Current

Current is the rate at which charge flows. Learn conventional vs electron flow, current density, how wires are sized, how current is measured and why a few milliamps through the body can be deadly.

When a closed path exists between two points at different potentials, charges start to move. That flow of charge is electric current. In metal wires the moving charges are electrons; in batteries and electrolytes they are ions; in semiconductors they are electrons and 'holes'.

Current is what actually does the work in a circuit: it heats the element in a kettle, spins a motor and lights an LED. It is also what makes wires hot and what trips breakers, so sizing conductors and protection correctly is all about current.

An analogy

If voltage is the water pressure, current is the flow rate — litres per second through the pipe. A wide pipe (thick wire) carries more flow with less resistance; a narrow pipe restricts it.

Current is charge in motion

One ampere is one coulomb of charge passing a point every second — about 6.24 × 10¹⁸ electrons per second. Current must flow in a closed loop: whatever leaves the source must return to it.

Conventional current vs electron flow

By convention, current flows from + to − through the external circuit. Electrons actually move the other way (− to +). Every formula, arrow and symbol in engineering uses conventional current; electron flow only matters in device physics.

Why wires get hot: current density and ampacity

Current crowded into a small cross-section (high current density J) produces more heat per unit volume. Every cable has an ampacity — the continuous current it can carry without exceeding its insulation's temperature rating — which depends on conductor size, insulation type, installation method and ambient temperature.

Electrons drift surprisingly slowly (fractions of a millimetre per second). The signal travels near the speed of light because the electric field propagates along the wire, pushing all electrons at once.

Measuring current

An ammeter goes in series (the current must pass through it) and should have near-zero resistance. Clamp meters measure the magnetic field around a single conductor without breaking the circuit; clamping both line and neutral together reads zero, because their fields cancel.

• Shunt resistor + amplifier: cheap and accurate, but not isolated.
• Hall-effect sensor: isolated, measures DC and AC.
• Current transformer (CT): isolated, AC only, used in metering and protection.

Skin effect and AC current distribution

At high frequency, AC current crowds toward the conductor's surface, within the skin depth δ = √(2ρ / (ωμ)). For copper at 50 Hz, δ ≈ 9.3 mm; at 100 kHz, δ ≈ 0.21 mm. That is why high-frequency transformers use Litz wire (many thin insulated strands) and busbars are made as flat strips.

Current and the human body

Roughly 1 mA is perceptible, 10 mA causes muscle 'let-go' failure, and 30–50 mA across the chest can trigger ventricular fibrillation. Residual-current devices (RCD/GFCI) trip at 30 mA (or 5–10 mA) when the currents in line and neutral don't balance — the missing current is flowing through something else, possibly a person.

Formulas

• Definition: I = Q / t (1 A = 1 C/s)
• Current density: J = I / A
• Drift velocity: I = n · A · q · v_d
• Electron charge: q = 1.602 × 10⁻¹⁹ C

Worked example: How many electrons?

Given: I = 2 A; t = 5 min = 300 s; q = 1.602 × 10⁻¹⁹ C

Find: Total charge and number of electrons passing a point.

• Q = I · t = 2 × 300 = 600 C
• N = Q / q = 600 / 1.602 × 10⁻¹⁹
• N ≈ 3.75 × 10²¹ electrons

Answer: 600 C ≈ 3.75 × 10²¹ electrons

Worked example: Drift velocity in a copper wire

Given: I = 10 A; A = 1 mm² = 1 × 10⁻⁶ m²; n(Cu) = 8.5 × 10²⁸ m⁻³

Find: Average electron drift velocity.

• v_d = I / (n · A · q)
• = 10 / (8.5 × 10²⁸ × 10⁻⁶ × 1.602 × 10⁻¹⁹)
• = 10 / 13 617 ≈ 7.3 × 10⁻⁴ m/s

Answer: ≈ 0.73 mm/s — slower than a snail

Common mistakes

• Wrong: Connecting an ammeter in parallel with a load. — Right: An ammeter must be in series. In parallel its near-zero resistance shorts the supply and blows the meter's fuse.
• Wrong: Assuming the current 'gets used up' as it passes through a lamp. — Right: Current is the same everywhere in a series loop; energy is used, not charge.

Applications

• Cable sizing: Electricians size cables so that current density stays within the insulation's thermal limit and voltage drop stays under ~3–5 %.
• Battery management: A BMS integrates current over time (coulomb counting) to estimate a battery's state of charge.
• Safety devices: Fuses and MCBs react to overcurrent; RCDs react to current imbalance (leakage to earth).

Key takeaways

• I = Q/t: one ampere is one coulomb per second.
• Current flows in closed loops and is the same everywhere in a series path.
• Conductor size is chosen from ampacity (heat) and voltage drop.
• Ammeters go in series; clamp meters measure one conductor's magnetic field.

Going further

• Kirchhoff's current law is charge conservation: Charge can't pile up at a node in a circuit, so currents in must equal currents out. Where charge does accumulate (a capacitor plate), displacement current C·dV/dt keeps the law valid.
• Current sources: An ideal current source forces a fixed current whatever the load voltage. LED drivers, battery chargers (CC phase) and transistor current mirrors approximate one, and they are the natural way to drive devices whose brightness or torque depends on current.
• Electromigration: In IC interconnects, current densities above ~10⁶ A/cm² physically push metal atoms along, creating voids and eventual open circuits. Chip designers check every wire against electromigration current-density rules.