Charge and Current

Electric charge is measured in coulombs (C), though we often think of it in terms of electron charges. A single electron carries a charge of 1.6 × 10⁻¹⁹ C, which means you'd need approximately 6.3 × 10¹⁸ electrons to produce just one coulomb of charge!

Not all materials allow charge to flow. Conductors (like metals) permit the movement of charge, while insulators prevent it. When we want to measure how quickly charge is flowing, we use current, which is the rate of flow of charge. The formula for current is:

Current (A) = Change in charge (C) / Change in time (s)

or mathematically: I = ΔQ/Δt

Remember this! The distinction between conductors and insulators is crucial - conductors have free electrons that can move, while insulators keep electrons firmly in place.

Metals make excellent conductors because they contain positive ions and free delocalised electrons due to metallic bonding. When you connect a battery to a metal wire, creating a potential difference, these free electrons drift from the negative terminal toward the positive terminal. This coordinated movement of charged particles is what creates an electric current.

Electron Drift and Current Calculation

When electrons move through a conductor, they don't travel instantly - they have a measurable drift velocity. Think of it as the average speed at which electrons travel through the material. The time taken for electrons to travel along a section of conductor equals the length divided by this drift velocity $t = L/v$.

The number of free electrons within a section of conductor can be calculated using the formula N = ALn, where A is the cross-sectional area, L is the length, and n is the charge carrier density (the number of free electrons per cubic meter).

Current is essentially a measure of how many electrons pass through a point in the conductor per second, multiplied by each electron's charge. This gives us the important relationship:

I = nAve

where I is current, n is charge carrier density, A is cross-sectional area, v is drift velocity, and e is the electron charge.

Making connections: The formula I = nAve shows that current increases with larger cross-sectional area, higher electron density, or faster drift velocity - like how water flows faster through a wider pipe or when pushed harder.