What Is a Resistor? Ohm's Law, Voltage and Current Explained

In everyday life

Toasters and hair dryers make heat from electricity. Inside them is a metal wire that conducts poorly, such as nichrome wire. Current is sent through this wire on purpose, to make it hot. This difficulty of passing current is resistance.

On the circuit boards of home appliances, you can find small parts painted with colored bands. These are resistors. Small devices such as smartphones use tiny square resistors, smaller than a sesame seed (chip resistors). The resistor is one of the most basic parts in electronic circuits.

Your phone gets warm when you play a demanding game. That is also related to resistance, because every path electricity takes inside a chip has a little resistance. This article starts with what voltage and current mean, and builds up step by step.

How it works 1: voltage, current and resistance

Electricity is carried by very small particles that can move through a metal. These particles are called electrons. When you connect a battery, the electrons all through the circuit start to move a little at once. This is what "electricity flowing" means.

The amount of electricity that passes a point each second is called current. Its unit is the A (ampere). One thousandth of 1 A is 1 mA (milliampere).

The strength of the push that drives current is called voltage. Its unit is the V (volt). Voltage is always a difference between two points. A 1.5 V battery means the difference between its plus and minus ends is 1.5 V.

Apply the same voltage to different things, and different currents flow. This difficulty of flow is resistance, and its unit is the Ω (ohm). If 1 V makes 1 A flow through something, its resistance is 1 Ω.

How it works 2: Ohm's law

In most metals, doubling the voltage exactly doubles the current. Current is proportional to voltage, and resistance sets the ratio. The German physicist Ohm published this relation in 1827 (Encyclopaedia Britannica). It is called Ohm's law.

In words, voltage = current × resistance. If we write voltage as V, current as I and resistance as R, this becomes V = IR. Turned into a division, it reads current = voltage ÷ resistance. If you know any two of the three, you can work out the third.

Let's check with an example. Connect a 100 Ω resistor to a 1.5 V battery. The current is 1.5 ÷ 100 = 0.015 A, or 15 mA. Double the resistance to 200 Ω, and the current halves to 7.5 mA.

Not everything is proportional, though. A diode is a part that lets current flow only one way. In diodes and LEDs, the current rises sharply once the voltage passes a certain level ("What Is a Diode?"). Even in metals, resistance rises a little as the temperature goes up. Think of Ohm's law as a rule that holds well under set conditions.

How it works 3: the three things that set resistance

The resistance of something like a wire depends on three things. It is larger when the wire is longer, and smaller when the wire is thicker. A long path is harder to get through, and a wide path lets many electrons pass side by side.

The third is the material. Even with the same shape, materials differ greatly in how easily they conduct. This difficulty, which belongs to each material, is called resistivity. At 20 °C, taking copper as 1, aluminum is about 1.6 times higher and nichrome, used in heaters, about 60 times. We calculated these from a table in a physics reference by Georgia State University in the US.

As a formula: resistance = resistivity × length ÷ cross-sectional area. The cross-sectional area is the area of the cut face when you slice the wire straight across. By how easily they conduct, materials are grouped into conductors, semiconductors and insulators (conductors vs. semiconductors vs. insulators).

Use 1: setting an LED's current

A resistor is a part made to have a set resistance value. Its most common job is to hold the current to just the right size. A typical example is the resistor used with an LED.

Past a certain voltage, an LED's current rises sharply. If you connect it straight to a power supply, too much current flows and the LED breaks ("How Do LEDs Work?"). So a resistor is connected in line with it (in series) to set the current. Here, the voltage across the LED can be treated as almost constant.

Let's work out the numbers. The supply is 5 V, and a red LED takes about 2 V (ROHM's red LED is 1.9 V typical at 20 mA). We want 10 mA to flow. The resistor gets the rest: 5 − 2 = 3 V.

From Ohm's law, resistance = 3 V ÷ 0.01 A = 300 Ω. A guide from an electronic parts retailer uses the same method (Akizuki Denshi, a Japanese parts shop). In practice, you pick the closest value that is sold (LED resistor calculator).

Use 2: splitting a voltage

Connect two resistors in a row across a power supply, and the same current flows through both. The voltage across each one is current × resistance. So the voltage splits in the ratio of the two resistances. With two equal resistors, each gets exactly half.

Connect two 10 kΩ (10,000 Ω) resistors to 5 V, and the point between them sits at 2.5 V. The current is 5 V ÷ 20,000 Ω = 0.25 mA. This circuit is called a voltage divider. It is used in circuits that measure a battery's voltage and in circuits that read sensor signals (voltage divider calculator).

The differences between series and parallel connections are summed up in a table in series vs. parallel circuits.

How electricity turns into heat

As electrons move through a metal, they keep bumping into things such as vibrating atoms. Each bump turns part of the electrical energy into energy that shakes the atoms, in other words, heat. This is how resistance produces heat. Here, the picture of the atomic world is greatly simplified.

The energy used each second is called power, and its unit is the W (watt). Power is voltage × current. Since voltage is current × resistance, power can also be written as current × current × resistance. Joule in Britain found this link between current, resistance and heat in 1840 (Encyclopaedia Britannica).

