Electrical laws

In plain English: Push harder (more volts) and more current flows; add resistance and less flows. Cover the quantity you want in the triangle and what remains is the formula.

Where you'll meet it: Sizing LED resistors, predicting current draw, working out what a mystery resistor is doing — the single most used equation in electronics. Note it only holds for ohmic materials: diodes, LEDs and filament bulbs don't obey it.

In plain English: A longer wire is a longer straw — harder to push through. A thicker wire is a wider straw — easier. The material sets the baseline: copper's ρ is tiny, nichrome's is deliberately large. Warming a metal raises R roughly as R = R₀(1 + αΔT).

Where you'll meet it: Choosing wire gauges, understanding why long thin PCB traces drop voltage, designing shunt resistors and heating elements, and why sensor leads matter in precision work.

In plain English: Volts are the push, amps are the flow — multiply them and you get how much energy per second is being converted. Combine with Ohm's law to get the I²R and V²/R forms.

Where you'll meet it: Choosing resistor wattage ratings, sizing power supplies and heatsinks, estimating battery life. If a part is getting hot, this law says exactly how hot-headed it is.

In plain English: Current squared is the headline: double the current through a wire and it makes four times the heat. This is why fuses blow and why thick wires exist.

Where you'll meet it: Explains fuse ratings, wire gauge choices, and why a slightly overloaded resistor smells the way it does. It is Watt's law (I²R) accumulated over time.

In plain English: Charge doesn't pile up at a junction. Whatever flows in must flow out — like water at a pipe tee. If 3 A comes in and one branch takes 1 A, the other carries 2 A, no exceptions.

Where you'll meet it: Splitting current between parallel branches, checking that measured branch currents add up, and the basis of nodal analysis in circuit theory courses.

In plain English: Walk any complete loop and the volts gained from sources exactly equal the volts dropped across components — like returning to the same floor after a walk up and down stairs.

Where you'll meet it: Voltage dividers, working out the drop left over for an LED after its resistor, and mesh analysis. If your loop doesn't sum to zero on paper, you've missed a drop.

In plain English: Like charges push, opposite charges pull, and the effect dies off fast with distance — halve the gap and the force quadruples. It is the electrical twin of Newton's gravity law.

Where you'll meet it: Explains static shocks, why capacitor plates attract, and how CRTs and electrostatic speakers steer charge. The starting point of all electrostatics.

In plain English: Imagine charge as a sprinkler and field lines as water: count the lines crossing any bag you draw around it and you know how much charge is inside — the bag's shape doesn't matter.

Where you'll meet it: Derives the field inside coax cable and between capacitor plates, and explains shielding: inside a closed conductor the enclosed charge is zero, so a metal case blocks external fields (the Faraday cage).

In plain English: Magnetic field lines never start or end — they always close into loops. Snap a magnet in half and you get two smaller magnets, never a lone north pole. Whatever flux enters a closed surface must leave it.

Where you'll meet it: Why every field-line diagram you draw must close on itself, why transformer cores are designed as closed magnetic loops, and one of Maxwell's four equations.

In plain English: Current creates a magnetic field circling around it — wrap your right hand around the wire with the thumb along the current and your fingers show the field direction.

Where you'll meet it: Gives the field of straight wires, solenoids and toroids — the design math behind inductors, electromagnets and clamp meters (which measure current by its magnetic field alone).

In plain English: The magnetic cousin of Coulomb's law: add up the tiny field from every scrap of wire to get the total. Ampère's law is the shortcut when the geometry is symmetric; this works everywhere.

Where you'll meet it: Calculating the field of loops and coils where Ampère's law has no easy symmetry — e.g. the field at the centre of a single circular loop, a standard exam and viva question.

In plain English: Parallel currents pull together, antiparallel currents push apart — each wire sits in the other's magnetic field. Two wires 1 m apart carrying 1 A each feel exactly 2 × 10⁻⁷ N per metre; that tidy number is no accident — it's how the ampere itself was defined until 2019.

Where you'll meet it: The old SI definition of the ampere, busbar bracing in switchgear (fault currents slam parallel conductors together violently), and the standard 'force between parallel conductors' exam numerical.

In plain English: A changing magnetic field through a coil creates a voltage. Change it faster, or add more turns, and you get more volts. A steady field induces nothing — it's the change that counts.

Where you'll meet it: The working principle of transformers, generators, guitar pickups, induction cooktops and wireless charging. Also why an inductor fights any change in its current.

In plain English: Nature resists change: push a magnet into a coil and the coil pushes back; pull it out and the coil tugs it back in. Energy conservation wearing a magnetic costume.

Where you'll meet it: Explains the flyback voltage spike when you switch off a relay coil (and why it needs a flyback diode), eddy-current brakes, and why motors draw less current once spinning (back-EMF).

In plain English: The electric field pushes a charge along the field; the magnetic field pushes it sideways — always at right angles to its motion, so it steers the charge but never speeds it up.

Where you'll meet it: The force that spins every motor (F = BIL on a wire), deflected the beam in CRT TVs, bends particle paths in mass spectrometers, and generates the voltage in Hall-effect sensors.

In plain English: Same three fingers, two jobs: left hand when current causes motion (motor), right hand when motion causes current (generator). Remember the left-hand fingers as F-B-I from thumb inward: Force, field (B), current (I).

Where you'll meet it: Every 'which way does it spin / which way does current flow' question — motors, generators, loudspeakers, and the direction check when wiring a DC motor at the bench.

In plain English: Swap volts→ampere-turns, current→flux, resistance→reluctance and every series/parallel trick from circuits works on magnetic cores. Iron has tiny reluctance; even a hairline air gap has huge reluctance and hogs most of the MMF.

Where you'll meet it: Transformer and machine core design, why air gaps dominate an inductor's behaviour, and the standard magnetic-circuit numericals: series cores, parallel limbs, gap plus iron path.

In plain English: Every coulomb of charge escorts a fixed number of ions to the electrode, so twice the current or twice the time deposits exactly twice the metal.

Where you'll meet it: Electroplating and anodising calculations, copper plating of PCB through-holes, and the reason battery capacity is rated in ampere-hours — charge is chemistry.

In plain English: Pass the same charge through silver and copper cells in series: you get more grams of silver because each silver ion needs only one electron while copper needs two, and silver atoms are heavier.

Where you'll meet it: The classic series-cells exam problem, and how the coulomb (and the ampere before 2019) was once defined — by weighing deposited silver.

In plain English: Light spreads out over a growing sphere, so double the distance and the same light covers four times the area — a quarter of the brightness. Same geometry as Coulomb's and gravity's inverse squares.

Where you'll meet it: Lux-level design for rooms and streets, photography exposure, and every 'find the illuminance under the lamp' numerical in the Utilization paper.

In plain English: Tilted light smears over more area, so it's dimmer — the same reason winters are cold: the sun's rays arrive at a slant. At the point directly below a streetlight θ = 0 and you get full brightness; down the road it falls off fast.

Where you'll meet it: Streetlight spacing design, combining with the inverse square law for the standard 'illumination at a point away from the lamp post' problem (E = I·cos³θ/h² form).