Resistance
Electrical resistance is the opposition a conductor offers to the flow of current, measured in ohms (symbol Ω), where one ohm is the resistance that lets one ampere flow under one volt. Resistance is what turns electrical energy into heat, what sets voltages in dividers, and what limits how fast signals can move along the tiny wires of a chip.
Resistance depends on both the material and the shape, and the relation is simple enough to write in plain text: R = rho × L / A. Here rho (the Greek letter ρ) is the resistivity of the material in ohm-metres, L is the length of the conductor and A is its cross-sectional area. A long thin wire resists more than a short thick one, just as a long narrow pipe resists water more. Copper has a resistivity of roughly 1.7 × 10⁻⁸ ohm-metres, among the best of common metals, while glass and quartz exceed it by more than twenty orders of magnitude. Semiconductors sit in between and, crucially, can be tuned: doping silicon with small amounts of impurity changes its resistivity by many orders of magnitude, which is the point of the whole technology.
Temperature changes resistance in opposite ways for metals and semiconductors. In a metal, a warmer lattice vibrates harder and scatters the moving electrons more, so resistance rises with temperature; this is why a tungsten filament draws a surge of current when first switched on and why platinum is used for precise thermometers. In a semiconductor, heat frees additional charge carriers across the band gap, and that usually outweighs the extra scattering, so resistance falls as temperature rises, which is exploited in thermistors and is a hazard in power transistors, where a hot spot can draw more current and get hotter still.
Resistors are components made deliberately to supply a known resistance, and they do three main jobs. They limit current, for example protecting a light-emitting diode; they divide voltage, by placing two in series and tapping the midpoint; and they convert current to voltage, which is how many sensors and amplifiers read their signals. Common types include carbon-film and metal-film resistors with colour-coded bands, and on integrated circuits resistors are formed from doped silicon or thin metal films. On a chip a resistor is often avoided because it consumes much area; transistors are used where possible, a sign of how cheap the transistor became.
Resistance converts electrical energy into heat in what is called Joule heating, with power given by I² × R. The heat is wanted in a toaster and unwanted nearly everywhere else. Because the power grows with the square of current, halving the current in a wire cuts its heating to a quarter, which is why long-distance transmission lines use very high voltages and low currents. The same logic governs chips: a processor drawing large currents through power wiring suffers voltage drops and heating along the way, and the dissipation must be removed by heat sinks, fans or liquid cooling.
Interconnect resistance has become a central problem of chip scaling. As transistors shrank, the wires linking them shrank too, and thinner wires have higher resistance by the formula above, while surface and grain-boundary scattering make narrow metal lines worse than bulk resistivity suggests. Together with the capacitance between neighbouring wires, this resistance sets the delay of signals travelling across a chip, which no longer improves as transistors get faster. Chipmakers switched from aluminium to copper wiring, commercialised by IBM in the late 1990s, and continue to explore other metals and new via and power-delivery schemes. A common misconception is that resistance is a fixed property of a component: many devices, from thermistors to transistors in their on state, have resistance that varies with temperature, voltage or control signal.
Read resistance as the electrical friction of a material and its geometry, the property that turns current into voltage drop and heat, and whose behaviour in ever-thinner wires now limits how far chips can scale.