge, with light electrons around it. The electron and the proton carry the same amount of charge, of opposite sign, although the proton has about 1836 times the electron's mass (NIST: 1836.15; NEETS rounds it to 1837). A neutral atom has as many electrons as protons; one that loses an electron becomes a positive ion. The number of protons is the atomic number, which identifies the element.

The electrons sit in shells, and the outermost, the valence shell, decides how a material behaves. In a metal, NEETS explains, the atoms are packed so closely that one, two or three outer electrons per atom are hardly attached to any one atom: they are free electrons, and their drift is current. That is why metals are conductors, why tightly bound materials are insulators, and why silicon, in between, can be made into diodes and transistors. The Atomic Structure lesson in the Study Hub shows the shells of copper, silicon and argon in its atom widget; the Periodic Table lists every element's valence electrons.

Like charges repel and unlike charges attract. Charge is measured in coulombs: one coulomb is the charge of about 6.24 × 10¹⁸ electrons (since 2019 the electron's charge is defined as exactly 1.602176634 × 10⁻¹⁹ C, per NIST; older texts round this to 6.25 × 10¹⁸), and NEETS defines one ampere as one coulomb passing a point in one second.

Magnets and magnetic fields

Competency 2.2 asks for the principles of electromagnetism, and 2.2.1 for the different types of magnetic fields. NEETS sorts magnets by where their field comes from:

A magnet's field is drawn as lines of force (flux) that leave its north pole and enter its south pole; like poles repel and unlike poles attract, and the earth itself is a huge natural magnet. The shape of the field depends on what makes it:

• Around a straight wire carrying current: circles around the wire, in planes at right angles to it, with no north or south pole (NEETS, Kuphaldt). Reverse the current and the circles reverse direction.
• Around a coil: the circles of the turns join into one field with a north and a south pole, like a bar magnet's. NEETS lists what sets its strength: the number of turns, the current, the coil's length-to-width ratio and the core material.
• Steady or alternating: direct current makes a steady field; alternating current makes a field that builds, collapses and reverses every half-cycle. That changing field is what section 3 puts to work.

How electricity and magnetism are linked

Competency 2.2.2 asks you to explain the direct relationship between electricity and magnetism. It runs both ways:

• Current makes magnetism. In 1820 Hans Christian Oersted showed that a current in a wire deflects a compass needle: every current is accompanied by a magnetic field at right angles to it. Kuphaldt's left-hand rule gives the direction: with the thumb along the electron flow, the curled fingers show the field. Texts that use conventional current do the same with the right hand.
• Changing magnetism makes voltage. Michael Faraday found that a voltage appears across a wire whenever the magnetic flux cutting it changes. This is electromagnetic induction. NEETS lists three conditions: a conductor, a magnetic field, and relative motion between them, so that the conductor cuts the lines of force. Stop the motion and the voltage stops; reverse it and the voltage reverses.

Kuphaldt states Faraday's law: the induced voltage equals the number of turns times the rate of change of the flux. Faraday's law itself is not on ETA's sheet, but its consequences are: the sheet's inductor voltage, V = L(di/dt), is the same law applied to a coil's own field (section 10).

Lenz's law gives the direction. NEETS: the voltage a coil induces in itself, the counter emf, always opposes the change in current that caused it. That opposition to change is what an inductor is, and it is why a motor draws less current once it is turning (section 6).

Uses of magnetism

Competency 2.3 asks for uses of magnetism in electronics. NEETS: much of today's equipment could not work without it.

Uses of electricity

Competency 2.4 asks you to explain basic uses for electricity. The U.S. Energy Information Administration: we use electricity for lighting, heating, cooling, refrigeration, operating appliances and machinery, and public transportation. Every one of these is a conversion. NEETS describes power consumption the same way: an electrical device converts electrical energy into another form, and its power rating, in watts, says how fast.

Motors and generators

Competency 2.5 asks you to describe how electricity runs a motor and how mechanical motion makes a generator produce current, and 2.5.1 points to ETA's EM5 module for more depth. The two machines are built from the same parts, and NEETS notes that most DC generators can be run as motors and vice versa.

• Generator. NEETS: a generator converts mechanical energy into electrical energy by magnetic induction. Conductors (the armature) are turned through the field of the pole pieces; the voltage depends on the field's strength, the angle and speed at which the conductors cut it, and the length of conductor in the field. A loop turning at a steady rate in a uniform field gives a sine wave. An AC generator (alternator) brings it out through slip rings; a DC generator uses a commutator, a split ring that reverses the loop's connections each time its voltage reverses, so the output is pulsating DC.
• Motor. NEETS: a current-carrying conductor in a magnetic field, at right angles to the flux, tends to move at right angles to the flux. The armature becomes an electromagnet, its field and the field poles' push and pull, and the commutator keeps the armature current in the direction that keeps it turning.
• Counter emf. A turning motor is also a generator. Its generated voltage opposes the supply (counter emf) and holds the armature current down. NEETS: it does not exist until the armature begins to turn, and the armature's DC resistance is very low, so a motor draws a large current at start, which is why large DC motors use starting resistors.

