Charge — OCR A-Level Physics

The coulomb (symbol C) is the SI unit of electric charge. It is defined as the amount of charge transferred by a current of 1 ampere in 1 second: 1 C = 1 A × 1 s. This means that if a steady current of 1 A flows for 1 s, the total charge that has passed is 1 C. For example, a current of 2 A flowing for 5 s transfers 10 C of charge. The coulomb is a derived unit, defined in terms of the ampere and the second. In calculations, charge is often expressed in coulombs, and it is important to convert units such as millicoulombs (1 mC = 1 × 10⁻³ C) or microcoulombs (1 μC = 1 × 10⁻⁶ C) when necessary. The coulomb is used to quantify the charge on particles, in capacitors, and in current flow.

The elementary charge, denoted e, is the smallest unit of electric charge that can exist freely. Its value is approximately 1.6 × 10⁻¹⁹ C. This is the magnitude of charge on a single proton (positive) or a single electron (negative). For example, an electron has charge −e = −1.6 × 10⁻¹⁹ C, while a proton has charge +e = +1.6 × 10⁻¹⁹ C. The elementary charge is a fundamental constant and is used to calculate the charge on ions or charged objects by multiplying by the number of excess or deficit electrons. For instance, an object with 5 excess electrons has a net charge of 5 × (−1.6 × 10⁻¹⁹ C) = −8.0 × 10⁻¹⁹ C. The value is often given in data sheets, and students should be able to use it in calculations.

Quantisation of charge means that the net electric charge on any particle or object can only take discrete values that are integer multiples of the elementary charge e. In other words, charge is not continuous; it comes in 'packets' of size e = 1.6 × 10⁻¹⁹ C. For example, an object can have a charge of +2e, −3e, or zero, but never +1.5e. This arises because charge is carried by discrete particles like electrons and protons. When an object is charged, it gains or loses whole electrons, so its net charge is always an integer multiple of e. Mathematically, Q = n e, where n is an integer (positive, negative, or zero). This principle is fundamental in physics and explains why charge is quantised. In calculations, you can determine the number of excess or deficit electrons by dividing the net charge by e.

Electric current is the rate of flow of charged particles, and the identity of those particles depends on the conductor. In a metal, outer electrons are delocalised from the positive ion lattice, so the charge carriers are electrons; a current of 1 A means 1 C of charge passes a point each second, and since each electron carries about 1.60 × 10⁻¹⁹ C, that is roughly 6.25 × 10¹⁸ electrons per second. In an electrolyte, the liquid or solution contains positive and negative ions that are free to move, so both ion types drift in opposite directions and together carry the current; the electrodes deliver or remove charge, driving chemical change. In both cases the current direction is defined by conventional current, and the carriers move much more slowly than the signal.

Conventional current is defined as the direction in which positive charge would flow, from the positive terminal of a source, through the external circuit, to the negative terminal. In metallic conductors the actual moving charges are electrons, which are negatively charged, so electron flow is in the opposite direction to conventional current. This convention predates the discovery of the electron and is retained because circuit analysis, Kirchhoff's laws and most equations such as I = ΔQ/Δt assume positive charge flow. In an electrolyte, positive ions move in the conventional current direction while negative ions move the other way, so both contribute to the same conventional current. Always state which direction you mean when describing a circuit.

Kirchhoff's first law states that the sum of currents entering a junction equals the sum of currents leaving it, so the algebraic sum of currents at a junction is zero. It is a statement of conservation of charge: charge cannot accumulate at a junction in a steady circuit, so the rate at which charge arrives must equal the rate at which it leaves. For a junction with currents I₁ and I₂ entering and I₃ leaving, I₁ + I₂ = I₃. The law applies to any junction in a network, including parallel branches, and is used with Kirchhoff's second law to solve circuit problems. It holds for conventional current directions, and the same result follows from electron flow because the magnitudes are unchanged.