Electrical Resistance: How It Works and How to Choose a Resistor
A resistor can limit LED current, set a measurement range or absorb energy during a power-supply test. The same electrical property also causes unwanted voltage loss in cables and heating at poor connections. Resistance describes how a component or conductive path relates applied voltage to the current flowing through it.
Resistance is represented by R and measured in ohms, Ω. A resistor is a component manufactured to provide a specified resistance. Wires and motor windings have resistance too, although resistance alone does not describe everything they do.
What Ohm’s Law Actually Tells You
For an ohmic component under approximately constant physical conditions, V = IR. The voltage across the component equals the current through it multiplied by its resistance. Rearranging gives I = V/R or R = V/I.
For example, 24 V across 2.4 kΩ produces 10 mA. If resistance stays unchanged, doubling the voltage doubles the current. At a fixed voltage, increasing resistance reduces current.
That proportional relationship does not apply universally. A diode or LED has a nonlinear current-voltage characteristic. Calculating V/I at one operating point does not prove that the component behaves like the same fixed resistor elsewhere.
Calculate Heat Before Choosing the Package
For steady DC operation, resistor dissipation is P = VI = I²R = V²/R. The 2.4 kΩ resistor carrying 10 mA at 24 V releases 0.24 W as heat. Understanding the difference between volts, amperes and watts is essential when selecting the component.
A nominal 0.25 W part would operate close to its stated rating in that example. The usable rating depends on ambient temperature and the mounting conditions behind the specification. Choose suitable margin and check the derating curve rather than assuming a printed wattage applies in every enclosure.
Resistance Depends on Material and Geometry
For a uniform conductor at a given temperature, with approximately uniform current distribution, R = ρL/A. Here ρ is material resistivity, L is length and A is cross-sectional area.
A longer conductor has more resistance; a larger cross-sectional area gives less resistance. Doubling length doubles resistance. Doubling area halves it, provided the other conditions stay the same. Resistivity belongs to the material; resistance also depends on the shape and dimensions of the part.
This distinction explains why cable length and conductor size affect voltage drop. In a two-wire DC circuit, both the outgoing and return conductors contribute to the loop resistance.
Temperature Can Increase or Decrease Resistance
Many metals, including copper, increase in resistance as they warm up. An NTC thermistor behaves differently: its resistance falls as temperature rises. A PTC element increases in resistance within its positive-temperature-coefficient operating region. Its response curve depends on the device.
A Pt100 sensor has a nominal resistance of 100 Ω at 0°C. Its predictable resistance change is used to measure temperature. By contrast, precision circuit resistors are often selected to keep temperature-related changes small.
Temperature coefficient of resistance is commonly specified in ppm/°C or ppm/K. A coefficient of 50 ppm/°C corresponds to approximately 0.25% change over 50°C under a linear approximation. That change is separate from the component’s initial tolerance.
Fixed, Adjustable and Special-Purpose Resistors
Fixed resistors include carbon-film, metal-film, thick-film, thin-film and wirewound constructions. Their suitability depends on accuracy, noise, stability, power and pulse requirements. SMD describes surface mounting; it does not identify a single resistor technology.
A potentiometer provides an adjustable connection along a resistive track. With three terminals, it can operate as a voltage divider. Using the wiper and one end gives a two-terminal variable resistance, subject to the applicable current and track-dissipation limits. Rheostats are used for variable-resistance applications.
Special-purpose components include current-sense shunts, high-voltage resistors, pulse-rated parts and fusible resistors. Matching the resistance value alone does not make a general-purpose replacement suitable for one of these roles.
Reading Values and Specifications
Depending on the package, the value may appear as colour bands or a printed code. 4R7 means 4.7 Ω, while 4K7 means 4.7 kΩ. In the common three-digit system, 472 means 47 × 10² = 4,700 Ω. Other coding systems exist, and some miniature parts have no marking.
A 4.7 kΩ ±1% specification allows a value from 4,653 Ω to 4,747 Ω at the stated reference conditions. Tolerance describes resistance accuracy, not power capacity. Selection should also consider rated dissipation, maximum working voltage, temperature coefficient, package and any pulse specification.
Series and Parallel Connections
Series resistors add directly: 1 kΩ + 2.2 kΩ = 3.2 kΩ. For parallel resistors, 1/Req = 1/R1 + 1/R2. Two 1 kΩ resistors in parallel produce 500 Ω.
The equivalent resistance describes the network at its terminals. It does not remove the need to check power in each individual resistor. Unequal values, unequal cooling and component tolerances can affect how the electrical and thermal demands are distributed.
Why a Voltage Divider Changes When Loaded
For an unloaded divider with R1 between the supply and output, and R2 between the output and the reference node, Vout = Vin × R2/(R1 + R2). Two 10 kΩ resistors across 12 V give an unloaded midpoint voltage of 6 V.
Now connect a 10 kΩ load from that midpoint to the reference node. It appears in parallel with the lower resistor, reducing the lower branch to 5 kΩ. The output becomes 12 × 5/(10 + 5) = 4 V.
This is why the input impedance of an analogue voltage receiver matters. A resistor divider can scale a signal, but it is not a substitute for a voltage regulator supplying a changing load.
Resistors in Industrial Control
A PLC or measurement module may use resistors to scale signals, establish input states or measure current. In a suitable receiving circuit, a 4–20 mA signal develops 1–5 V across 250 Ω. A current input may already include this measurement resistance, so its wiring instructions must be checked before adding another resistor.
A load resistor draws power from a source for testing or another defined circuit purpose. In a variable frequency drive system, a braking resistor dissipates regenerative energy through a braking chopper. Continuous power and pulse energy are important in these applications, alongside the required resistance.
Resistance Is Not the Whole of Impedance
Impedance includes resistance and the effects of inductance and capacitance in AC operation. Both use ohms, but they describe different things. Measuring a motor winding’s DC resistance does not, by itself, predict the motor’s normal running current.
Real resistor components also have parasitic inductance and capacitance. At higher frequencies, skin effect can alter current distribution and AC losses in conductors. Two parts with the same measured DC resistance may therefore perform differently in a fast or high-frequency circuit.
Measuring Resistance Without Misreading the Circuit
Use a multimeter’s resistance function only on a de-energised circuit after stored energy has been safely removed and absence of voltage verified. Parallel paths can make an in-circuit reading misleading; lifting one end of the resistor may be necessary.
For very low resistances, test-lead and contact resistance can become a significant part of the reading. A suitable four-wire Kelvin measurement reduces this error. An OL display may mean an open circuit or a value beyond the selected range. A continuity beep does not necessarily mean zero ohms.
If a resistor has failed, investigate the cause as well as the component: excessive voltage, excess current, another failed part or inadequate cooling may be responsible. A correct replacement must match the electrical duty and operating conditions, not just the printed resistance.
Technical references: OpenStax: resistivity and resistance · Where Ohm’s law applies · Vishay: resistor characteristics · Fluke: resistance measurement · Texas Instruments: RTD measurements