Current, voltage and resistance

Competency 2.6 asks you to explain the differences between current, voltage and resistance. The Ohm's Law lesson in the Study Hub teaches all three with the water-pipe picture; in short:

Voltage can exist with no current (a battery on the shelf), but current needs both a voltage and a complete path. Resistance sets how much current a given voltage drives, which is Ohm's law (section 13).

Resistive materials and resistors

Competency 2.7 asks you to tell the types of resistive materials apart and explain how resistors are used. NEETS gives four things that set a conductor's resistance: the material (how many free electrons it has), the length (resistance is directly proportional to it), the cross-sectional area (inversely proportional) and the temperature. Kuphaldt puts the first three into one formula, which is not on ETA's sheet, with ρ the material's specific resistance (resistivity):

Temperature coefficient. Most conductors have a positive coefficient: resistance rises as they warm. Carbon has a negative one, and alloys such as constantan and manganin are close to zero, which suits precision resistors (NEETS). The last column of the color-code chart on ETA's sheet is a resistor's temperature coefficient in ppm per degree; a thermistor is a resistor built to have a large one.

How resistors are used: to limit current (an LED's series resistor), to divide a voltage (a bias network or a volume control), to set a time constant with a capacitor, and to load a source. Every resistor has a power rating, the heat it can safely dissipate; section 14 sizes one. Color codes and standard values are in Component Values and the Resistor Tools, and ETA lists resistor types again under Competency 3.1.

Capacitors: purposes, types and construction

Competency 2.8 asks for the purposes of capacitors and their common types and construction. A capacitor is two conductive plates separated by an insulator, the dielectric; it stores energy in the electric field between them. Kuphaldt and Murata give the same three ways to raise its capacitance: more plate area, less spacing between the plates, and a dielectric of higher permittivity. One farad stores one coulomb at one volt. The Capacitors & Reactance and Capacitor Charging lessons in the Study Hub cover reactance and the RC time constant.

Purposes: Murata lists noise removal, supply-voltage smoothing and filters, plus decoupling a power supply; its first lesson shows a capacitor holding a lamp steady while the supply dips, which is short-term energy storage. A capacitor blocks DC once charged but appears to pass AC, because it keeps charging and discharging (Murata), which is how it couples a signal from one stage to the next while blocking DC. With a resistor it sets a time constant (the sheet's τ = R × C), and with an inductor it tunes: NEETS's variable capacitor tunes most radio receivers.

ETA's sheet has three capacitor formulas: the charge, the stored energy, and the current that flows while the voltage changes (the sheet writes it I = C(dV/dt)):

Inductance and coils

Competency 2.9 asks how inductance relates to magnetism, and for coil construction, cores and uses. Inductance is magnetism turned back on the circuit that made it: when a coil's current changes, its own changing field cuts its own turns and induces a counter emf that opposes the change (Lenz's law, section 3). Winding the wire into a coil makes every turn's field cut the other turns, so a coil, or inductor, has far more inductance than a straight wire. The Inductors & Reactance lesson in the Study Hub covers X_L and the voltage spike when a coil is switched off.

Cores. An air core (or a nonmagnetic form) gives low, stable inductance for RF coils. An iron core gives high inductance for power-frequency chokes and transformers, built from thin insulated laminations to cut eddy-current losses (Kuphaldt). For radio frequencies, Kuphaldt notes cores of insulated iron powder, which keep eddy currents small at high frequency; his LVDT example uses a ferrite core at 1 to 200 kHz. Uses: chokes that pass DC and block AC (Kuphaldt: "choke" comes from blocking high-frequency AC in radio circuits), power-supply filters, tuned circuits with a capacitor, transformers, and relay and solenoid coils.

Diameter and wire size. Competency 3.3.1 asks how a coil's diameter and wire size affect its values. Diameter acts through the coil's area: Kuphaldt lists coil area as one of the four factors that set inductance, with the turns, the length and the core, and NEETS puts it as twice the radius, four times the inductance (the table above). Wire size is not on either list; it changes the inductance only through the turns it leaves room for. On a given form, heavier wire takes more room per turn, so fewer turns fit, and with inductance going as the square of the turns, the inductance falls. What heavier wire does change directly is the winding's resistance. Lower resistance wastes less power as heat and lets the coil carry more current (Kuphaldt: transformer windings must be of the proper gauge to avoid heating), and it raises the coil's Q, because Q = X / R (Kuphaldt; section 5 of the Circuits guide). A 10 mH winding at 1 kHz has X_L = 6.28 × 1000 × 0.01 ≈ 62.8 Ω; counting only the wire's resistance, from the Wire Gauge tool's copper table at 20 °C:

Why cores are laminated. Competency 3.4.2 asks why laminations are used. Kuphaldt: iron conducts electricity as well as magnetic flux, so the core's changing field induces currents in the iron itself. These eddy currents circulate through the core's cross-section and turn power into heat, perhaps the most significant of a transformer's core losses. Building the core from thin sheets, each coated with insulating varnish, leaves very little width for the eddy currents to circulate in, which is why laminated cores are standard in almost all low-frequency transformers. Eddy-current loss rises with frequency, so 400 Hz transformers for aircraft and military use need thinner laminations, and at radio frequencies cores are made of iron powder whose granules are each insulated, or the coil is wound on air and has no core loss at all.

