Ohm’s law and resistance

What Ohm’s law says

Across an ohmic conductor, the voltage U (in volts) and the current I flowing through it (in amperes) are proportional:

U = R × I

The constant R is the conductor’s resistance, in ohms (Ω). It does not depend on the applied voltage: double U and I doubles too, so the ratio U / I stays the same.

Where a wire’s resistance comes from

For a uniform wire of length L and cross-section S:

R = ρ × L / S

• ρ (rho) is the metal’s resistivity: very low for copper and aluminium, higher for iron, much higher for heating alloys (nichrome).
• A wire twice as long has twice the resistance.
• A wire with twice the diameter has four times the cross-section, hence a quarter of the resistance.

Reading a U = f(I) graph

Plot the measured (I, U) pairs: the points line up on a straight line through the origin. Its slope is the resistance: the steeper the line, the larger R. This is the surest way to check that a component follows Ohm’s law.

What the simulation leaves out

A real wire heats up as current flows, and its resistance rises slightly with temperature. The simulation keeps the temperature constant to isolate Ohm’s law; tell students it is a simplification.

Equipment (in the simulation)

An adjustable power supply, a conducting wire whose metal, length and diameter you choose, a voltmeter across the wire, an ammeter in series.

Steps

1. Set the wire: copper, 10 cm, 0.2 mm diameter. Set the voltage to 2 V.
2. Read U and I on the meters, then press Record measurement: the row is added to the notebook.
3. Repeat for 4 V, 6 V, 8 V. Each time, work out U / I in your head before reading R.
4. Change the length (20 cm, then 30 cm) at fixed voltage: what happens to the current?
5. Change the diameter (0.4 mm): compare with the 0.2 mm wire.
6. Change the metal, everything else equal: rank the metals from best to worst conductor.
7. Open the Graph screen: check that your points line up, and read the slope.

What to write down

For each measurement: the wire (metal, length, diameter), U, I and R = U / I. The notebook does it for you; you can export it as CSV or, with a BEFREE Academy account, save it.

Common pitfalls

• Reading the current in milliamps and the voltage in volts, then mixing units in the calculation.
• Comparing two wires after changing two parameters at once: change one thing only between two measurements.

Where it fits

After measuring voltages and currents in a series circuit, before electrical power. One 45-minute session is enough: 10 minutes of free exploration, 25 minutes of protocol, 10 minutes of pooling results.

Suggested sequence

1. On the board (projector or shared phone): launch the simulation, ask “what will the current do if I double the voltage?”, then check.
2. In pairs, on phones: follow the protocol and fill in the measurement notebook.
3. Pooling: each pair gives its slope; compare values, discuss the differences (reading, rounding).
4. Written record: Ohm’s law, the wire resistance formula, a graph.

Without a network

After a first load, the simulation stays available offline on the device that opened it. For a room without a connection, open the simulation on each phone the day before, or download the archive when the page offers one.

Assessment

With a BEFREE Academy account, students answer five questions after the session; the teacher sees the results in BEFREE Academy. Without an account, the three exploration prompts on the page work as oral questions.

To be provided by the team

[Printable activity sheet (PDF) and answer key: to be written and uploaded, then set “ficheEnseignant” in the simulations file.]