Almost everything in this skill is one idea applied at different speeds. A voltage pushes, something resists, and a current results — that is direct current (DC). Let the push reverse many times a second and you get alternating current (AC), where components that did nothing in a steady circuit suddenly dominate it, because they respond to change rather than to level. Magnetism is what links the two worlds: a changing field makes a voltage, which is how power reaches you at all. Read this for the shape — what causes what, which quantity is shared and which divides, and where the everyday intuitions quietly fail.
Each chapter opens with the short version. Tap one to read the detail.
Charge, current, and the direction nobody means literally
~2 min
Whether a material conducts comes down to how tightly its atoms hold their outer electrons. Current then has two directions in circulation at once: electrons move one way, and the convention everybody draws points the other.
Start with why copper conducts and rubber does not. A conductor is a material whose electrons are loosely bound to their atoms, so a large number of them move freely; copper, silver and gold each have a single valence electron, which is what puts them at the top of the list. An insulator is the mirror image — electrons tightly bound, needing large amounts of energy to free them, with valence shells that are more than half filled. Conduction is a property of that binding, not of how a material looks or feels.
Now the direction, which trips up almost everyone. Electron flow runs from the negative side of the source, through the wire, and back to the positive side: negative potential to positive potential. But as electrons vacate their atoms they leave behind positively charged vacancies — holes — and those effectively travel the opposite way. That flow of positive charge is conventional current, and it is what circuit diagrams draw.
So both answers are correct and they point in opposite directions. Neither is a mistake; they are two descriptions of one event, and the only error is mixing them inside a single explanation.
Keep one more distinction straight from the start: direct current flows continuously in the same direction, as from a battery, while alternating current periodically reverses, as in household supply. Everything later in this guide is one of those two cases.
Rule: answer in conventional current unless the question says electron flow — and when you read a diagram, remember its arrows show positive charge moving, not electrons.
Ohm's law, stated three ways on purpose
~2 min
Voltage, current and resistance are one relationship you can enter from any side. The handbook states it three ways deliberately, because which form you need depends on which quantity is missing.
Ohm's law fixes the relationship between the three basic quantities. Applied voltage equals circuit current times circuit resistance: E = IR. Rearranged, current equals applied voltage divided by resistance: I = E/R. Rearranged again, resistance equals voltage divided by current: R = E/I.
Those are not three facts to memorize but one fact entered from three doors, and the training material states all three explicitly for a practical reason — in a real problem you are always given two of the components and asked for the third. Deciding which form to use before you start is most of the work.
The quantity people neglect is the one that actually gets things hot. Power is what the circuit dissipates, and it can be written from any pair you already have: from voltage and current, from current and resistance, or from voltage and resistance. A component fails on power, not on voltage alone, which is why a resistor of the right resistance can still burn out in the wrong circuit.
Conductance is worth knowing as the reciprocal of resistance — the same physical fact described from the other end, useful because parallel branches add conductances where they do not add resistances.
Rule: identify which of E, I and R you are missing, then pick the matching form of Ohm's law — and if the question is about heat, damage or rating, it is a power question, not a resistance one.
Series and parallel: what is shared, what divides
~2 min
Series shares current and divides voltage; parallel shares voltage and divides current. One consequence is worth committing to memory, because it is the check that catches most arithmetic errors.
Two resistors in series carry the same current and split the voltage between them, so their resistances add. That is the voltage divider: with a known total current, each drop is simply that current times that resistor, and the drops sum to the supply.
In parallel the resistors see the same voltage and split the current. The combined value is called the equivalent resistance — described in the handbook as the total circuit resistance as seen by the voltage source, found by dividing source voltage by total circuit current.
Here is the consequence that catches people, and the handbook states it without qualification: in all cases the equivalent resistance will be less than any of the individual parallel circuit resistors. That feels wrong, because adding components sounds like it should add opposition. It does not, and the reason is the source's point of view — more paths means more total current drawn for the same voltage, so the resistance the source sees must fall.
The practical version: two 100-ohm resistors in parallel give 50 ohms, and adding a third branch of 1,000 ohms pulls the total down again, never up. Any parallel answer larger than the smallest branch is an arithmetic error you can catch without redoing the sum.
Rule: name what is shared before you calculate. Same current means series and voltages add; same voltage means parallel and currents add — and a parallel total above the smallest branch is always wrong.
Induction: only change makes a voltage
~2 min
A magnetic field sitting still induces nothing. A voltage appears only while the field through a circuit is changing, and the polarity of that voltage always fights the change that caused it.
Induction is the bridge between the magnetic and electrical halves of this subject, and it has one precondition: something must be changing. A conductor moving through a magnetic field has a voltage induced in it; the size depends on the parameters you vary — field strength, the length of conductor in the field, and how fast the two move relative to each other.
The misconception to kill early is that a strong magnet held near a coil produces a voltage. It does not. Strength is not the trigger; change is. This is why a generator that stops turning stops generating, and why the card reader needs the swipe rather than the card resting on it.
Then there is the direction, and the handbook gives it in one sentence worth holding onto: Lenz's law states that an induced voltage will have a polarity that will oppose the magnetic field that caused the induced voltage. Read that as a statement about resistance to change — the induced effect always pushes back against whatever produced it. That is also why generators are harder to turn when loaded: the current you draw creates the opposition you feel.
