1.1What is current, really?

Picture a hosepipe. Water doesn't teleport from one end to the other — it's a continuous stream of water molecules moving past any given point. Current is exactly the same idea, but with electric charge instead of water. It's the amount of charge that flows past a point in a circuit every second.

Formally: Electric current is the rate of flow of charge. It's measured in amperes (A), or amps for short.

The little "Δ" symbol (delta) just means "change in". So ΔQ means "the amount of charge that has flowed" and Δt means "the time that has passed". You'll see this notation a lot in physics — don't let it intimidate you, it's just shorthand.

1.2Electric charge — the stuff that's actually moving

Charge is a property that some particles have. Protons are positively charged, electrons are negatively charged. In a solid metal wire, it's the electrons that are free to move around — they're the charge carriers.

Since one electron is 1.6×10⁻¹⁹ C, it takes a huge number of electrons to make just 1 coulomb — specifically 6.25 × 10¹⁸ electrons. That's why current in a wire looks "smooth" and continuous even though it's really billions of discrete tiny charges bumping along.

1.3Conventional current vs. electron flow — the classic trap

Here's something that trips up almost every student at least once: conventional current and electron flow point in opposite directions.

Electrons are negative, so they're repelled from the negative terminal and attracted to the positive terminal — they flow from − to +. But conventional current was defined before scientists knew electrons even existed, based on the (wrong!) assumption that positive charge was flowing. That definition stuck, so by convention we still say current flows from + to − around a circuit, even though what's physically moving (electrons) goes the other way.

1.4Measuring current

Current is measured with an ammeter, and it must always be connected in series with the component you're measuring — meaning the current has to flow through the ammeter on its way around the circuit. This works because current is the same at every point along a series circuit, so inserting the ammeter into the loop doesn't disturb what you're trying to measure (assuming it has negligible resistance).

2.1What is p.d., really?

Think of current as "how much water is flowing" and potential difference (p.d.) as "how much energy each bit of water is carrying" — like the difference between a gentle stream and a stream flowing down a steep hill. Both might have the same flow rate, but the one on the hill can do a lot more work (turn a bigger water wheel) because each drop carries more energy.

A cell or battery makes one end of a circuit positive and the other negative — this sets up a potential difference (also called voltage) across the circuit, which is what pushes charge around and does work.

So potential difference is literally the energy transferred per coulomb of charge as it moves between two points. A 12 V battery gives 12 joules of energy to every coulomb of charge that passes through it.

2.2Measuring voltage

Potential difference is measured with a voltmeter, connected in parallel (i.e. "across") the component you're measuring — not in the main current path. This is the opposite way round to an ammeter, and it's a very common exam trip-up.

3.1Defining resistance

Resistance is the opposition to current — think of it like friction in a pipe. A narrow, bumpy pipe (high resistance) lets less water through for a given push than a wide, smooth one (low resistance).

Resistance is measured in ohms (Ω). One ohm is defined as one volt per ampere — i.e. a resistance of 1 Ω means it takes 1 volt to push 1 amp of current through it.

• Higher resistance → smaller current (for the same p.d.)
• Lower resistance → larger current (for the same p.d.)

3.2Ohm's Law itself

R = V/I is always true — it's just a definition of resistance. Ohm's Law is a stronger, more specific statement:

The key phrase examiners look for is "directly proportional" AND "constant temperature". This means a component only obeys Ohm's Law if its I–V graph is a straight line through the origin — a resistor at constant temperature does this, but a filament lamp (which heats up) does not.

3.3Measuring resistance experimentally

To find a component's resistance, you build a circuit with a low-voltage power supply (typically 1–2 V, to avoid heating the component and changing its resistance), the component itself, an ammeter in series, and a voltmeter in parallel across the component. Take readings of I and V, then calculate R = V/I.

To get a full I–V graph, you add a variable resistor to the circuit so you can change the current and p.d. and take multiple readings, plotting current (y-axis) against potential difference (x-axis).

4.1Kirchhoff's First Law — the electric current rule

This is just the conservation of charge applied to a circuit junction. Charge can't be created or destroyed, and it can't pile up at a junction — so whatever flows in must flow out.

Key vocabulary: a junction is a point where at least three circuit paths meet; a branch is a path connecting two junctions. In a series circuit (no junctions), the current is the same everywhere. In a parallel circuit, current splits at each junction, but the total in always equals the total out.

