Resistor - Wikiparency

# Resistor A **resistor** is a two-terminal component chosen for the resistance it presents rather than for any other property. It converts electrical energy into heat at a rate set by the current through it, and that heat is not incidental: it is what limits how small a resistor can be, how far its value drifts from the number printed on it, and how long it lasts. The microsim on this page puts a voltage across a resistor and lets the reader watch it warm itself, drift, and run up against a power rating that shrinks as the surrounding air gets hotter. The idealised resistor of circuit theory obeys [[Ohm's_law]] exactly, at every frequency and every temperature, and dissipates power without changing. A real one does none of these things perfectly. Its resistance moves with temperature, and since it heats itself, its resistance depends on the power it is carrying. It has inductance and capacitance that matter at high frequency. It generates a small noise voltage simply by being warm. Most of the engineering of resistors is the management of these departures rather than the achievement of the resistance itself. ## Electronic symbols and notation Two symbols are in use: a zig-zag line, standard in North America, and a plain rectangle, standard in [[International_Electrotechnical_Commission|IEC]] practice and most of the rest of the world. Both carry a reference designator beginning with R and a value. Values are written to avoid the decimal point, which survives poor reproduction badly. In the RKM notation a letter stands in for the multiplier and marks the decimal position, so 4R7 is 4.7 ohms, 4k7 is 4,700 ohms and 4M7 is 4.7 megohms. The ohm symbol is often dropped entirely on schematics, where a bare number beside an R designator is unambiguous. ## Theory of operation Resistance relates the [[Voltage|voltage]] across a component to the [[Electric_current|current]] through it. For a uniform bar of material the resistance follows from the geometry and the [[Electrical_resistivity_and_conductivity|resistivity]] of the material: it rises with length and falls with cross-sectional area. This is why a resistor is usually a thin film or a long wire rather than a block, and why the same resistance can be built either as a short path through a poor conductor or a long path through a good one. [[Power_(physics)|Power]] dissipation is the other half of the theory and the half that dominates practice. The power turned into heat is the product of voltage and current, which for a resistor can be written in terms of either quantity alone. This is Joule heating, and it is the mechanism by which a resistor does its work: in a current-limiting role the energy the resistor removes from the circuit leaves as heat, and there is nowhere else for it to go. Because resistance varies with temperature and temperature varies with dissipated power, the operating point of a real resistor is the solution of a loop rather than the value of a formula. The microsim solves that loop. Where the [[Temperature_coefficient|temperature coefficient]] is positive, heating raises the resistance, which lowers the power, which limits the heating: the loop is self-correcting. Where it is negative, as in carbon composition, heating lowers the resistance and raises the power, and the loop can run away. ## Nonideal properties The departures from the ideal divide into three groups. The first is value: the manufactured resistance differs from the nominal one by a stated tolerance, and it then drifts with temperature by its temperature coefficient, with age, and with applied voltage in some constructions. A precision application must budget all of these, not only the tolerance. The second is reactance. Every resistor has some series inductance, pronounced in wirewound types where the resistive element is literally a coil, and some shunt capacitance between its terminals and between adjacent turns. Above some frequency the impedance of a resistor stops being its resistance, in the same way that a [[Capacitor|capacitor]] stops being a capacitance above its self-resonance and an [[Inductor|inductor]] loses its inductance in saturation. The third is power handling, which is a thermal question rather than an electrical one. A rating is quoted at a stated ambient temperature and must be derated above it, on the reasoning that what actually fails is the part reaching its maximum internal temperature. The derating curve in the microsim has the common shape: full rated power up to a knee, then falling linearly to zero at the maximum internal temperature. ## Fixed resistors Fixed types are distinguished by how the resistive element is made. Carbon composition resistors use a moulded mixture of carbon and a binder; they tolerate short overloads well, but have loose tolerances, a large negative temperature coefficient and noticeable excess noise. Carbon and metal film types deposit a thin layer on a ceramic rod and trim it to value, and are the general-purpose choice: metal film offers low noise and a small temperature coefficient. Metal oxide film trades some of that precision for better tolerance of heat and surges. Wirewound types wind resistance wire on a former and handle the largest powers, at the cost of the series inductance that the winding implies. Foil types, in which a bulk metal foil is bonded to a substrate, give the best stability available. ## Variable resistors A resistor whose value can be adjusted is either a [[Potentiometer|potentiometer]], wired as a three-terminal divider with a wiper that picks off a fraction of the voltage, or a rheostat, wired as a two-terminal variable resistance. The same physical part usually serves both roles depending on how many terminals are connected. Trimmers are the same idea built for occasional adjustment during calibration rather than for use by an operator. Some resistors vary with a physical quantity instead of a shaft. A [[Thermistor|thermistor]] varies strongly and deliberately with temperature and is used to measure it or to limit inrush current; a [[Varistor|varistor]] drops sharply in resistance above a threshold voltage and is used to clamp transients; a photoresistor varies with illumination. ## Measurement Resistance is measured either directly with an [[Ohmmeter|ohmmeter]] function, which passes a known current and measures the resulting voltage, or by comparison in a bridge. The [[Wheatstone_bridge]] compares an unknown against a known standard