Rule: if nothing is changing, nothing is induced. When a problem hands you a field strength but no motion and no time variation, the induced voltage is zero — and when it does induce, expect the polarity to oppose.
Alternating current and the numbers that are quoted
~2 min
An AC wave averages to zero over a cycle, which is useless for describing how much work it does. The figure everyone quotes instead is the effective, or RMS, value — 0.707 of the peak.
In an alternating-current circuit the current and voltage reverse direction continuously, so the plain average over a full cycle is zero. That number describes nothing about how much a heater heats, so a different one is needed.
The handbook builds it rather than asserting it. Plot the current, then plot the current squared: the squared curve has twice the frequency and varies about a new axis that is always positive. The average of those squared values is half the peak squared, and the square root of that average is the effective value. Work it through and the effective value is the peak divided by the square root of two — in the handbook's own working figure, 0.707 times the maximum.
That is where the name comes from: root of the mean of the squares, RMS. It is called the effective value because it is the DC current that would do the same heating.
Keep its companion straight too, because the two are easy to swap: the average value over a half cycle is 0.637 times the peak, a different number for a different purpose. Mixing the two, or mixing either with the peak, is the classic error — and it is silent, because the answer still looks plausible.
Rule: assume any AC voltage or current you are quoted is RMS unless it says peak, and convert once, at the start, so a single calculation never carries two conventions.
Reactance and impedance: opposition that depends on frequency
~2 min
Capacitors and inductors oppose alternating current by an amount that changes with frequency, and they shift current out of step with voltage. Combine that with resistance and you get impedance, the AC replacement for R.
A resistor opposes current identically at every frequency. Capacitors and inductors do not — their opposition, called reactance, is computed from the operating frequency, which is the whole point. Give a capacitor a higher frequency and its capacitive reactance falls; give an inductor a higher frequency and its inductive reactance rises. The component did not change; only the frequency did.
The mistake to clear first is the shorthand that a capacitor simply "blocks DC and passes AC", as though it were a switch. It is not — and the error matters, because it makes people treat one number as the answer for a part whose opposition is different at every frequency. It is a slope, not a switch: the same part offers very different opposition at 50 hertz and at 5 kilohertz.
Each also shifts the timing between current and voltage, in opposite directions — which is why they partly cancel rather than simply adding. Impedance is the vector sum of the resistance and the net reactance in a circuit, and because the two reactances oppose one another it is the net figure that counts, never the two added arithmetically.
Two things then make impedance easy to use. First, it plays exactly the role resistance plays in DC — the handbook puts it plainly: impedance in an AC circuit corresponds to the resistance of a DC circuit, and the voltage drop across an element is V = IZ. Ohm's law survives intact, with Z in place of R. Second, the angle that falls out of the vector sum, the phase angle, is not decoration: it states the phase relationship between the applied voltage and the current.
Rule: reactance is meaningless without a frequency — quote one or you have said nothing. And add resistance to reactance as perpendicular quantities, never by simple addition.
The p-n junction, and turning AC into DC
~2 min
Joining p-type and n-type material makes a junction that conducts easily one way and barely at all the other. That asymmetry is a diode, and pointing diodes at an AC supply is how rectifiers produce DC.
A hole is a vacancy in the electron structure of a material, and it behaves as a positive charge. Hold onto that, because the whole junction story is told in holes and electrons moving toward each other.
A diode is forward biased when the positive terminal of a source is connected to its anode and the negative terminal to its cathode. The source's positive side repels holes in the p-type material toward the p-n junction while the negative side repels electrons toward it from the other direction; carriers reach the junction, some break through, and holes and electrons combine on the far sides. Current flows. Reverse the connection and the carriers are pulled away from the junction instead of toward it, so conduction largely stops.
That is the entire behavior of a diode, and it is worth noticing what it is not: not a component with a resistance you can quote, because the relationship between voltage and current is not proportional. A diode is the standard example of a part that Ohm's law does not describe.
The payoff is rectification. One diode in series with an AC supply passes only the half-cycles of one polarity — a half-wave rectifier, which throws half the input away. Arrange several so that both halves of the cycle are routed the same way through the load and you have a full-wave rectifier, which is why mains AC can feed equipment that needs DC.
Rule: work out which way the source pushes the carriers. Toward the junction means forward bias and conduction; away from it means reverse bias and effectively none — and never try to assign a diode a resistance.
What actually injures people
~2 min
Regulators frame the danger as four outcomes — shock, electrocution, fire and explosion — and most injuries trace to a short list of ordinary failures rather than exotic faults.
The Occupational Safety and Health Administration (OSHA) frames its electrical standards around protecting people from shock, electrocution, fires and explosions. Worth noticing that fire and explosion sit beside shock: a circuit can injure without anyone touching a conductor.
The named causes are ordinary rather than exotic. OSHA lists contact with power lines, lack of ground-fault protection, a path to ground that is missing or discontinuous, equipment used in a way it was not prescribed for, and improper use of extension and flexible cords. None of those is an unusual fault; they are routine conditions left uncorrected.
Arc flash is treated as its own hazard, with the framing question being whether work is happening energized, or deenergized but not locked out. That distinction — deenergized is not the same as safe — is the part most often skipped.
This is orientation, not a safety qualification: real work is governed by the standards themselves and by local rules, and nothing here substitutes for them.
Rule: before touching anything, answer OSHA's own question — is this energized, or deenergized but not locked out? Only the second, with the lockout actually done, is a safe state.
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