Resistors

The resistor is the simplest and most common electronic component: two wires and a body that turns some electrical energy into heat in a precisely controlled way. This article explains how it works inside, how to read its markings, which kind to choose, and how to use, size and test one.

No background is assumed. Every technical word is explained the first time it appears, and recap links point back to the earlier articles in this section.

1. A short recap: current, voltage and resistance

• Current (symbol I, unit ampere, A) is the rate at which charge flows. Voltage (V, unit volt, V) is the energy each unit of charge gains or loses between two points. Resistance (R, unit ohm, Ω) is how strongly something opposes current. (Recap: current, voltage and resistance.)
• Ohm's law ties them together: V = I × R.^[1]
• Resistivity (ρ, "rho") is a material's own resistance regardless of shape. Metals have low resistivity, insulators very high. (Recap: conductors and resistivity.)
• Temperature changes resistance: up in metals, down in pure semiconductors. (Recap: temperature effects.)

2. What a resistor is, and how it resists

A resistor is a component made to have a specific, stable resistance between its two terminals (connection points).^[2] Circuits use resistors to limit current, divide voltages, and hold signal lines at known levels.^[2] On a schematic, a drawing of a circuit, a resistor appears as a zigzag line or a plain rectangle.^[2]

Where the energy goes

Inside any conductor, free electrons drift along under the push of the voltage, but they keep colliding with the vibrating atoms of the solid, its lattice. Each collision hands energy to the atoms, which vibrate harder: the material warms up.^[3] A resistor is simply a part designed to do this in a predictable amount. The energy delivered by the voltage source is converted into thermal energy in the resistor.^[1] That is why every resistor has a power limit (see Power: heat, and choosing a wattage).

Setting the value: material, length and area

For a uniform piece of material, resistance is:^[4]

R = ρL / A

where ρ is the resistivity in ohm-meters (Ω·m), L is the length and A the cross-sectional area. A longer path means more collisions, a wider one carries more current.^[4]

Worked example. Take 1 m of wire 0.5 mm in diameter, so A = π × (0.25 × 10⁻³ m)² ≈ 1.96 × 10⁻⁷ m². Copper (ρ = 1.72 × 10⁻⁸ Ω·m) gives about 0.088 Ω. Nichrome, a nickel-chromium alloy with ρ = 100 × 10⁻⁸ Ω·m, gives about 5.1 Ω, roughly 58 times more.^[4] That is why resistors use resistive alloys, carbon or metal oxides rather than copper.

Most everyday resistors are film resistors: a thin resistive layer on a ceramic (insulating) rod or chip.^[5]​^[2] To reach the exact value, the maker cuts a spiral groove through the film, leaving a long, narrow strip; more turns mean a higher resistance.^[2] Lasers now do this trimming, and a lacquer coat protects the result.^[5] The groove applies R = ρL/A directly: it makes L longer and the strip, and so A, narrower.

3. The four numbers that describe a resistor

Value, in ohms

Resistances span a huge range, so metric prefixes are used: 1 kΩ (kilohm) is 1,000 Ω, and 1 MΩ (megohm) is 1,000,000 Ω. A 4,700 Ω resistor is written 4.7 kΩ, and 5,600,000 Ω is 5.6 MΩ.^[2] Current-sensing resistors go the other way, down to milliohms (mΩ, thousandths of an ohm).^[5]

Tolerance

Tolerance is how far a new resistor may differ from its marked value, as a percentage.^[5] A 4.7 kΩ ±5% part may measure anywhere from 4,465 to 4,935 Ω. In use, the value can shift further through drift and temperature.^[5]

Power rating

The power rating, in watts (W), is the most heat the resistor can continuously get rid of without exceeding its temperature limit. It is normally specified up to an ambient (surrounding air) temperature of 70 °C. Above that, the allowed power falls along a derating curve (Figure 2).^[5] Common leaded resistors are rated ¼ W or ½ W, and a ½ W body is visibly larger.^[2]

Temperature coefficient

The temperature coefficient of resistance (TCR) says how much the value changes per degree, in parts per million per kelvin (ppm/K; one kelvin is the same step as one degree Celsius).^[5] The change is:

