Physics IA · B · The particulate nature of matter · topic 10 of 30

Wire resistance: does R really scale with length? · IB Physics IA idea: guide, sample graph and step-by-step plan

easy kit, but the evaluation can be rich

Everyone knows R doubles when the wire is twice as long. You're going to find out how well that holds, and what the line is hiding.

Difficulty●○○ Gentle
KitStandard: ammeter, voltmeter, wire, rule
TimeAbout 8 hours
FitsSL and HL
  • ✓ you like circuits
  • ✓ you enjoy a clean straight-line graph
  • ✓ you want a result you can compare with a data book

The big idea

← the intercept is the interesting bit

For a uniform wire, R = ρL/A, so a graph of resistance against length is a straight line through the origin, and its gradient gives the resistivity. Real data rarely behave that neatly. Contact resistance at the clips adds a fixed amount, and a hot wire has a higher resistance. The interest is in what the intercept and any curvature tell you and whether your resistivity matches a trusted value.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Compare two metals

Repeat with constantan, nichrome or copper wire of the same diameter.

→ Two gradients, so you compare resistivities; a heating effect that differs between metals gives you more to evaluate.
Change the diameter too

Use two or three diameters of the same material at a set of lengths.

→ Tests the 1/A part of the formula; your analysis combines two graphs and the uncertainty of the diameter gets large.
Let it heat up

Use a larger current deliberately and measure resistance against time or against current.

→ Brings in the temperature coefficient; becomes a thermal investigation as well as an electrical one.
Four-wire measurement

Use separate leads for current and voltage, or a method that removes the clip resistance.

→ Targets the biggest systematic error head-on; the evaluation compares two methods.
Use a data logger

Replace the meters with a logger that records voltage and current as you slide the contact.

→ Many more points, smaller random uncertainty; you must justify the sampling choice.
Use the slide-wire as a potential divider

Measure how the potential difference along the wire depends on the contact position.

→ A different circuit and a new graph; keeps the same physics but tests the assumption of uniform wire.

Your Physics IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable and its range (which lengths, in what unit, and how many values).
  • Names one dependent variable and how it is found (R from V and I, and at what current?).
  • Says what stays fixed: wire material and diameter, current level, temperature, the clips.
  • Says what you will compare your result with (a book value for resistivity, a straight-line prediction, or both).
  • Is narrow enough to finish with 6 to 8 lengths, a repeat at each, and a check on the diameter.

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The set-up

One way to set it up. Draw your own version, with your real wire, meters and resolutions, for the Method section.

AVLlow-voltage supply:small currentammeter in seriesvoltmeter across justthe clipped lengthclips: press the same way,same place, every timemetre rule: read Lbetween the clips

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; where resistance of wires matters (power cables, heating elements, strain gauges); what you expect and why.
Background physics~450
R = ρL/A and where it comes from in terms of electrons and the lattice; what you predict for the gradient and the intercept; why heating changes R.
Variablestable
Independent, dependent and controlled variables, each with how you set, measure or keep it constant, and why it matters.
Method~400
How you hold the wire straight; where and how you attach the clips; how you keep the current small; how you measure the diameter, and where along the wire.
Safety, ethics, environment~60
Short and specific: a warm wire, the current you chose and why it is safe.
Raw datatable
One table: length, voltage and current for each repeat, with resolution and uncertainty in each header.
Processing~250
How you get R and its uncertainty from V and I; how you get the wire's cross-section area and its uncertainty; one worked example of each.
Graphs and analysis~350
R against L with error bars; line of best fit and a worst-fit line; what the gradient and intercept mean physically.
Conclusion~450
Answer the question with numbers: how closely R follows L, the resistivity you find, and how it compares with the accepted value.
Evaluation~650, the biggest part!
Strengths, weaknesses ranked by effect (diameter, contact resistance, heating, meter uncertainty), and improvements tied to each.
Referencesnot counted
Every source you used, including the book value for resistivity.

What your Physics IA graph could look like

ask what the gap means!

Made-up data, to show you the form of a strong graph, not the answer. Yours will look different. example only

010203040506070800123456789Wire length L / cm (± 0.1 cm)Resistance R / Ω (± 0.1 Ω)R = ρL/A, no contact resistancewith a fixed 0.3 Ω at the clipsyour data, with error barsline misses the origin:what does the intercept mean?ILLUSTRATIVE · MADE-UP DATA
  • Axis labels name the quantity and its unit, with the instrument uncertainty.
  • Error bars on every point. For a wire, the vertical bars are the long ones, from the meters.
  • Both lines drawn: the data follow the shifted one, and the gap between them is the story.
  • Start the axes at zero here. The intercept is part of the answer, so it must be visible.
  • Another graph to consider: R against current at one fixed length, to test whether heating is bending your line.

Which uncertainty matters most?

Rank by the effect on your result (here, resistivity from one reading at L = 40 cm), not on the raw readings. The diameter is squared, so it hurts twice as much as it looks.

Diameter (± 0.01 mm of 0.25 mm)8%Clip resistance (0.3 Ω of 4 Ω)7.5%Ammeter (± 0.005 A of 0.25 A)2%Voltmeter (± 0.01 V of about 1.1 V)0.9%Length (± 1 mm of 400 mm)0.25%biggest effect: discuss this first!% uncertainty in resistivity, from one readingILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

measure the diameter properly

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictFind R = ρL/A and a trusted resistivity for your wire. Write down what the graph should look like, and what you expect the intercept to be.
  2. Trial run (1 lesson)Build the circuit and take a few readings. Do the meters settle? Does the wire warm? Does moving a clip change R by more than your resolution? Fix these now.
  3. Choose a currentPick a current large enough to read well and small enough to keep the wire cool. Write down how you checked that it does not warm up.
  4. Measure the diameter wellMeasure at several places and in two directions with a micrometer. Zero error? Decide how you will get its uncertainty, since it matters a lot.
  5. Decide lengths and repeatsChoose 6 to 8 lengths across a wide range. Decide how you will reset and reconnect, so a repeat is a real repeat.
  6. Collect the dataRecord V and I with resolution and units. Leave the circuit on for as short a time as you can between readings.
  7. ProcessTurn each pair into R with an uncertainty. Calculate the wire's area and its uncertainty.
  8. Graph and fitPlot R against L with error bars and a best-fit line. Say what the gradient and intercept should be if the model holds, and what they actually are.
  9. Compare and evaluateCompare your resistivity with the book value, taking the uncertainty into account. Rank the weaknesses by the effect on that result, then link each improvement to one.
  10. Write, then checkWrite in the order of the layout. Tables, graphs and equations are not counted. Run the checklist below before your teacher sees the draft.

Physics you'll need

Traps to avoid in this Physics IA

  • Letting the wire heat up: R rises with temperature, so a long run at high current curves your line.
  • Ignoring contact resistance at the clips, so the line does not go through the origin and you never ask why.
  • Measuring the diameter once, in one place, then squaring a poor measurement.
  • Clipping on a bit differently each time, so the length you read is not the length the current flows through.
  • Forcing the best-fit line through the origin without testing whether the data want to go there.
  • A wire that is coiled, kinked or touching itself, so some of the length is shorted out.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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