Ohm's Law I = U/R: Verifying It with a Fixed Resistor

Push harder on the same piece of wire and more current flows; make it harder to get through and less current flows. Both statements sound obvious. Turning them into I = U/R, a law you can calculate with, takes two rounds of measurement: hold the resistance fixed and change the voltage, then hold the voltage fixed and change the resistance. It is the clearest use of controlled variables anywhere in middle school physics.

The hard part is not the wiring. It is working out what the rheostat is actually for. Once that clicks, the logic of the whole experiment falls into place.

Safety first (read this before you start)

• Use a school power supply or a battery pack only, at no more than 6 V. Never work from a household wall outlet.
• When the wiring is done, check before you close the switch: ammeter in series, voltmeter across the resistor, right ranges selected, terminals the right way round.
• Before closing the switch, move the rheostat slider to its maximum-resistance end. This protects the circuit; skipping it is how meters get wrecked on the first click.
• Open the switch after each reading. A resistor left carrying current warms up, its resistance drifts, and the data drifts with it.
• Always disconnect the supply before swapping resistors or changing any connection.

Materials

• A school power supply, or a pack of 3–4 dry cells;
• Three fixed resistors: 5 Ω, 10 Ω, 20 Ω;
• A rheostat (20 Ω, 1 A is typical);
• An ammeter (0–0.6 A) and a voltmeter (0–3 V);
• A switch and connecting leads.

Procedure

1. Build the circuit. Supply, switch, rheostat, the fixed resistor R and the ammeter all in series in one loop; the voltmeter in parallel across R.
2. Push the slider to the maximum-resistance end, check everything, then close the switch.
3. Round one: keep R at 10 Ω and change the voltage. Move the slider so the voltmeter reads 1.0 V, 1.5 V, 2.0 V and 2.5 V in turn, recording the ammeter each time.
4. Open the switch and swap R for the 5 Ω resistor.
5. Round two: keep U at 2.0 V and change the resistance. Close the switch, move the slider until the voltmeter is back at 2.0 V, and record the current. Repeat with 10 Ω and 20 Ω, resetting the voltage to 2.0 V every single time.
6. Tabulate the two rounds separately and work out U/I for each row.

What you should see

Round one: R fixed at 10 Ω

Round two: U fixed at 2.0 V

Plot round one as I against U and you get a straight line through the origin. Plot round two as I against R and you get a curve bending down towards the axis. Those two shapes are what "proportional" and "inversely proportional" look like, and students should draw both themselves.

Real readings will be off by a few hundredths, mostly from estimating between scale marks, contact resistance and warming. As long as the U/I values agree closely with one another, the relationship holds.

The science: how the three quantities connect

Put the two rounds together: current is proportional to voltage and inversely proportional to resistance. Written out, that is Ohm's law:

I = U / R

Voltage is what pushes the charges along, resistance is what holds them back, and current is the outcome of that contest. Twice the push, twice the flow; twice the obstruction, half the flow.

The equation rearranges to U = IR and R = U/I, which is handy for finding the other two quantities. But rearranging is a piece of algebra, not a change of physics. R = U/I is a recipe for measuring a resistance, not a claim that voltage and current determine it. Put ten times the voltage across the same wire, get ten times the current, and the R you calculate is still the same number — which is precisely what round one demonstrates when U/I comes out as 10 every time.

So what does set the resistance? The conductor itself: its material, its length, its cross-sectional area, and its temperature. Nothing about the circuit it happens to be sitting in. Students mix this up constantly, and that first table is the most direct rebuttal available.

Ohm's law in everyday life

• A dimmer lamp changes the current by changing the resistance in series with the bulb; less current, dimmer light. The old rotary kind is literally a rheostat.
• The element in an electric kettle is short and thick, so its resistance is low; on the same mains voltage it draws a large current and heats fast.
• A phone cable that is too thin or too long charges slowly, because the cable's own resistance takes a share of the voltage.
• A fuse turns the relationship to protective use: low resistance, low melting point, and it burns through first once the current exceeds its rating, cutting the whole path.
• Digital thermometers and light-dependent resistors convert temperature or light into a change of resistance, which I = U/R then turns into a change of current that the electronics can read.

Five things students get wrong

• "R = U/I, so resistance is proportional to voltage and inversely proportional to current." This is the classic error of the whole topic. U and I change together and the ratio does not move; resistance is a property of the conductor, independent of what you connect it to. When a student says this, put round one's table in front of them: the voltage goes from 1.0 V to 2.5 V and U/I stays at 10 throughout.
• Forgetting to reset the voltage. Swap resistors in round two without moving the slider and the voltmeter drifts, which means two variables changed at once and the data supports no conclusion at all. This is the single most common procedural mistake here.
• Swapping the meters. An ammeter goes in series and has almost no resistance, so across a resistor it is a short circuit. A voltmeter goes in parallel and has enormous resistance, so inserted into the loop it chokes the current to nearly zero. Before connecting either, ask out loud: is this meter measuring the current through something, or the voltage across something?
• Closing the switch with the slider at minimum resistance. The circuit resistance is then at its lowest, the current can jump past full scale, and the needle slams over — sometimes fatally for the meter. Sliding to maximum first is a habit, not an option.
• Using a small bulb as the fixed resistor. A filament's resistance climbs steeply with temperature, so as you raise the voltage the resistance rises too, U/I is nowhere near constant, and round one yields no proportionality. Ohm's law investigations need a fixed resistor. Save the bulb for a later lesson on how resistance varies with temperature, where it shines.

Teaching notes

• Time and grouping: 45 minutes, groups of two or three — one wiring, one reading meters, one recording, rotating partway through.
• Say this before they start: slider to maximum, check before closing, open the switch after each reading.
• Prep that pays off: make sure the resistor values are clearly marked, and set every meter to the same range in advance so nobody has to change range mid-table.

The step most often skipped. Before round two, ask students to predict what doubling the resistance does to the current. Plenty will say "it goes down a bit" rather than "it halves". Once the 20 Ω row gives 0.10 A next to 10 Ω's 0.20 A, the inverse relationship is finally something they have seen rather than been told.

How to tell they have it. Two questions. First: move this resistor to a 6 V supply — what is the current? (They should reach for I = U/R.) Second: and what is its resistance then? (The same number as before. Answering that one correctly is what proves they have not fallen into the "R depends on U" trap.)

Take it further

• In the simulator, drag the resistance very low and the voltage very high and watch the current climb. Then ask what happens in reality when resistance approaches zero. (A short circuit — which is exactly why a real circuit must contain a load.)
• Wire two 10 Ω resistors in series and measure the total; then in parallel and measure again. Do you get 20 Ω and 5 Ω? This is the doorway to combining resistances.
• Measure the resistance of a pencil lead. Put the voltmeter across a length of lead, the ammeter in series, and compute U/I. Repeat with a longer piece and compare — length has a visible effect.
• Run a "a filament is not a fixed resistor" control. Replace the resistor with a small bulb and repeat round one, computing U/I at 1.0 V through 2.5 V. The ratio climbs steadily instead of holding still, because the glowing filament gets much hotter and its resistance rises with it.
• Look up the rated voltage and power on an appliance at home, work backwards to its operating resistance with I = U/R, and think about why a kettle's resistance is so much lower than a phone charger's.

When a student can say "resistance belongs to the conductor" and calculate confidently with I = U/R in the same breath, this experiment has done its job.