Charge, Current and Charge Carriers

Electric charge is one of the most fundamental quantities in physics. All electrical phenomena arise from the existence and movement of electric charge. In this lesson we explore the nature of charge, how current is defined, and the microscopic model of charge carriers moving through a conductor.

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Electric Charge

Electric charge is a property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charge: positive and negative.

Property	Detail
SI unit of charge	Coulomb (C)
Elementary charge (e)	1.60 × 10⁻¹⁹ C
Charge of an electron	−1.60 × 10⁻¹⁹ C
Charge of a proton	+1.60 × 10⁻¹⁹ C
Charge is quantised	Q = ne, where n is an integer

Charge is conserved — it cannot be created or destroyed. In any process the total charge before equals the total charge after.

Charge is quantised — it always comes in whole-number multiples of the elementary charge e. You cannot have a charge of 0.5e.

Exam Tip: When a question says "charge flows", always think about which charge carriers are actually moving. In metals, it is free electrons. In electrolytes, it is positive and negative ions. In semiconductors, it is electrons and holes.

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Electric Current

Current is the rate of flow of electric charge past a point in a circuit.

$I = \frac{\Delta Q}{\Delta t}$I=ΔtΔQ​

where:

• I = current (A)
• ΔQ = charge flowing (C)
• Δt = time taken (s)

Rearranging: Q = It

The SI unit of current is the ampere (A). One ampere means one coulomb of charge flows past a point per second.

Conventional Current vs Electron Flow

• Conventional current flows from positive to negative (the direction a positive charge would move).
• Electron flow is from negative to positive (electrons carry negative charge, so they move in the opposite direction to conventional current).

In circuit analysis, we always use conventional current direction. This is a historical convention established before the electron was discovered, but it is perfectly consistent and used universally in physics and engineering.

Common Misconception: Students sometimes think conventional current is "wrong" and electron flow is "right". Both are valid descriptions. Conventional current is the standard used in all circuit equations and diagrams at A-Level.

Worked Example 1 — Charge and Current

A current of 3.5 A flows through a lamp for 2 minutes. Calculate the total charge that flows.

Solution:

t = 2 minutes = 2 × 60 = 120 s

Q = It = 3.5 × 120 = 420 C

Worked Example 2 — Number of Electrons

How many electrons pass through the lamp in the worked example above?

Solution:

Each electron carries charge e = 1.60 × 10⁻¹⁹ C.

Number of electrons: n = Q/e = 420 / (1.60 × 10⁻¹⁹) = 2.63 × 10²¹ electrons

Exam Tip: Always convert time to seconds before using Q = It. A very common error is to leave time in minutes.

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Charge Carriers in a Conductor

In a metallic conductor, the charge carriers are free electrons (also called conduction electrons or delocalised electrons). These electrons are not bound to any particular atom and can move through the metal lattice.

When no potential difference is applied:

• Free electrons move randomly in all directions at high speeds (around 10⁶ m s⁻¹ at room temperature).
• There is no net flow of charge in any direction, so no current flows.

When a potential difference is applied across the conductor:

• An electric field is established inside the conductor.
• Free electrons experience a force (F = eE) and acquire a small drift velocity in the direction from negative to positive terminal.
• This drift velocity is superimposed on their random thermal motion.
• The drift velocity is very small — typically around 10⁻⁴ m s⁻¹ (a fraction of a millimetre per second).

Common Misconception: Students often think electrons travel at the speed of light through a wire. They do not. The drift velocity is extremely slow. What travels at close to the speed of light is the electric field (the signal), which causes all free electrons throughout the wire to start drifting almost simultaneously.

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The Transport Equation: I = nAvq

The relationship between current and the microscopic properties of charge carriers is given by:

$I = nAvq$I=nAvq

where:

• I = current (A)
• n = number density of charge carriers (m⁻³) — the number of free charge carriers per unit volume
• A = cross-sectional area of the conductor (m²)
• v = mean drift velocity of the charge carriers (m s⁻¹)
• q = charge on each carrier (C) — for electrons, q = e = 1.60 × 10⁻¹⁹ C

Derivation of I = nAvq

Consider a section of wire with cross-sectional area A. In time Δt, charge carriers with drift velocity v travel a distance vΔt along the wire.

The volume of wire through which carriers pass in time Δt is:

Volume = A × vΔt

The number of charge carriers in this volume is:

N = n × A × vΔt

The total charge passing through the cross-section in time Δt is:

ΔQ = N × q = nAvΔt × q

Therefore the current is:

I = ΔQ/Δt = nAvq

Typical Number Densities

Material	n (m⁻³)	Classification
Copper	8.5 × 10²⁸	Metal (good conductor)
Silicon (pure)	1.0 × 10¹⁶	Semiconductor
Glass	≈ 0	Insulator

The enormous difference in n explains why metals are good conductors and insulators are not. Metals have approximately 10¹² times more free charge carriers per unit volume than pure semiconductors.

Worked Example 3 — Drift Velocity

A copper wire has a cross-sectional area of 1.5 × 10⁻⁶ m² and carries a current of 2.0 A. The number density of free electrons in copper is 8.5 × 10²⁸ m⁻³. Calculate the mean drift velocity of the electrons.

Solution:

I = nAvq

Rearranging: v = I / (nAq)

v = 2.0 / (8.5 × 10²⁸ × 1.5 × 10⁻⁶ × 1.60 × 10⁻¹⁹)

v = 2.0 / (8.5 × 1.5 × 1.60 × 10²⁸⁻⁶⁻¹⁹)

v = 2.0 / (20.4 × 10³)

v = 2.0 / 20400

v = 9.8 × 10⁻⁵ m s⁻¹ (approximately 0.1 mm s⁻¹)

This confirms that drift velocity is extremely small — less than a tenth of a millimetre per second.

Worked Example 4 — Comparing Drift Velocities

The same current flows through a thick wire and a thin wire made of the same material, connected in series. Compare the drift velocities.

Solution:

Since both wires carry the same current I (series circuit) and are made of the same material (same n and q):

From I = nAvq: v = I / (nAq)

The thinner wire has a smaller A, so v must be larger in the thin wire.

This is analogous to water flowing faster through a narrow section of pipe.

Exam Tip: Questions on I = nAvq are common. Remember that for a given current, drift velocity is inversely proportional to cross-sectional area and inversely proportional to number density. Semiconductors have much smaller n than metals, so for the same current in the same size wire, the drift velocity in a semiconductor would be much larger.

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Conservation of Charge in Circuits

At any junction in a circuit, the total current flowing in equals the total current flowing out. This is a consequence of the conservation of charge (and is formalised as Kirchhoff's first law, covered in Lesson 9).

If a current of 5 A flows into a junction and splits into two branches carrying 3 A and 2 A, charge is conserved: 5 = 3 + 2.

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Summary of Key Equations

Equation	Meaning
Q = It	Charge = current × time
I = ΔQ/Δt	Current = rate of flow of charge
Q = ne	Charge is quantised (n is an integer)
I = nAvq	The transport equation linking current to charge carrier properties