In the LED example, the resistor's power is 3 V × 0.01 A = 0.03 W (30 mW). Resistors with wire legs (leaded resistors) commonly come in types that can handle up to 1/4 W (0.25 W) (KOA datasheet). This "usable up to here" limit is called the rating. 30 mW is about one eighth of the rating, so this resistor barely gets warm.

Double the current, and the heat goes up four times, because heat depends on the square of the current. Where large currents flow, even a tiny resistance makes a lot of heat.

Why chips get hot

The transistors in a chip are switches that let electricity through or stop it ("What Is a Transistor?"). But even while a transistor lets current through, its resistance is not zero. This remaining resistance is called on-resistance.

In a chip, many transistors switch hundreds of millions of times per second. Each time they switch, they store charge in the wiring and other parts, or let stored charge go. The current that flows then passes through the on-resistance and the wiring resistance, and turns into heat. Small currents also leak from transistors that are not switching. Static vs. dynamic power covers this breakdown in detail.

Almost all the power a chip uses ends up as heat. Take the H100, a chip for AI computing that NVIDIA announced in 2022. Its server version, called SXM, is designed to use up to 700 W (NVIDIA product information). That is close to the heat of a small electric heater, coming from a single part. Cooling is designed so that this heat can escape.

The path heat escapes along follows the same pattern as Ohm's law. How hard it is for heat to escape is called thermal resistance. You can estimate temperature rise = thermal resistance × power (ROHM). Temperature difference takes the place of voltage, and heat flow takes the place of current (junction temperature calculator). How the heat is carried away is explained in "How Are Chips Cooled?".

Wiring inside a chip and resistance

Inside a chip, thin metal wires connect the transistors. The wiring is stacked in many layers: thinner in the lower layers, thicker in the upper ones (multilevel interconnect). After IBM announced copper wiring in 1997, the main wiring metal changed from aluminum to copper (IBM history page).

As in How it works 3, a wire's resistance is inversely proportional to its cross-sectional area. Halve both the width and the thickness, and the area drops to one quarter. Then the same length has four times the resistance. The finer chips get, the more their wiring resistance grows.

Let's compare numbers. A copper wire 1.6 mm across, like those used in house wiring, has about 0.0000085 Ω of resistance per 1 mm. A copper wire in a chip, 50 nm wide and 100 nm thick, has about 3,400 Ω per 1 mm. A nm (nanometer) is one millionth of a millimeter. For the same length, that is about 400 million times higher. Both values were calculated with copper's resistivity from the table.

In reality, though, a thin wire's resistance is even higher than this, because the table value is for a large block of copper. Electrons in copper travel about 40 nm on average before they bump into something (a paper by Gall of Rensselaer Polytechnic Institute in the US). When a wire is about that wide or narrower, electrons hit the wire's surfaces more often. They also hit the borders between the tiny crystals that make up the metal more often. So the copper itself conducts less well. In Intel's "10 nm" generation of 2018, the tightest wiring spacing was 36 nm (TechInsights). This spacing is the width of one line plus one gap, so a line is about half of it. The number in a generation's name is not an actual dimension ("What Does 2nm or 3nm Mean?").

So in the very thinnest places, metals other than copper are starting to be used. For example, Intel's "10 nm" generation used cobalt for the lowest two wiring layers (Intel's 2017 paper). Copper vs. cobalt vs. ruthenium interconnects compares copper with the other metals in a table. Wiring resistance also delays signals ("RC Time Constant Explained").

What happens in the power wiring

The power wiring that delivers electricity to a chip also has resistance. When current flows, the voltage drops along the way, by the amount Ohm's law gives. This voltage drop is called IR drop. I stands for current and R for resistance. If the voltage that reaches the transistors drops, they slow down or malfunction.

Let's use some numbers, just to illustrate. Say 100 A flows into a chip with a 1 V supply. If the path has 0.001 Ω of resistance, the voltage drops by 100 × 0.001 = 0.1 V. Just one thousandth of an ohm costs a tenth of the voltage. The lower the voltage and the larger the current, the more wiring resistance matters.

One fix is to run the power wiring on the back of the chip. Power then reaches the transistors without passing through the thin wiring on the front. This is called backside power delivery. Intel uses it in a generation it calls 18A, and says it greatly reduces the voltage drop (Intel).

When current crowds into a thin wire, another problem appears. Pushed by the flowing electrons, metal atoms slowly move. Over a long time, gaps can form and break the wire, or bumps can form and touch the next wire. Lienig and colleagues at TU Dresden in Germany explain this. The effect is called electromigration, and it goes faster at higher temperatures ("Arrhenius Equation in Chips").

Common misconceptions

By the numbers

It may surprise you that 1 mm of wiring in a chip can reach thousands of ohms. Chips still work because most wires are very short and carry small currents. Long wires and power wiring use the thick wires in the upper layers.

Learn more

• Related explainers: "What Is a Capacitor?" (a part that stores charge), "RC Time Constant Explained" (delay caused by resistance and capacitance), "AC vs DC Explained" (how AC flow is held back), "What Is a Power Semiconductor?" (ways to cut on-resistance)
• Compare in a table: series vs. parallel circuits / conductors vs. semiconductors vs. insulators / copper vs. cobalt vs. ruthenium interconnects
• Try the numbers: resistor color code / combined resistance calculator / LED resistor calculator / interconnect RC delay calculator (intermediate level)
• Next terms: IR drop, electromigration, thermal resistance, on-resistance