ΔR / R = TCR × ΔT

A 10 kΩ metal film resistor at ±50 ppm/K, warmed by 50 °C, can shift by 50 × 10⁻⁶ × 50 = 0.25%, or 25 Ω. A carbon film part can have a TCR of −200 to −1,500 ppm/K,^[5] so the same warming could lower it by 1% to 7.5%. Each resistor also has a maximum operating voltage, the highest voltage it may continuously have across it.^[5]

4. Why resistors come in odd values: the E-series

You will not find 5 kΩ or 50 kΩ among the standard values. Resistors are made in values from the E-series of preferred numbers set out in standard IEC 60063.^[7] Each series divides every factor of ten (a decade) into n steps that grow by the same ratio, the n-th root of 10, rounded to two or three digits.^[5] E12 has 12 steps per decade, each about 21% larger than the last. E24 has 24 steps, and E12 is simply every second E24 value.^[7] The same pattern repeats in every decade: 4.7 Ω, 47 Ω, 470 Ω, 4.7 kΩ and so on.

From IEC 60063:2015, Table 1.^[7]

The steps are matched to tolerance. IEC 60063 pairs E12 with ±10%, E24 with ±5%, and E96 with ±1%.^[7] With these pairings, the possible spreads of neighboring values overlap slightly,^[5] so any resistance you need lies within reach of some standard part. Needing 5 kΩ, you would pick 5.1 kΩ from E24, or 4.7 kΩ from E12, and check that the circuit tolerates the difference.

5. Reading the color code

Leaded resistors usually show their value as colored bands, defined in standard IEC 60062.^[2]​^[8] Each color stands for a digit, a multiplier, a tolerance or a TCR, depending on which band it is in.

From IEC 60062:2016+AMD1:2019, Table 1 (TCR values are ±).^[8] Older charts sometimes list different tolerances for orange, yellow and gray; the standard's values are shown.

The band layout tells you how to use the table:^[8]

• 4 bands: digit, digit, multiplier, tolerance.
• 5 bands: digit, digit, digit, multiplier, tolerance, for tighter-tolerance parts.
• 6 bands: as 5 bands, plus a TCR band.
• 3 bands: digit, digit, multiplier, with no tolerance band, meaning ±20%.

Which end first? The first band sits nearest one end of the body. The tolerance band is at least 1.5 times wider than the others, which marks the end you finish at.^[8] Gold and silver are never first, because they have no digit.

Worked examples.

• Yellow, violet, red, gold: 4, 7, ×100, ±5% gives 47 × 100 = 4,700 Ω = 4.7 kΩ ±5%.^[2]
• Red, yellow, white, orange, brown: 2, 4, 9, ×1,000, ±1% gives 249 kΩ ±1%. A sixth red band would add a TCR of ±50 ppm/K.^[8]
• Violet, green, yellow, gold: 75 × 10,000 = 750 kΩ ±5%.^[8]
• Yellow, violet, gold, gold: 47 × 0.1 = 4.7 Ω ±5%. Gold as the third band means a value below 10 Ω.

When colors are ambiguous, red against orange or brown against violet under poor light, measure the part instead (see Testing a resistor).

6. Reading surface-mount codes

Surface-mount (SMD) resistors are small rectangular chips soldered onto pads on the surface of a circuit board, rather than through holes.^[2] Their size code gives length and width: "0805" means 0.08 by 0.05 inch, and "1206" is 0.12 by 0.06 inch, which metric listings call 3216 (3.2 by 1.6 mm).^[2]​^[5] The smallest chips carry no marking at all; Yageo, for example, leaves its 0201 and 0402 sizes blank.^[9] The rest use printed codes:^[10]​^[9]

• 3 digits (usually ±2% to ±10% parts): two digits then the number of zeros. 472 = 47 followed by two zeros = 4,700 Ω; 103 = 10 kΩ; 105 = 1 MΩ.
• 4 digits (±1% and tighter): three digits then the number of zeros. 1002 = 100 followed by two zeros = 10 kΩ; 3160 = 316 Ω.
• The letter R marks the decimal point: 4R7 = 4.7 Ω; R22 = 0.22 Ω.
• EIA-96 (used on some small 1% chips): two digits and a letter. The digits are an index from 01 to 96 into a table of the 96 three-digit E96 values; the letter is a multiplier (X = ×0.1, Y = ×0.01, A = ×1, B = ×10, C = ×100, D = ×1,000, E = ×10,000, F = ×100,000).^[9]

Index values from the Yageo EIA-96 table.^[9]

