Ohm's law

A car headlight drawing 2.50 A from a 12.0 V battery has a resistance of 12.0 ÷ 2.50 = 4.80 Ω.

Double the push, double the flow

The German physicist Georg Simon Ohm was the first to show by experiment that the current in a metal wire is directly proportional to the voltage across it. Double the voltage and the current doubles; halve it and the current halves. Raise the resistance and the current falls in the same proportion. Put together, these give Ohm's law: I = V ÷ R. Rearranged, it gives two more useful forms, V = I × R and R = V ÷ I. One ohm is one volt per ampere.

I = V ÷ R. V = I × R. R = V ÷ I. Volts are amps times ohms.

Try it with the bulb in the lab. A 6 V battery across a 12 Ω bulb gives I = 6 ÷ 12 = 0.5 A. With 12 V the current becomes 1 A, and with 3 V it is 0.25 A. The car headlight in the lead works the other way round: OpenStax measures 2.50 A at 12.0 V, so R = 12.0 ÷ 2.50 = 4.80 Ω. And if a resistor of 15 Ω carries 0.2 A, the voltage across it must be V = 0.2 × 15 = 3 V. This last form, the IR drop, tells you how much voltage each part of a circuit uses up.

Plot it: a straight line

Set the lab's battery slider anywhere from 0 to 12 V and the small graph in the corner adds a point for the resistor: voltage across it on the horizontal axis, current through it on the vertical axis. For a fixed resistor every point lands on one straight line through zero, and the slope of that line is 1 ÷ R. Change the resistor to 24 Ω and a new, flatter line starts; change it to 6 Ω and the line is steeper. A material whose line stays straight is called ohmic. Copper, aluminium and the resistors in electronics are ohmic over the voltages we use.

Drag to turn. Scroll or pinch to zoom.

Move the battery slider and watch the dots line up on the I-V graph. Then change R1 with the menu and sweep the voltage again: the new line has a different slope, 1 ÷ R.

A resistor gives a straight I-V line. A filament bulb does not: as it heats, its resistance rises and the curve bends over. (Shape only, not to scale.)

When Ohm's law bends

Ohm's law is a rule found by experiment, like the law of friction, and it does not hold for everything. A filament bulb is the classic exception. The tungsten coil gets hotter as more current flows, and hot metal resists more. OpenStax gives the cold resistance of the headlight as only 0.350 Ω, against 4.80 Ω when it glows. So at the instant you switch it on, the current is about 12.0 ÷ 0.350 ≈ 34.3 A, almost fourteen times the steady 2.50 A, and it falls within a fraction of a second as the filament heats. Diodes, including LEDs, are far from ohmic: they let current through one way and almost none the other.

The circuit lab keeps each bulb at a fixed resistance so that the numbers come out cleanly; the course text says so wherever it matters. Real bulbs would show a smaller current change than the lab when you raise the voltage, because their resistance climbs with temperature.

Resistances from tiny to huge

Resistances in the world span an enormous range. OpenStax lists a metre of thick copper wire at about 10⁻⁵ Ω, the human heart at about 10³ Ω, a dry person from hand to foot at about 10⁵ Ω and the ceramic insulators that hold up power lines at 10¹² Ω or more. Ohm's law works the same way at every scale, which is why it is the first tool for nearly every circuit question.

BackgroundIn 1825 and 1826 Ohm ran a set of experiments to find how the length and thickness of a wire, and the metal it was made of, changed the current through it. Ammeters had not been invented yet, so he hung a magnetic needle near the wire and used how strongly the current turned it as his measure. He found that for a given wire the current grew in proportion to the strength of the battery, and he published the law in 1827 in a book called Die galvanische Kette, The Galvanic Circuit. The Smithsonian Libraries note that his work was ridiculed at first and only received proper attention later in his life. Today the unit of resistance carries his name, and its symbol is the Greek capital omega, Ω.

Key points

I = V ÷ R, V = I × R, R = V ÷ I; 1 Ω = 1 V/A.
For a fixed resistor the I-V graph is a straight line with slope 1 ÷ R.
Filament bulbs are not ohmic: hot filaments resist more.
A cold headlight (0.350 Ω) briefly draws about 34.3 A.

A 9 V battery is connected across 30 Ω. Current in amperes?
A bulb carries 0.25 A with 3 V across it. Resistance in ohms?
0.2 A flows through a 15 Ω resistor. Voltage across it in volts?
Headlight: 12.0 V and 2.50 A. Resistance in ohms? (two decimals)
The same headlight cold is 0.350 Ω. Current at switch-on, in amperes? (one decimal)
The voltage across a fixed resistor is doubled. The current:
- Doubles
- Halves
- Stays the same
- Becomes four times
On an I-V graph (I up, V across), which resistor has the steepest line?
- 6 Ω
- 12 Ω
- 24 Ω
Why is a filament bulb not ohmic?
- Its resistance rises as it heats
- It has no resistance
- Current flows only one way
In the lab, R1 is 24 Ω and the battery is set to 4.5 V. Current through R1 in amperes? (three decimals)
1 ohm equals:
- 1 V per A
- 1 A per V
- 1 J per C
- 1 C per s

Sources for this course (14)

OpenStax College Physics 2e (openstax.org/books/college-physics-2e): 18.1 Static electricity and charge (amber and the Greek word elektron, like charges repel, glass and silk, Franklin)
20.1 Current (I = ΔQ/Δt, 1 A = 1 C/s, truck battery 720 C in 4.00 s, calculator 0.300 mA, conventional current traced to Franklin, drift speed of order 10⁻⁴ m/s, 12-gauge copper wire 2.053 mm, copper density 8.80 × 10³ kg/m³)
20.2 Ohm's law (Ohm first showed I ∝ V by experiment, ohmic materials, headlight 12.0 V and 2.50 A = 4.80 Ω, dry person hand to foot about 10⁵ Ω)
20.3 Resistance and resistivity (Table 20.1: silver 1.59, copper 1.72, gold 2.44, aluminium 2.65, tungsten 5.6, iron 9.71, nichrome 100, all × 10⁻⁸ Ω·m; headlight cold 0.350 Ω)
20.4 Electric power and energy (P = IV = V²/R = I²R, kWh, 1 kWh = 3.6 × 10⁶ J, 60 W bulb for 1000 h at 12 cents per kWh = $7.20, 15 W CFL)
20.6 Electric hazards and the human body (thermal and shock hazards, short circuit 120 V across 0.100 Ω = 144 kW, worn cord 2.00 Ω at 10.0 A = 200 W, fuses and circuit breakers, Table 20.3 shock effects, dry skin 200 kΩ, wet 10.0 kΩ)
21.1 Resistors in series and parallel
21.2 Electromotive force and internal resistance
21.3 Kirchhoff's rules
23.8 Electrical safety (three-wire system, earth/ground wire, double insulation, GFI trips above 5 mA)
NIST CODATA elementary charge 1.602176634 × 10⁻¹⁹ C exact (physics.nist.gov/cgi-bin/cuu/Value?e)
Safety text is general information, not advice for working on mains wiring. Linda Hall Library, Scientist of the Day: Georg Ohm (lindahall.org/about/news/scientist-of-the-day/georg-ohm, experiments 1825 and 1826 with a compass needle, Die galvanische Kette 1827)
Smithsonian Libraries, Die galvanische Kette (library.si.edu/digital-library/book/diegalvanischeke00ohmg, first publication of Ohm's law, ridiculed at first)
IEC 60038:2009 standard voltages (230 V grew out of 220 V and 240 V systems; 220 V still used).

Checked: 2026-10-17