Labo Élec

electrical lab simulator
0 1 / 20

Reminder sheet

Ohm's law & resistance

Bastaya

U = R·I, the law that rules this lab. A resistance, a voltage, a current: know two of them and the third surrenders.

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).

Formulas

Ohm's lawU = R · I
QuantitySymbolUnit
VoltageUV
ResistanceRΩ
CurrentIA
Pouillet's lawR = ρ · lS
QuantitySymbolUnit
ResistanceRΩ
ResistivityρΩ·m
Lengthlm
Cross-sectionSm²

Copper ρ ≈ 1.7 × 10⁻⁸ Ω·m; aluminium 2.8 × 10⁻⁸; iron 1.0 × 10⁻⁷.

Temperature effectR = R₀ · (1 + α · Δθ)
QuantitySymbolUnit
Resistance at 20 °CR₀Ω
Temperature coefficientα/°C
Temperature changeΔθ°C

Worked example

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.

Common mistakes

  • Leaving the cross-section in mm² in Pouillet's law: 1 mm² = 10⁻⁶ m², otherwise the resistance is a million times too small.
  • Believing that the resistance changes when the voltage changes: for an ohmic conductor, R is fixed (at constant temperature); it is the current that changes.
  • Confusing resistance R (Ω, a property of the component) with resistivity ρ (Ω·m, a property of the material).

IEC symbols

Resistor
GVoltage source
Switch

Mini circuit

Open in the sandbox

Frequently asked questions

Does Ohm's law apply to a lamp?
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.
How do I read the colour bands of a resistor?
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.

61 exercises in this topic

This chapter is covered by the paths: Discovery, General electricity, ISL-oriented exercises

All sheets · All formulas · Glossary of electrical quantities · Standard electrical symbols (IEC 60617)

Practise this topic
Simulated time00:00:00
Q = I·t-
W = P·t-

Workbench

Circuit diagram CEI 60617

How does it work?

The perfboard: each big hole is a circuit node. You push a single leg of a component (resistor, lamp...) into it. The 4 small holes around it are connected to it: that is where chips and leads plug in.

  1. Drag a component onto the board: it snaps onto the grid. R rotates it.
  2. To join neighbouring big holes, click Jumper chip in the palette (or C) then drag on the board: a line of chips is laid at once. Bridged holes become a single node.
  3. For long links and for the power supply (placed next to the board), drag a lead from one big hole to another (or to a terminal).
  4. As soon as a loop is closed, the circuit is solved in real time (Ohm + Kirchhoff) and the diagram follows.
  5. Zoom with the wheel (or + / −, two-finger pinch); drag the background to pan, 0 fits the board. The + buttons around the board add a row or a column.

Del delete · R rotate · C chip brush · Esc cancel · wheel zoom · drag the background to pan

Confirmer

Importer un montage

Export