EIA-96 codes cannot be decoded by arithmetic; you need the table, which the Yageo and SparkFun references print in full.^[9]​^[2]

7. Kinds of fixed resistor

A fixed resistor has one set value. The main types differ in their resistive material.^[5]

Vishay's "Basics of Linear Fixed Resistors" (typical figures, not limits), except the metal oxide row, which is from one product family, KOA's MOS/MOSX datasheet.^[5]​^[6]

• Carbon film: a carbon layer on a ceramic rod. Most standard, no-frills leaded resistors are carbon film or metal film.^[2] It is made in high volume as a commodity part, and has a large negative TCR.^[5]
• Metal film: a metal alloy layer, often sputtered (deposited atom by atom in a vacuum). Low noise, tight tolerance, low TCR and good stability make it suited to precision work.^[5]
• Metal oxide film: a metal oxide layer that tolerates heat well. Typically sold as small power resistors with flameproof coatings, such as KOA's MOS series, rated to +200 °C.^[6]
• Carbon composition: the whole body is a pressed mix of carbon and binder, with no trimming, so tolerances are wide. They are noisy, resist moisture poorly, drift in storage, and are becoming obsolete for general use.^[11] They survive short overloads well for their size, so they remain in use for surge and pulse duties such as power supplies and welding controls.^[5]​^[11]
• Wirewound: resistance wire wound on a ceramic or fiberglass core. Very tough: the surface may reach +450 °C. The winding adds inductance (a coil effect covered in article 5), so they suit power, not high frequencies.^[5]
• SMD thick film and thin film: chip resistors on a ceramic substrate. Thick film is screen-printed from a resistive paste. It is cheaper, and good enough wherever low noise, low TCR and low drift are not priorities. Thin film is sputtered metal with better tolerance, TCR and noise.^[5]

8. Variable resistors: potentiometers, trimmers and rheostats

A potentiometer ("pot") is a resistive track between two end terminals, with a third terminal on a sliding contact called the wiper.^[12] Wired as three terminals, it is an adjustable voltage divider (see The voltage divider): the wiper delivers any fraction of the voltage across the ends.^[12] A volume knob is the classic example.^[2]

A trimmer (trimming potentiometer) is a small potentiometer included so a circuit can be tweaked, correcting for variations in other parts or for changes due to aging.^[12]

A rheostat is a variable resistor used with only two terminals, one end and the wiper, to control current in a series circuit. Bourns notes this rheostat mode accounts for over half of all trimmer applications.^[12]

9. Special resistors: thermistors, photoresistors and varistors

Some resistors are designed to change value with temperature, light or voltage:

• Thermistors change resistance strongly with temperature. NTC types fall in resistance as they warm; PTC types rise.^[14] They were covered in Conductors, Insulators, and Semiconductors.
• Photoresistors, also called light-dependent resistors (LDRs) or photocells, are usually made of cadmium sulfide (CdS) and drop in resistance as light increases.^[15] One typical part measures about 200 kΩ in the dark and 10 kΩ in dim light (10 lux).^[15] One datasheet part takes about 60 ms to respond to light,^[16] and Adafruit advises using photocells for "is it light or dark?" jobs, not for measuring precise light levels.^[15]
• Varistors are voltage-dependent resistors, usually zinc oxide ceramic. Their resistance falls steeply as voltage rises. Connected across (in parallel with) the circuit they guard, they become a low-resistance path during a surge and clamp the voltage.^[17] They protect against transients from lightning and switching and respond in under 20 nanoseconds.^[18]

10. Resistors in circuits

Ohm's law in practice

Ohm's law, V = IR, works in all three arrangements: I = V/R and R = V/I.^[1] For example, 12 V across 2.2 kΩ drives 12 ÷ 2,200 ≈ 5.5 mA (milliamperes, thousandths of an ampere). The voltage across a resistor carrying current is called the voltage drop.^[19]

Series and parallel

Resistors are in series when they are connected end to end, so the same current must pass through each. Their resistances simply add:^[19]

R_s = R₁ + R₂ + R₃ + …

Resistors are in parallel when each is connected across the same two points, so each gets the full voltage and the current divides between them. The total is found from the reciprocals:^[19]

1/R_p = 1/R₁ + 1/R₂ + 1/R₃ + …

The parallel total is always less than the smallest single resistor, because each one adds another path.^[19]

Worked examples (Figure 5), with a 9 V battery:

