Electrical resistance and conductance

• 1. Introduction

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  Electrical resistance and conductance govern every circuit on Earth, from the filament in an incandescent light bulb glowing white hot, to the cables stretched between transmission towers carrying power across entire continents. Resistance is a measure of how strongly an object opposes the flow of electric current; conductance, its reciprocal, measures how easily that current passes. The SI unit for resistance is the ohm, symbolized by the Greek letter omega, while conductance is measured in siemens. What decides whether copper wire and rubber tubing behave so differently? How does the same property that wastes energy in power lines also cook your food on an electric stove? And what happens when resistance disappears altogether, falling all the way to zero?

• 2. The Pipe Analogy

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  Water pressure pushing through a pipe is one of the most useful ways to picture what resistance actually does. Current flowing through a wire behaves much like water moving through a pipe, and the voltage drop across that wire corresponds to the pressure difference that keeps the water moving. Critically, it is the difference in pressure between the two ends of the pipe that drives the flow, not the absolute pressure at either end. If the pressure on both sides is equal, no water moves at all, regardless of how high that pressure might be.

  Geometry matters enormously in both systems. A long, narrow pipe resists flow far more than a wide, short one. In the same way, a long, thin copper wire has higher resistance than a short, thick copper wire made of the same metal. The relationship is precise: resistance is proportional to the length of the conductor and inversely proportional to its cross-sectional area. Double the length and resistance doubles; double the diameter and resistance drops by a factor of four.

  Material choice is equally decisive. A pipe filled with hair restricts flow far more than a clean pipe of identical dimensions. Electrons move freely through copper but face more resistance in steel wire of the same shape, and they essentially cannot move at all through rubber, whatever its geometry. That contrast between copper, steel, and rubber traces back to microscopic structure and electron configuration, a property called resistivity.

• 3. Ohm's Law and Its Limits

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  For many materials, current through the material is directly proportional to the voltage applied across it, over a wide range of voltages and currents. This relationship is called Ohm's law, and materials that obey it are called ohmic. Wires and resistors are the everyday examples. On a graph of current against voltage, an ohmic device produces a straight line through the origin with a positive slope.

  Diodes, fluorescent lamps, transformers, incandescent light bulb filaments, and batteries do not obey Ohm's law. In those cases, current is not proportional to voltage, so resistance is not constant but shifts depending on the operating conditions. Engineers still find it useful to talk about resistance in these nonlinear devices; the ratio of voltage to current at a specific point is called the chordal or static resistance, while the slope of the curve at that point is called the differential resistance.

  Alternating current introduces a further layer of complexity. When current and voltage oscillate at different phases, as they do across a capacitor or inductor, the relevant quantity is no longer plain resistance but impedance. For a capacitor or inductor, maximum current flow occurs as voltage passes through zero, so current and voltage are 90 degrees out of phase. AC system designers generally try to keep that phase angle as close to zero as possible, because reactive power, the portion associated with a nonzero phase difference, does no useful work at a load. Adding a capacitor to a circuit with an inductive load can compensate for the phase shift at a specific frequency.

• 4. Resistivity and the Spectrum of Materials

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  The conductivity of Teflon is about ten to the thirtieth power times lower than the conductivity of copper. That number is almost incomprehensibly large, and it explains why copper carries electricity across cities while Teflon insulates cables. In metals, large numbers of electrons are not bound to any single atom and are free to drift across long distances. In an insulator like Teflon, each electron is tightly bound to a single molecule, and pulling it free demands a great deal of force. Semiconductors sit between these two extremes, which is why they are the building blocks of transistors and solar cells.

  Resistivity is not a fixed property; temperature shifts it. Near room temperature, the resistivity of metals typically rises as temperature increases, while the resistivity of semiconductors typically falls. In some semiconductors, exposure to light also changes resistivity, a property called photoconductivity. Devices that exploit this are called photoresistors, or light-dependent resistors, and they serve as a common type of light detector.

  Strain also changes resistance. Stretching a conductor under tension increases its length and decreases its cross-sectional area, both of which push resistance upward. Compressing the same conductor does the opposite. Devices built deliberately to exploit this behavior are called strain gauges, and they form the basis of many industrial sensors.

• 5. Joule Heating

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  James Prescott Joule gave his name to the heating effect that occurs whenever current flows through a resistance: electrical energy converts to thermal energy, warming the resistor in the process. The formula connecting these quantities sets power equal to the product of resistance and the square of current. That squaring of current is why high voltage transmission lines are built to carry power at high voltage and low current: for a given amount of power delivered, lower current means dramatically less energy lost as heat along the wire.

  The same effect that makes transmission losses unwelcome is deliberately harnessed in electric stoves and resistive heaters. An incandescent lamp pushes this further still: the filament is driven to such a high temperature that it radiates visible light, glowing white hot with thermal radiation, the phenomenon called incandescence.

  When a component whose resistance changes with temperature is used on purpose, it carries a specific name. A resistance thermometer is typically made of platinum and works by measuring the temperature from the observed resistance. A thermistor is made from ceramic or polymer. Both can serve as thermometers, but both can also act as circuit-protection devices similar to fuses, because a large current raises the component's temperature and therefore shifts its resistance, creating a feedback effect that designers can build into circuits.

• 6. Superconductivity

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  Superconductors are materials with exactly zero resistance and infinite conductance. Because there is no resistance, there is no Joule heating and no dissipation of electrical energy. A current set moving in a closed loop of superconducting wire will continue circling forever. Most metallic superconductors, such as niobium-tin alloys, require cooling to temperatures near 4 kelvin, which demands liquid helium. High-temperature superconductors are ceramic materials that operate near 77 kelvin and can be cooled with liquid nitrogen instead, but they are expensive, brittle, and delicate.

  Despite those demanding requirements, superconductors have found real technological applications. Superconducting magnets are among the most prominent, appearing in medical imaging equipment and particle accelerators. The absence of resistive losses makes them capable of sustaining magnetic fields that no ordinary electromagnet could produce without generating catastrophic heat.