A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Electric current I is the rate of charge flow through a cross-section: I = dQ/dt, measured in amperes (A = C/s). In a conductor, current arises from the drift of free electrons under an applied electric field; the drift velocity is surprisingly slow (~10⁻⁴ m/s) even though the signal propagates near the speed of light. Resistance R = ρL/A, where ρ is the material's resistivity, L is length, and A is cross-sectional area, quantifying how strongly a conductor opposes current flow.
Use the microscopic model (drift velocity, charge carrier density) to derive R = ρL/A from first principles. Then practice calculating R for wires of varied geometry and connect to macroscopic Ohm's law V = IR.
You already know from electric potential that a voltage difference (potential difference) across two points in a conductor creates an electric field inside it. That field exerts a force on the free electrons in the metal, pushing them along — but not freely. The electrons constantly collide with the vibrating lattice of metal ions, which slows them down. This perpetual collision is the microscopic origin of electrical resistance.
Because of these collisions, electrons don't accelerate indefinitely; they reach a steady average drift velocity — surprisingly slow, on the order of 10⁻⁴ m/s. Yet when you flip a light switch, the bulb responds instantly. The reason is that the electric field, not the electrons themselves, is what propagates — and it does so at nearly the speed of light. Every free electron in the entire circuit starts drifting almost simultaneously. Current, I = dQ/dt, measures how much charge passes a cross-section per second; it is a collective property of the flow, not the speed of any individual electron.
The geometry of a conductor determines how strongly it resists that flow. A longer wire means electrons must navigate more collision-prone material: R increases with length. A wider wire provides more parallel paths for electrons to travel: R decreases with cross-sectional area. Combined with the material's intrinsic resistivity ρ, these factors give the formula R = ρL/A. Resistivity is a material constant — copper has low ρ, rubber has high ρ — while resistance is a property of a specific piece of conductor with a specific shape.
One persistent source of confusion is the direction of current. By historical convention, current is defined as the direction positive charges would flow — from high to low potential. In metallic conductors, the actual charge carriers are electrons, which are negative and drift in the opposite direction. This "conventional current" convention was established before the electron was discovered, and it persists because the mathematics works out the same way. Always be explicit about which convention you are using, especially when analyzing semiconductor or electrochemical systems where positive carriers do exist.
When you encounter Ohm's law (V = IR) in the next topic, you will see resistance as the proportionality constant linking voltage and current. The groundwork you have here — that resistance arises from material properties and geometry, and that current is a flow rate rather than a particle speed — makes Ohm's law a logical consequence rather than a formula to memorize.