• Series, 1 kΩ + 2.2 kΩ: total 3.2 kΩ, current 9 ÷ 3,200 = 2.81 mA. The drops are 2.81 V and 6.19 V, adding back to 9 V.
• Parallel, the same two: 1/R_p = 1/1,000 + 1/2,200, so R_p ≈ 688 Ω. The 1 kΩ carries 9 mA and the 2.2 kΩ carries 4.09 mA, 13.09 mA in all.
• Two equal resistors in parallel give half the value: 1 kΩ with 1 kΩ makes 500 Ω. This is a handy way to make an odd value from stock parts.^[2]

The voltage divider

Two resistors in series across a supply share its voltage in proportion to their values. Taking the output from the point between them gives a voltage divider:^[13]

V_out = V_in × R₂ / (R₁ + R₂)

With two 10 kΩ resistors on 9 V, V_out = 4.5 V (Figure 4). SparkFun's example turns 5 V into 3.3 V using 1.7 kΩ and 3.3 kΩ.^[2] Put a sensor such as a photoresistor in place of one resistor and the output voltage tracks the light. That voltage can then be read by a microcontroller.^[2]

A divider is for signals, not for powering things. Anything connected to the output draws current through R₁ as well, which changes the ratio and wastes power as heat.^[13] For example, a 10 kΩ load across R₂ above makes that half 5 kΩ, and the output sags from 4.5 V to 3 V.

Limiting current: the LED resistor

A light-emitting diode (LED) lights when current flows through it in one direction. It drops a roughly fixed forward voltage, typically 1.7 to 3.4 V depending on color, and can draw enough current to burn itself out if connected straight to a supply. A series resistor sets the current:^[2]​^[20]

R = (V_S − V_F) / I_F

where V_S is the supply, V_F the LED's forward voltage and I_F the current you want. Take both LED figures from its datasheet; the LED in SparkFun's example datasheet is rated for 20 mA continuously.^[20]

Worked example (Figure 6): a red LED (V_F about 1.8 V)^[2] on a 5 V supply at 10 mA needs (5 − 1.8) ÷ 0.010 = 320 Ω. The next standard E12 value up is 330 Ω, giving 3.2 ÷ 330 ≈ 9.7 mA. Rounding up always errs on the safe side. Diodes and LEDs get their own article, number 6 in this series.

Pull-up and pull-down resistors

A digital input on a microcontroller (a small programmable computer chip) reads a voltage as HIGH or LOW. If it is connected to nothing, it floats, and its reading is unpredictable.^[21] A pull-up resistor connects the pin to the supply, so it reads HIGH until a button connects it to ground (0 V). A pull-down resistor does the reverse.^[21] About 10 kΩ is the usual choice, with 10 to 100 kΩ generally fine. Much lower wastes current when the button is pressed; much higher may be too weak to pull the pin reliably.^[21] With 10 kΩ on 5 V, a pressed button passes just 0.5 mA. Many microcontrollers have internal pull-ups that software can switch on.^[21] For more on the chips themselves, see the Microcontrollers section of this site.

11. Power: heat, and choosing a wattage

The power turned into heat in a resistor follows from Ohm's law:^[22]

P = VI = I²R = V²/R

Use whichever form matches what you know. A 9 V battery across 10 Ω gives 9² ÷ 10 = 8.1 W, far beyond any small resistor.^[23] The LED resistor above dissipates (0.0097 A)² × 330 Ω ≈ 0.031 W, so a ¼ W part is ample. A ¼ W, 100 Ω resistor placed across 12 V would have to shed 1.44 W, almost six times its rating.

How hot does a resistor get? Its temperature rise is roughly the power times its thermal resistance, in kelvins per watt, which depends on how it is mounted.^[5] KOA's metal oxide datasheet shows that at full rated power the surface rises about 105 °C above ambient for the 1 W size and about 205 °C for the 5 W size.^[6] A resistor running at its rating can be far too hot to touch.

Choosing a rating. Calculate the worst-case power, then pick a rating with real margin, apply the datasheet's derating curve for the actual ambient temperature, and allow for warm enclosures and poor airflow. Ohmite gives this advice.^[24] A simple habit for beginners is to choose a rating at least twice the calculated power. That is this article's rule of thumb, not a standard; the datasheet remains the authority.