Reactance, resistance and impedance

Competency 2.10 asks you to compare reactance with resistance and describe the current and voltage relationships, and 2.11 to compare impedance with both and explain its causes and effects.

ETA's sheet gives both reactances and the series impedance. Inside the square root, X_L and X_C subtract: the combined reactance is their difference, because they act in opposite directions, and resistance and reactance add at right angles, never directly.

Phase angles, polar and rectangular form, and circuits that are inductive or capacitive are in sections 3 and 4 of the Circuits guide; the reactance and impedance calculators are in the Calculator Suite.

Voltage sources and AC values

Competency 2.12 asks you to list voltage sources, AC and DC, batteries and natural generation. NEETS lists six ways to produce a voltage:

DC sources are cells and batteries, DC power supplies, solar cells and thermocouples; AC sources are alternators (the utility supply), transformers fed from them, and oscillators and signal generators. A primary cell can't practically be recharged; a secondary cell can, by forcing current back through it (Kuphaldt, NEETS). Every cell has internal resistance, so its terminal voltage sags under load. ETA's sheet has the formula:

Competency 2.12.1 asks you to identify peak, peak-to-peak and RMS values of AC sources. The peak is the height from zero to a crest; peak-to-peak is crest to crest, twice the peak for a sine wave; and the RMS (effective) value is the DC voltage that would heat the same resistor equally (Kuphaldt). RMS is what an AC voltmeter reads and what a 120 V outlet is rated in; a scope shows peak and peak-to-peak. ETA's sheet gives the sine-wave conversions:

Competency 2.12.2 asks you to identify duty cycle and pulse width of DC sources. The pulse width is the time the pulse is on (Tektronix measures it at 50% of the full voltage), and the duty cycle is the on time as a percentage of the whole period: Fluke's example is a signal on 60% of the time and off the other 40%. The average voltage follows the on time, which is how pulse-width modulation varies the power to a lamp, a heater or a solenoid. The formula is not on ETA's sheet:

See peak, RMS and average change on the Sine Wave Lab, and battery chemistries and run time in the Battery Calculator and the Power Supplies guide.

Ohm's law

Competency 2.13 asks you to list Ohm's law formulas for current, voltage, resistance and power, and 2.13.1 to calculate problems with each. ETA's sheet prints them as a wheel of twelve, using E for voltage:

Step-by-step practice is in the Ohm's Law lesson in the Study Hub, all twelve forms are on the Ohm's Law Wheel, and the numeric drills generate new Ohm's law problems every time.

Power consumption and requirements

Competency 2.14 asks you to explain how to calculate power consumption and requirements. Power, in watts, is the rate of using energy. Energy is power over time: NEETS defines the watt-hour as one watt used for one hour, and the kilowatt-hour (kWh), the unit on a utility bill, as 1000 watt-hours. Motors are often rated in horsepower, and NEETS gives one horsepower as 746 W. Efficiency is the useful power out divided by the power in, always less than 1: a device with an efficiency of 0.95 delivers 95 W for every 100 W it takes in, and loses 5 W as heat. None of these is on ETA's sheet:

Power requirements run the other way: add up what the loads need, then allow a margin. NEETS's rule for resistors is a 50% safety factor, so a resistor that dissipates 2 W gets a 3 W rating; carbon resistors come in 1/8, 1/4, 1/2, 1 and 2 W, and wirewound above 5 W. A power supply or battery must cover the largest load it will see, such as a mobile radio's transmit current, not just the idle current.

The Battery Calculator works a power budget and run time.

On the job: theory at the bench

Job practice, not exam content. These checks apply the sections above at the bench. The service manual and your employer's procedures come first.

1. Measure resistance with the power off. An ohmmeter supplies its own small current, and a part still in the circuit is measured in parallel with everything else across it; the Test Equipment guide covers in-circuit testing.
2. Test a battery under load. Internal resistance only shows when current flows (section 12), so a weak battery can read normal open-circuit and sag under load. Check the terminal voltage while it supplies a known load.
3. Know what the meter reads. Kuphaldt: average-responding meters are calibrated in RMS for a sine wave, and their reading is wrong on other waveshapes; a true-RMS meter reads correctly whatever the shape. On pulse and switching waveforms, use a true-RMS meter or a scope.
4. Mind the polarity of electrolytics. Kuphaldt: reverse voltage can destroy an electrolytic's thin dielectric. Match the marked lead when replacing one, and match or exceed its voltage rating.
5. Expect a motor's starting current. A motor draws far more current at start than running, because it has no counter emf until it turns (section 6). A motor that draws starting current all the time may be stalled or jammed.