Ohm's Law

The rule in one line

Voltage = current × resistance. Written as a formula, V = I × R.^[1] If you know any two of these, you can work out the third, which makes it one of the first tools for understanding any circuit.

Three quantities

• Voltage (V), in volts, is applied across a component, and the current through it results from that voltage.^[1]
• Current (I), in amperes, is the rate at which charge flows. One ampere is one coulomb per second,^[4] about 6.24 billion billion elementary charges passing a point every second.^[7]
• Resistance (R), in ohms (Ω), measures how difficult it is to pass a current through a wire or component.^{[2, 1]}

A helpful picture is water in a pipe: voltage is like the pressure, current like the flow, and resistance like a narrow section that holds the flow back. Like all analogies, it has limits, but it gets the direction of each effect right.

How it works

For most materials, the current that flows is directly proportional to the voltage applied.^[1] Double the voltage across a resistor and you double the current; halve it and the current halves. Plot current against voltage and you get a straight line. The steepness of that line is set by the resistance: the higher the resistance, the less current each volt produces.

Materials and components that behave this way are called ohmic. Resistors, the components built to provide resistance, are the classic example.^[1]

The math (optional)

The law can be rearranged three ways:

V = I × R I = V ÷ R R = V ÷ I

Worked example. A carbon resistor connected to a 9.00-volt battery carries a current of 3.00 milliamps (0.003 A). Its resistance is R = 9.00 ÷ 0.003 = 3,000 Ω, written as 3.00 kΩ.^[1]

Combined with the power formula P = I × V, Ohm’s law gives two more useful forms for the power turned into heat in a resistor: P = I² × R and P = V² ÷ R.^[3]

Resistors in a row (in series) add up: R = R₁ + R₂ + …, so two 1 kΩ resistors in series make 2 kΩ.^[5]

What sets the resistance?

Resistance depends on the material and the shape of a conductor:

R = ρ × L ÷ A

Here L is the length, A is the cross-sectional area, and ρ (rho) is the material’s resistivity, a measure of how strongly the material opposes current.^[2] A longer wire has more resistance, and a thicker one has less.^[2]

Resistivities vary enormously. At 20 °C, silver’s is about 1.59 × 10⁻⁸ Ω·m and copper’s about 1.68 × 10⁻⁸ Ω·m, while glass comes in somewhere between 10⁹ and 10¹⁴ Ω·m.^[2] So even the most conductive glass resists current more than 10¹⁶ times as strongly as copper.

Temperature matters too. The resistance of most metals, including copper, increases as they get hotter; semiconductors behave the opposite way.^[2] Superconductors have no resistance at all at low temperatures.^[2]

Common misconceptions

“Ohm’s law is a law of nature.” It isn’t in the same class as Newton’s laws or the laws of thermodynamics. It is an empirically observed rule that many materials follow.^[1]

“Everything obeys Ohm’s law.” Many devices don’t. A diode, for example, lets current flow freely in one direction but lets almost none through the other way. Its current is not proportional to its voltage, so it is nonohmic.^[1]

“A wire’s resistance is fixed.” It changes with temperature. A metal’s resistance rises as it heats up.^[2]

Where the energy goes

Whenever current flows through a resistance, electrical energy is converted into thermal energy in the conductor. The moving electrons collide with the ions of the material’s lattice, and their extra energy becomes heat.^[3] That’s useful in a toaster or heater, and wasteful in a long power cable.

That waste is why electricity is sent across the country at high voltage. For the same power, a higher voltage means a lower current, and the heat lost in the cables depends on the square of the current.^[6] As the US Energy Information Administration puts it, higher-voltage electricity makes long-distance transmission more efficient and less expensive.^[8]

History

Georg Simon Ohm (1787–1854), a German physicist, was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied. He published his findings in 1827.^[1] His experiments measured voltage and current in circuits with wires of different lengths.^[1]

Try it yourself

In the free Ohm’s Law simulation listed below, you can slide the voltage and resistance up and down and watch the current change. Then build real-looking circuits in the Circuit Construction Kit.