12. Testing a resistor

A multimeter set to its resistance (Ω) range measures ohms. It applies its own small, known test voltage and calculates the resistance from the result.^[25] Because of this:

1. Remove power first. Switch off the circuit and discharge any capacitors, because voltage already in the circuit gives false readings.^[26]​^[25]
2. Measure out of circuit when you can. In circuit, other parts connected across the same two points form parallel paths, and the meter reads their combination, usually lower than the resistor alone (Figure 7).^[26] Unsoldering one lead is enough.
3. Keep your fingers off both probe tips. Your body is another parallel path.^[26]
4. Pick the range. "OL" or a lone "1" means the value is above the range; switch up.^[27]​^[25] Auto-ranging meters do this for you.^[26]
5. Compare with the tolerance. A 10 kΩ ±5% resistor is good anywhere from 9.5 to 10.5 kΩ.^[27] Touch the probes together first; test leads themselves add about 0.2 to 0.5 Ω, which matters only for very low values.^[26]

What a failed resistor looks like

Heat is the most common cause of resistor failure. Running at or above the rating, or in a hotter place than designed for, leads to drift in value, cracking, discoloration and, in severe cases, a complete open circuit (a break, so no current flows).^[24] Repeated heating and cooling can also crack terminations into an open. Moisture causes slower drift.^[24] So look for a darkened, scorched, blistered or cracked body or burnt circuit board around it. Then measure it: an open resistor reads OL on every range, and a drifted one reads well outside its tolerance. A burnt resistor is often a symptom. Before fitting a replacement, work out why it overheated (too small a rating, too little cooling, or a fault elsewhere drawing extra current); otherwise the new one may fail the same way.^[24]

13. Everyday uses and safety

Resistors are in almost every circuit.^[5] You will meet them setting LED currents, biasing microcontroller inputs, scaling voltages for measurement, as sensors (thermistors and photoresistors), as surge protection (varistors), and as low-value current-sensing shunts in power supplies and battery management.^[2]​^[5]

Coming up in this section: 4 Capacitors (insulators as dielectrics, and storing charge), 5 Coils (Inductors), 6 Diodes (including LEDs), 7 Transistors, and 8 Transformers.

The whole story in brief

• A resistor turns electrical energy into heat as electrons collide with the lattice. Its value is set by R = ρL/A, usually by trimming a spiral groove in a thin film.
• Four numbers describe it: value (Ω, kΩ, MΩ), tolerance (%), power rating (W, derated above about 70 °C) and temperature coefficient (ppm/K).
• Values come from the E-series (E12, E24, E96), geometric steps matched to tolerance.
• Leaded parts use color bands: two or three digits, a multiplier, a tolerance and sometimes a TCR. The wide band comes last. SMD parts use 3-digit, 4-digit or EIA-96 codes.
• Metal film is the precise all-rounder, carbon film the commodity part, metal oxide and wirewound the power types, and thick and thin film the chip versions.
• Series resistances add; parallel ones combine to less than the smallest. Two resistors make a voltage divider.
• Resistors limit LED current with R = (V_S − V_F)/I_F and pull inputs up or down.
• Check power with P = I²R = V²/R and choose a rating with margin.
• Test unpowered and out of circuit. A burnt or open resistor often points to a deeper fault.

Sources

All links were checked in October 2026. External links open in a new tab.

