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Electricity underpins almost every modern technology, from the phone in your pocket to the national grid. Before we can analyse circuits, light bulbs, potential dividers or semiconductors, we need to be completely secure with the two most fundamental quantities in electrical physics: electric charge and electric current.
This lesson opens OCR A-Level Physics A Module 4.2 (Electrons, waves and photons), specifically Section 4.2.1 (Charge and current). Everything that follows in Module 4 — drift velocity, resistance, Kirchhoff's laws, potential dividers, even photoelectric effect calculations — rests on the definitions introduced here.
Electric charge (symbol Q) is a fundamental property of matter, just like mass. It is measured in coulombs (C) in the SI system. Charge comes in two varieties, positive and negative, and objects with opposite charges attract while those with like charges repel.
The charge carriers relevant at A-Level are:
| Particle | Charge | Magnitude |
|---|---|---|
| Electron | Negative | e = 1.60 × 10⁻¹⁹ C |
| Proton | Positive | +e = +1.60 × 10⁻¹⁹ C |
| Ion | Positive or negative | integer multiple of e |
The magnitude of the electron's charge, e = 1.60 × 10⁻¹⁹ C, is called the elementary charge. It is one of the most important constants in physics and you must commit it to memory — OCR does provide it on the data sheet, but you will use it so often that looking it up every time wastes precious exam seconds.
Exam Tip: When writing e in calculations, always include the units: e = 1.60 × 10⁻¹⁹ C. Dropping the units is a classic way to lose a mark for "incomplete working".
One of the deepest experimental facts in physics is that electric charge is quantised. This means any observed charge is always an integer multiple of the elementary charge e:
Q = ± n·e, where n = 0, 1, 2, 3, …
You cannot have half an electron's charge on a normal object. Even though quarks (inside protons and neutrons) carry fractional charges of ±e/3 and ±2e/3, they are never found in isolation, so the smallest free charge we measure is always e.
This was demonstrated experimentally in 1909 by Millikan's oil drop experiment, which you may see referenced in the exam. Millikan balanced tiny charged oil droplets in an electric field and measured the minimum possible change in their charge — every answer was an integer multiple of e.
A small metal sphere carries a charge of −4.8 × 10⁻¹⁸ C. How many excess electrons does it have?
Always check: the answer must be a whole number. If you get 30.04 electrons, you have a rounding error or a wrong exponent.
Electric current (symbol I) is the rate of flow of electric charge. Its SI unit is the ampere (A), one of the seven base units.
I = ΔQ / Δt
If a steady current of I amperes flows for time t seconds, the total charge transferred is:
Q = I · t
One coulomb is defined as the charge that passes a point in a circuit when a current of one ampere flows for one second: 1 C = 1 A s.
A current of 0.25 A flows through a resistor for 2.0 minutes. Calculate the total charge transferred.
How many electrons does this correspond to?
That is a staggering number — nearly 200 billion billion — passing every point of the wire in just two minutes. Electrical circuits move enormous numbers of charge carriers.
Here is a historical quirk that traps careless candidates every year. When Benjamin Franklin defined the direction of current in the 18th century, he did not know about electrons. He chose positive to negative as the direction of "current flow" — which turned out to be the opposite of the direction the (negatively charged) electrons actually move.
We now know:
Both descriptions give the same physical reality; the charge that is transferred per second is identical. We use conventional current in all circuit diagrams and calculations because the symbols and equations were all developed that way.
flowchart LR
BP[Battery +] --> W1[Wire] --> R[Resistor] --> W2[Wire] --> BN[Battery -]
BN -.->|electrons flow this way| BP
Common Exam Mistake: Drawing a current arrow from the negative terminal. Examiners mark this wrong even if the rest of the answer is correct. Current arrows always go from + to −.
In the SI system, the ampere is one of the seven base units. All electrical units (the coulomb, volt, ohm, farad, henry, tesla, etc.) are derived from it. Since 2019, the ampere has been redefined in terms of the elementary charge e itself — by fixing e = 1.602176634 × 10⁻¹⁹ C exactly, the ampere is effectively "one coulomb per second" where the coulomb is now tied to a counted number of elementary charges.
You are not expected to recite the new definition, but you should recognise that:
Exam Tip: OCR has asked "Express the coulomb in terms of SI base units." Answer: C = A s.
To measure current you use an ammeter, connected in series with the component whose current you want to measure. An ideal ammeter has zero resistance, so that inserting it does not disturb the circuit.
Real ammeters have a small but non-zero resistance; a cheap multimeter on the 10 A range may have ~0.01 Ω, while a laboratory digital meter may be effectively zero to the precision needed at A-Level.
flowchart LR
B[Battery] --> A((Ammeter)) --> R[Resistor] --> B
Never connect an ammeter in parallel across a cell or a resistor. Because the ammeter has very low resistance, doing so creates a near short-circuit, causing a huge current that can destroy the meter, the battery, and possibly burn wires.
At this stage of the course we deal almost entirely with direct current (DC): the current flows in one direction only, with a constant (or slowly varying) magnitude. Batteries, solar cells and lab power supplies all provide DC.
Alternating current (AC) changes direction periodically (50 Hz in the UK mains). You will study AC in more detail later in the course; for Module 4.2 all our calculations are DC unless specified otherwise.
A capacitor is charged by a steady current of 15 mA for 4.0 s. Calculate:
(a) The charge delivered. (b) The number of electrons that passed through the wire.
(a) Q = I · t = 15 × 10⁻³ × 4.0 = 0.060 C (or 60 mC)
(b) n = Q / e = 0.060 / 1.60 × 10⁻¹⁹ = 3.75 × 10¹⁷ electrons
Notice the consistent use of base units: 15 mA converted to 0.015 A before substitution. OCR mark schemes insist on this; forgetting to convert is one of the single most common errors in calculations.
To build intuition, here is a rough ladder of electrical currents you might encounter:
| Scale | Typical current |
|---|---|
| Nerve impulse | ~10 pA (10⁻¹¹ A) |
| Wristwatch | ~1 μA (10⁻⁶ A) |
| LED indicator | ~20 mA (0.02 A) |
| Torch bulb | ~0.2 A |
| Kettle (UK mains) | ~10 A |
| Car starter motor | ~200 A |
| Lightning strike | ~30 kA (30 000 A) |
The quantity Q = It means that even tiny currents over long times can transfer enormous charge, and very large currents over short times can do huge amounts of damage — hence the importance of fuses and circuit breakers in real installations.
In the next lesson we will look inside a metallic conductor to see how the microscopic motion of electrons produces the macroscopic current we have just defined.