Ohm's law
U = R · I
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | U | V |
| Resistance | R | Ω |
| Current | I | A |
Elec Class
learn electricity hands-on
Lesson · chapter 4 of 15
The voltage across a resistor equals its resistance multiplied by the current flowing through it: U = R × I. If you know two of these three quantities, you can find the third.
The result is worked out before your eyes, line by line, just like on the board.
1I'm looking for
2I enter the known values
Formula used I = UR
3The result
Current I25.5 mA
With 12 V across it, a resistance of 470 Ω carries a current of 25.5 mA.
The definition, the key points to remember and everyday examples.
Ohm's law: the voltage across a resistor is proportional to the current through it, U = R·I. The resistance, in ohms, opposes the current.
Pouillet's law: the resistance of a wire depends on its material (resistivity ρ), grows with its length and decreases with its cross-section. For metals it rises with temperature (R = R₀(1 + αΔθ)). Commercial resistors follow the E12 series and carry their value as colour bands (two digits, multiplier, tolerance).
Voltage is the pressure pushing the water; current is the flow rate; resistance is a narrowing in the pipe. The narrower the pipe, the less water gets through for the same pressure. The picture has its limits (current doesn't "leak" out of a cut wire), but it helps you remember what U = R × I means.
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | U | V |
| Resistance | R | Ω |
| Current | I | A |
| Quantity | Symbol | Unit |
|---|---|---|
| Resistance | R | Ω |
| Resistivity | ρ | Ω·m |
| Length | l | m |
| Cross-section | S | m² |
Copper ρ ≈ 1.7 × 10⁻⁸ Ω·m; aluminium 2.8 × 10⁻⁸; iron 1.0 × 10⁻⁷.
| Quantity | Symbol | Unit |
|---|---|---|
| Resistance at 20 °C | R₀ | Ω |
| Temperature coefficient | α | /°C |
| Temperature change | Δθ | °C |
Four steps to solve a problem, then an example solved line by line.
Write down the known values with their units, and what you're looking for.
kΩ to Ω, mA to A, mm² to m²: otherwise the result is off by a factor of 1,000.
U = R × I, R = U / I or I = U / R: isolate the quantity you want before calculating.
Substitute, calculate, write the unit, then ask yourself whether the order of magnitude makes sense.
A 470 Ω resistor is supplied at 12 V: what current flows through it? Then: what is the resistance of 100 m of 1.5 mm² copper wire (ρ = 1.7 × 10⁻⁸ Ω·m)?
Ohm's law: I = U / R = 12 / 470 = 0.0255 A = 25.5 mA.
Pouillet's law, with the cross-section in m² (1.5 mm² = 1.5 × 10⁻⁶ m²):
R = ρ · l / S = 1.7 × 10⁻⁸ × 100 / 1.5 × 10⁻⁶ = 1.13 Ω.
U = R × I: the voltage U (in volts) equals the resistance R (in ohms) multiplied by the current I (in amps). From it you get R = U / I and I = U / R.
Divide the voltage by the current: R = U / I. For example, 12 V and 0.05 A give R = 12 / 0.05 = 240 Ω. Remember to convert mA to A before dividing.
With the triangle, U on top, R and I at the bottom: cover the quantity you want, and the formula is what's left. Cover U: R × I; cover R: U / I; cover I: U / R.
Resistance R (in Ω) belongs to a specific component or wire. Resistivity ρ (in Ω·m) belongs to a material: copper has ρ ≈ 1.7 × 10⁻⁸ Ω·m, whatever the length of the wire.
In a metal, the atoms vibrate more as it heats up and get in the way of the electrons. It is written R = R₀ (1 + α Δθ), with α ≈ 0.004 /°C for copper.
A component whose U = f(I) characteristic is a straight line through the origin: its resistance doesn't depend on the current. A standard resistor is ohmic; a lamp or a diode is not.
At any instant, yes: U = R·I. But the filament heats up and its resistance rises with the current: the U = f(I) characteristic of a lamp is not a straight line. It is said not to be an ohmic conductor.
The first two bands give two digits, the third the number of zeros (multiplier), the fourth the tolerance (gold 5 %, silver 10 %). Yellow-violet-red = 47 × 100 = 4 700 Ω.
From the simplest to the most complete, each problem comes with a step-by-step solution.
In the lab, vary the voltage across a 220 Ω resistor, record I at each step and plot U = f(I): the slope of the line gives R.
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