1. OpenStax, College Physics 2e, section 20.2 "Ohm's Law: Resistance and Simple Circuits": https://openstax.org/books/college-physics-2e/pages/20-2-ohms-law-resistance-and-simple-circuits
2. SparkFun Learn, "Resistors" tutorial (all pages): https://learn.sparkfun.com/tutorials/resistors/all
3. OpenStax, College Physics 2e, section 20.1 "Current" (free electrons colliding with the lattice and generating thermal energy): https://openstax.org/books/college-physics-2e/pages/20-1-current
4. OpenStax, College Physics 2e, section 20.3 "Resistance and Resistivity" (Table 20.1, resistivities at 20 °C): https://openstax.org/books/college-physics-2e/pages/20-3-resistance-and-resistivity
5. Vishay Beyschlag, application note 28771, "Basics of Linear Fixed Resistors" (PDF): https://www.vishay.com/docs/28771/basics.pdf
6. KOA Speer, MOS/MOSX "Reduced Size Metal Oxide Power Type Leaded Resistor" datasheet (derating curve and surface temperature rise chart; PDF): https://www.koaspeer.com/pdfs/MOS.pdf
7. IEC 60063:2015, "Preferred number series for resistors and capacitors" (free preview pages, PDF): https://cdn.standards.iteh.ai/samples/21131/0b431abe83d64551accdfaebc210796e/IEC-60063-2015.pdf
8. IEC 60062:2016+AMD1:2019, "Marking codes for resistors and capacitors" (free preview pages, PDF): https://cdn.standards.iteh.ai/samples/20940/b5fb592a1a1749c79f33e4d987f7fefb/IEC-60062-2016.pdf
9. Yageo, "Chip Resistor Surface Mount Marking" product specification, v.3 (2017; includes the EIA-96 table; PDF): https://yageogroup.com/content/Resource%20Library/Product%20Guide-Catalog/yageo_PYu-R_Marking_3_19050818_924.pdf
10. Vishay, "SMD Resistor Marking" and color-code reference, document 20020 (PDF): https://www.vishay.com/docs/20020/smdresistormarking.pdf
11. Vishay, "Carbon Composition Resistor Cross Reference" (comparison of carbon composition and metal film, document 31049; PDF): https://www.vishay.com/docs/31049/carbcompcrossref.pdf
12. Bourns, The Best of Trimmer Primer (trimming potentiometer handbook; PDF): https://www.bourns.com/docs/default-document-library/bourns%5Ftrimmer%5Fprimer.pdf
13. SparkFun Learn, "Voltage Dividers" tutorial (all pages): https://learn.sparkfun.com/tutorials/voltage-dividers/all
14. Texas Instruments, application report SNOAA12, "Methods to Reduce Thermistor Linearization Error, Memory, and Power Requirements Over Wide Operating Temperature Ranges" (introduction covers NTC and PTC types; PDF): https://www.ti.com/lit/an/snoaa12/snoaa12.pdf
15. Adafruit Learning System, "Photocells" (L. Ada; PDF): https://cdn-learn.adafruit.com/downloads/pdf/photocells.pdf
16. Advanced Photonix, PDV-P8103 CdS photocell (light dependent resistor) datasheet (PDF): https://www.advancedphotonix.com/media/pages/our-products/light-dependent-resistor-ldr/pdv-p8103/e28dce9e68-1718287431/ds-pdv-p8103.pdf
17. TDK Electronics, "SIOV Metal Oxide Varistors: General Technical Information" (PDF): https://www.tdk-electronics.tdk.com/download/185716/b0f23a2d5302fdabdd2bd029b5d38079/siov-general.pdf
18. Vishay BCcomponents, technical note 29079, "Varistors Introduction" (PDF): https://www.vishay.com/docs/29079/varintro.pdf
19. OpenStax, College Physics 2e, section 21.1 "Resistors in Series and Parallel": https://openstax.org/books/college-physics-2e/pages/21-1-resistors-in-series-and-parallel
20. SparkFun Learn, "Light-Emitting Diodes (LEDs)" tutorial (all pages): https://learn.sparkfun.com/tutorials/light-emitting-diodes-leds/all
21. SparkFun Learn, "Pull-up Resistors" tutorial (all pages): https://learn.sparkfun.com/tutorials/pull-up-resistors/all
22. OpenStax, College Physics 2e, section 20.4 "Electric Power and Energy": https://openstax.org/books/college-physics-2e/pages/20-4-electric-power-and-energy
23. SparkFun Learn, "Electric Power" tutorial (all pages): https://learn.sparkfun.com/tutorials/electric-power/all
24. Ohmite, "Common Causes of Resistor Failure and How to Prevent Them" (blog, August 2026): https://www.ohmite.com/blog/2026/08/24/common-causes-of-resistor-failure-and-how-to-prevent-them
25. NI (National Instruments), "Digital Multimeter Measurement Fundamentals" (section "Resistance Measurements with a DMM"): https://www.ni.com/en/shop/electronic-test-instrumentation/digital-multimeters/dmm-measurement-fundamentals.html
26. Fluke, "How to Measure Resistance with a Digital Multimeter": https://www.fluke.com/en-us/learn/blog/digital-multimeters/how-to-measure-resistance
27. SparkFun Learn, "How to Use a Multimeter" tutorial (all pages; section "Measuring Resistance"): https://learn.sparkfun.com/tutorials/how-to-use-a-multimeter/all