and is read at balance, where the detector current is zero; because the reading depends on a ratio at null rather than on absolute meter accuracy, a bridge can be far more precise than a direct measurement with the same instruments. Small resistances demand a four-terminal (Kelvin) connection, in which current is forced through one pair of leads and voltage sensed across another, so that the resistance of the leads and contacts does not appear in the result. A general-purpose [[Multimeter|multimeter]] reading a milliohm-scale resistance with two leads is measuring mostly its own leads. ## Standards Preferred values follow the E series, a set of geometric sequences chosen so that consecutive values differ by about one tolerance band: E24 for five percent parts, E96 for one percent. The consequence is that a design asking for an arbitrary resistance must either accept the nearest preferred value or combine several parts. Separate standards cover marking, dimensions, and the environmental and endurance tests a part must survive, together with the temperature and power conditions under which a rating may be quoted. ## Resistor marking Through-hole resistors are marked with the [[Electronic_color_code|colour code]]: bands for significant figures, a multiplier, a tolerance, and on precision parts a fifth band for a third figure and sometimes a sixth for the temperature coefficient. The code exists because a cylindrical part gives no guaranteed reading orientation and coloured bands are legible from any angle. [[Surface-mount_technology|Surface-mount]] resistors are too small for bands and carry printed numeric codes instead: three or four digits with the last as a multiplier, or the EIA-96 scheme of two digits and a letter for parts too small even for that. ## Common usage patterns Resistors appear in a few recurring arrangements. Two in series form a voltage divider, the basic way of scaling a voltage down. One in series with a signal path limits current, the role a resistor plays beside a light-emitting diode or a transistor base. A resistor to a supply rail or to ground acts as a pull-up or pull-down, defining a node that would otherwise float. A resistor across a source or load sets a termination, matching a line to avoid reflections. In each case the resistance is chosen for a ratio or a current, and the power rating is then checked against the worst case rather than the nominal one. The microsim is a tool for that second step. ## Electrical and thermal noise A resistor at any temperature above absolute zero generates a small random voltage across its terminals, [[Johnson–Nyquist_noise|thermal noise]], whose power depends on the temperature and the bandwidth of the measurement but not on the resistance value, and not on whether any current flows. It sets the noise floor of any circuit built from resistors and is the reason the input resistance of a sensitive amplifier is kept low where the source allows it. Real resistors add excess noise above the thermal floor, roughly in inverse proportion to frequency and dependent on construction and on the current flowing. Carbon composition is the worst of the common types and metal film among the best, which is the usual reason to prefer film in the first stage of an amplifier. ## Failure modes Resistors fail open more often than they fail short, because the usual mechanisms interrupt the resistive path: a film burns through, a winding parts, a solder joint fatigues. Overload failures may be immediate, from a single pulse beyond the energy the element can absorb, or cumulative, from running warm for a long time. Drift is the quieter failure. A part that stays within its power rating but runs hot ages faster, and a circuit calibrated when new can move out of specification without anything appearing to have broken. This is the argument for derating deliberately rather than to the limit of the curve, and the microsim shows how little of a rating survives once the ambient temperature rises. ## Microsim The microsim treats the resistor as a thermal object as much as an electrical one. The reader sets an applied voltage, a nominal resistance, a temperature coefficient, a power rating, a thermal resistance to the surrounding air, and an ambient temperature. It then solves the self-heating loop and plots what the part dissipates against what its rating allows at every ambient temperature on the axis, marking where the two cross. Three things are worth trying. Raise the ambient temperature and watch a part that was comfortable at room temperature run out of rating well before its nominal limit. Set the temperature coefficient negative, as carbon composition is, and raise the voltage until the loop becomes unstable. Then increase the thermal resistance, which is what happens when a part is crowded by its neighbours or mounted on a board with no copper to spread heat, and watch the body temperature rise with no change to the circuit at all.  **Microsim — three.js (Wikitube framework):** *The resistor: self-heating, temperature drift and derating* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/electronics/Resistor.html" data-title="Resistor"></div> *Built from `MICROSIM_GUIDE/specs/sims/Resistor.json`; part of the [[Electronics]] set ([[PORTAL_Electronics]]).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Resistor) : [Wikitube](https://en.wikitube.io/wiki/Resistor) Skeleton mirrored at revision 1372032062. Prose, emphasis and the microsim are Wikitube's own. ## See also - [[Ohm's_law]] - [[Electrical_resistance_and_conductance]] - [[Capacitor]] - [[Inductor]] - [[Wheatstone_bridge]] - [[Johnson–Nyquist_noise]] ## References The circuit theory and thermal behaviour described here — Ohm's law, Joule heating, the linear temperature-coefficient model, lumped thermal resistance, thermal noise and the power-derating curve — are standard textbook material and are not separately footnoted, per the Wikitube style guide §6.1. *Citation needed:* the construction-class figures in "Fixed resistors", "Electrical and thermal noise" and the derating knee used by the microsim are stated as typical classes rather than as any one manufacturer's part. Pinning them to specific datasheets and to the relevant IEC standard for marking and derating is queued for the next pass on this article; no source is asserted for them here. ## External links - Electronic colour code references and E-series preferred-value tables, to be pinned with the citations above.