Physics IA · B · The particulate nature of matter · topic 12 of 30

Capacitor discharge: what sets the time constant? · IB Physics IA idea: guide, sample graph and step-by-step plan

easy to log, easy to over-trust

τ = RC is the easy bit. The real investigation is how much your components and your voltmeter disagree with it.

Difficulty●●○ Medium
KitStandard: capacitors, resistors, voltmeter, data logger
TimeAbout 10 hours
FitsSL and HL (capacitors are beyond the course)
  • ✓ you like exponential decay
  • ✓ you can use a data logger or spreadsheet
  • ✓ you enjoy catching a meter changing the circuit

The big idea

← ln V makes it a straight line

A capacitor discharging through a resistor loses charge exponentially, with time constant τ = RC. A graph of ln V against time is a straight line with gradient −1/τ, so you can read τ from data you record automatically. The interest is in the details: capacitors have wide tolerances, resistors have small ones, and a voltmeter with finite resistance is another path for the current. Do your measured time constants match R × C, within the uncertainties?

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 →

Vary R, keep C

Use five or six resistors, same capacitor and starting voltage.

→ Graph of τ against R should be a straight line through the origin with gradient C: you can find C and check it against its label.
Vary C, keep R

Use several capacitors, or combine them in parallel and series.

→ Graph of τ against C; combinations let you test the rules for adding capacitors at the same time.
Measure the meter

Change the voltmeter or add a known resistance in parallel to see its effect.

→ Turns a source of error into your independent variable, and tests the parallel-resistor model.
Charging as well as discharging

Record both, same R and C.

→ Compare the two time constants; the analysis of an increasing exponential is different and shows more skill.
Energy and the half-time

Compare the time for the voltage to halve with the time for the energy to halve.

→ Tests understanding of the exponential and of energy as ½CV²; a stretch, because both ideas come from outside the course.
Different capacitor types

Electrolytic, ceramic and film capacitors with the same nominal value.

→ Compares the real values with the labels and with their tolerances, and may show leakage.

Your Physics IA research question: run the check

write it FIRST, then check it

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

  • Names one independent variable with its range (which resistances or capacitances, and how many).
  • Names the dependent variable and how you will get it (time constant from a fit, or a time to halve?).
  • Says what stays fixed: the starting voltage, the other component, the meter and the logging rate.
  • Says what you will compare with (τ = RC with measured, not just labelled, values).
  • Is narrow enough for about 10 hours, with at least 6 values and repeats.

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The set-up

Charge the capacitor with the switch closed, then open it and log the voltage as it decays. Draw your own version with real component values.

Vswitch closed: charge,open: it dischargesC: note itstoleranceR: knownresistorvoltmeter +data loggercheck the voltmeter's own resistance:it is in parallel with C and R

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 capacitors discharge (camera flash, defibrillators, timing circuits) and what you expect the graph to show.
Background physics~450
Capacitance, the discharge equation and where τ comes from, and why ln V against t is linear.
Variablestable
Independent, dependent and controlled variables, including starting voltage and logging rate.
Method~400
The circuit, how you charge and discharge, how you log, how you measured the real R and C, and the meter you used.
Safety, ethics, environment~60
Polarity of electrolytic capacitors, voltage limits, a discharged capacitor before handling.
Raw datatable
A sample of the logged data (the rest in an appendix or described), with resolution and rate stated.
Processing~250
How you got τ from each run, and its uncertainty; one worked example for each type of calculation.
Graphs and analysis~400
ln V against t for a run, then τ against R or C with error bars, and the meaning of the gradient.
Conclusion~400
Does τ = RC hold? Any difference between measured and predicted τ, with uncertainties.
Evaluation~650, the biggest part!
Weaknesses ranked by effect on τ, linked to specific improvements.
Referencesnot counted
Sources for the discharge equation and component data.

What your Physics IA graph could look like

gradient = C: nice!

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

010203040506070809010005101520253035404550Resistance R / kΩ (± 5%)Time constant τ / s (± 1 s)τ = RC, C = 470 μFwith a 1 MΩ voltmeter in parallelyour data, with error barsthe gradient is C: does itmatch the label, within its tolerance?ILLUSTRATIVE · MADE-UP DATA
  • The gradient is the capacitance, so this graph tests the label on the capacitor, not just the formula.
  • Error bars on both axes: resistor tolerance on x, the fit on y. Use the measured resistance, not the colour code, if you can.
  • The dashed curve shows a meter that is not ideal. The effect grows with R, which is the clue to look for.
  • Straight line through the origin: if yours has an intercept, ask what is in parallel or in series that you forgot.
  • Another graph to consider: ln V against t for a single run. A good straight line shows the decay is exponential, and its gradient is −1/τ.

Which uncertainty matters most?

Rank by the effect on your result, here the predicted τ at 100 kΩ. A capacitor's tolerance can dwarf everything else, which is a reason to measure its real value.

Capacitor tolerance (±20%)20%Voltmeter loading (1 MΩ)9%Resistor tolerance (±5%)5%Reading τ (±1 s in 47 s)2.1%biggest effect: discuss this first!% uncertainty in τ at R = 100 kΩ, C = 470 μFILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

measure the real R and C first

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

0 of 10 done

  1. Read and predictCapacitors are not in the IB course, so read up on capacitance and the discharge equation first, and cite where you learned it. Sketch V against t and ln V against t. Decide what you expect the time constant to depend on, and why.
  2. Trial run (1 lesson)Charge to a fixed voltage, discharge through one resistor and log. Is the decay a clean exponential? Does the logger sample fast enough? Does the voltmeter change the result?
  3. Measure your componentsMeasure the real R and, if you can, the real C (with a meter or by the decay itself). Tolerances are not uncertainties you can ignore.
  4. Choose range and repeatsChoose at least 6 values of R (or C), a starting voltage, a logging rate, and the number of repeats. Write down your reasons.
  5. Collect the dataDischarge fully between runs. Save raw data. Note temperature and any odd behaviour.
  6. ProcessDecide how to get τ (a fit to ln V against t, or a half-time) and how to find its uncertainty.
  7. Graph and fitPlot τ against R (or C), add error bars, find the gradient with uncertainty and compare with the measured value of the other component.
  8. Compare with theoryDoes the line match τ = RC within uncertainties? Does the voltmeter explain any difference at large R?
  9. EvaluateRank the uncertainties by their effect on τ and link each improvement to a specific weakness.
  10. Check before your teacher's draftRun the checklist above, then get your RQ or draft checked. Your teacher reads one draft only.

Physics you'll need

Traps to avoid in this Physics IA

  • Trusting the label on a capacitor whose tolerance can be ±20% or more.
  • A voltmeter of low resistance in parallel with a large R, so the circuit you analyse is not the one you built.
  • Starting each run before the capacitor has fully discharged.
  • A logging rate too slow for the short time constants, or too fast for the long ones.
  • Fitting only part of the decay and not saying which part, or why.
  • Connecting an electrolytic capacitor the wrong way round.

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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