Resistance and resistors

Resistance appears in every circuit: in the conductors that carry current, in the loads that do work, and in the components that control current in electronics and controls. Lesson 3 used Ohm's law to relate voltage, current and resistance. This lesson looks at resistance itself: what determines the resistance of a wire or component, how resistance changes with temperature, the types of resistors and how they are marked, how resistors are rated for power, and devices whose resistance changes with temperature, light, voltage or position. These ideas explain why wires heat up, why lamps draw a surge at switch-on, how temperature sensors work, and how to read and replace components in control circuits.

What determines resistance

The resistance of a uniform conductor depends on four things: the material, the length, the cross-sectional area and the temperature. Longer conductors have more resistance, because electrons must travel farther through the material; thicker conductors have less, because there are more paths side by side. The relationship is:

where \(R\) is resistance in ohms, \(\rho\) (rho) is the resistivity of the material in ohm-metres (Lesson 2 lists values), \(L\) is the length in metres and \(A\) is the cross-sectional area in square metres. For copper at 20 °C, \(\rho = 1.72 \times 10^{-8}\) Ω·m.

Conductance

Conductance is the opposite of resistance: how easily a component lets current flow. Its symbol is \(G\) and its unit is the siemens (S):

Conductance is convenient for parallel circuits, where conductances simply add (Lesson 5). A 10 Ω resistor has a conductance of 0.1 S; two in parallel have 0.2 S, which is 5 Ω.

Resistance and temperature

The resistance of most metals rises with temperature, because the atoms vibrate more and impede the flow of electrons. For copper, resistance rises by about 0.393% per °C; for aluminum, about 0.403% per °C. The resistance at a new temperature is:

where \(\alpha\) is the temperature coefficient of resistance. Conductor tables list resistance at a standard temperature (often 75 °C for code calculations), because conductors under load run warm.

Incandescent lamp filaments show a dramatic version of this effect. A tungsten filament's resistance at its operating temperature (around 2,500 °C) is roughly 10 to 15 times its cold resistance. When the lamp is switched on, the cold filament draws a large inrush current for a fraction of a second, which is why lamps usually fail at switch-on. Some materials, such as carbon and semiconductors, have negative temperature coefficients: their resistance falls as they heat up.

Resistors

A resistor is a component made to have a specific resistance. Resistors limit current, divide voltages, set timing in circuits, pull signals to known levels, and turn electrical energy into heat in heaters and load banks. They are specified by three main ratings:

• Resistance, in ohms, with standard values in series such as E12 (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 and their multiples by powers of ten).
• Tolerance: how close the actual value is guaranteed to be to the marked value, such as ±5% or ±1%.
• Power rating: the maximum power it can dissipate continuously without overheating, such as 1/4 W, 1 W or 50 W.

Types include carbon film and metal film resistors (small, for electronics), wirewound resistors (for higher power and precision), large ceramic or grid resistors (for motor starting, braking and load banks), and surface-mount resistors on circuit boards.

Reading resistor markings

Small through-hole resistors are marked with coloured bands. With four bands, the first two give digits, the third a multiplier (the number of zeros), and the fourth the tolerance. Five-band resistors use three digit bands. Surface-mount resistors use number codes: "472" means 47 followed by 2 zeros, 4,700 Ω.

Power ratings and heat

A resistor dissipates power as heat, \(P = I^2 R = V^2/R\) (Lesson 3). If the power exceeds the rating, the resistor overheats, changes value, burns or fails open. Good practice is to choose a power rating at least twice the calculated dissipation and to allow space and airflow for cooling; resistors in enclosures and at high ambient temperatures must be derated further.

Variable resistors

Some resistors are designed to be adjusted. A potentiometer has three terminals: the two ends of a resistive track and a sliding contact (the wiper). Used as a voltage divider, it gives an adjustable output voltage, as in speed setting knobs on drives and volume controls. A rheostat uses only two terminals (one end and the wiper) as an adjustable resistance in series with a load, historically used for dimming and motor speed control but wasteful because it turns the dropped voltage into heat.

Resistors that sense the world

Several devices change resistance in response to physical conditions and are widely used as sensors:

• Thermistors: NTC (negative temperature coefficient) thermistors decrease in resistance as temperature rises; they are used in temperature sensors and to limit inrush current. PTC thermistors increase sharply above a set temperature and are used as resettable fuses and in motor winding protection.
• Resistance temperature detectors (RTDs): precision platinum resistors, such as the Pt100, which has 100 Ω at 0 °C and rises about 0.385 Ω per °C; they are accurate and stable and used in HVAC, process control and data centres.
• Photoresistors (light-dependent resistors): resistance falls with light; used in simple light sensors such as photocells for outdoor lighting.
• Varistors (metal oxide varistors, MOVs): resistance falls sharply above a threshold voltage; used in surge protective devices to clamp voltage spikes.
• Strain gauges: resistance changes when stretched; used in load cells and pressure sensors.