4.2Kirchhoff's Second Law — the electrical voltages rule

This one is conservation of energy applied to a circuit loop. Every joule of energy the battery gives to the charge must be "spent" (transferred to other stores) as that charge goes around the loop and back to the battery — energy can't just vanish.

• Series circuit: the p.d. is split across all the components depending on resistance — the sum of the voltages equals the total e.m.f. of the supply.
• Parallel circuit: the p.d. is the same across each closed loop — the sum of voltages in each independent loop equals the total e.m.f.

5.1Resistors in series — resistances simply add

In series, the current has no choice but to flow through every resistor one after another — imagine several narrow sections of pipe joined end to end. Each one adds its own obstruction, so the total resistance just piles up.

Why this works (the derivation logic): In series, current I is the same through every resistor (Kirchhoff 1). The total p.d. is split: V = V₁ + V₂. Using V=IR for each: IR = IR₁ + IR₂. Since I is the same throughout, divide it out: R = R₁ + R₂. This tells you the combined resistance in series is always bigger than any individual resistor.

5.2Resistors in parallel — think "more paths, easier flow"

In parallel, current gets multiple alternative routes to choose from — like adding more lanes to a motorway. More lanes means traffic flows more easily overall, so adding resistors in parallel always decreases the total resistance, even though you're adding more components!

Why this works: In parallel, the p.d. is the same across every resistor (Kirchhoff 2): V = V₁ = V₂. The current splits: I = I₁ + I₂ (Kirchhoff 1). Using I = V/R for each: V/R = V/R₁ + V/R₂. Since V is the same, divide it out: 1/R = 1/R₁ + 1/R₂.

Quick check: the combined resistance in parallel is always less than the smallest individual resistor. If two equal resistors R are in parallel, the combined resistance is exactly R/2.

6.1Where the power equations come from

Power is just the rate of doing work (P = W/t). Combine that with V = W/Q and I = Q/t, and you get W = VIt, which leads straight to:

6.2The squaring effect — why doubling matters so much

Because I and V are squared in two of the three power equations, small changes in current or voltage cause much bigger changes in power:

• For a given resistance, if current or voltage doubles, power increases by a factor of 4 (2²).
• For a given power, if resistance doubles, current decreases by a factor of √2, and voltage increases by a factor of √2.

This is exactly why a small surge in mains voltage can cause a light bulb to blow — a modest voltage increase translates into a much bigger jump in power (and heat) being dissipated.

7.1Reading a component's "fingerprint"

Every electrical component has its own characteristic I–V graph shape — almost like a fingerprint that tells you what it is and how its resistance behaves as current changes. There are four shapes you must recognise instantly:

7.2Ohmic conductor (e.g. a resistor)

Current is directly proportional to p.d. — a straight line through the origin. This means the gradient (and therefore resistance, since gradient = 1/R) is constant. This is the only shape that truly obeys Ohm's Law.

7.3Semiconductor diode

A diode only lets current flow easily in one direction (forward bias — the direction of the arrowhead symbol), shown by the sharp upward curve on the right of the graph. In the opposite direction (reverse bias), almost no current flows at all — shown by the flat line hugging zero on the left. The diode only "switches on" once the p.d. crosses a threshold voltage, typically around 0.6 V.

7.4Filament lamp

As current increases, the filament gets hotter. Since it's a metal, higher temperature means higher resistance (more vibrating atoms = more collisions with the flowing electrons = harder to push current through). This growing resistance makes the current increase at a slower and slower rate as p.d. rises — giving the 'S' shaped curve. It does obey Ohm's Law for very small voltages (before it heats up much) but not overall.

7.5Thermistor

This is the opposite behaviour to a filament lamp! As current increases, the thermistor heats up, but in a thermistor higher temperature causes lower resistance (unlike a metal). Lower resistance lets even more current flow for each extra volt, so the graph curves upward more and more steeply — the reverse curve shape to the filament lamp.

Laws to know word-for-word

• Ohm's Law: The current through a component is directly proportional to the potential difference across it, providing the temperature is constant.
• Kirchhoff's 1st Law (current rule): The algebraic sum of the currents entering and leaving a junction is equal to zero.
• Kirchhoff's 2nd Law (voltages rule): The sum of the e.m.f.s in a closed circuit loop is equal to the sum of the potential differences around that loop.