What it shows
A capacitor charging through a resistor reaches 63 percent of the supply voltage after one time constant tau = R C, and discharges to 37 percent in the same time. With a large capacitor and a large resistor the process takes tens of seconds, slow enough to time by hand and to plot.
The science
Current flows into a capacitor until the voltage across it equals the supply, and the current falls as the capacitor voltage rises, so the charging follows V = V0 (1 minus e^(-t/RC)). The product R C has units of seconds and is called the time constant; after one time constant the voltage reaches 63 percent of V0, after five it is essentially complete. Discharging through the same resistor follows V = V0 e^(-t/RC), falling to 37 percent after one time constant. A 1000 microfarad capacitor with 47 kilo-ohm has tau of 47 seconds, which is easy to time and gives a textbook exponential curve.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A 1000 microfarad, 16 V electrolytic capacitor (about Rs 10)
- Resistors of 10, 22 and 47 kilo-ohm
- Three AA cells in a holder (4.5 V)
- A digital multimeter on DC volts
- A stopwatch or phone
- A red LED and a 220 ohm resistor for the discharge demonstration
- A breadboard or crocodile clips
Safety
For this project: Connect the electrolytic capacitor with its marked negative stripe to the negative side of the cells; reversed, it can heat and burst. Discharge it through a resistor before handling. Cells only.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Connect the cells, the 47 kilo-ohm resistor and the capacitor in series with the meter across the capacitor, checking the capacitor polarity.
Start the stopwatch at the instant of connection and record the capacitor voltage every 10 seconds for four minutes.
Disconnect the cells and bridge the gap with a wire so the capacitor discharges through the same resistor, and record the voltage every 10 seconds again.
Record both runs in a table of time, charging voltage and discharging voltage.
Plot both curves on one graph and read the time at which the charging curve reaches 63 percent of 4.5 V (about 2.8 V).
Compare that time with R C calculated from the labelled values, and repeat with the 22 and 10 kilo-ohm resistors.
Plot the natural log of the discharge voltage against time; the straight line has slope minus 1 / RC, a second way to get tau.
As a visible demonstration, charge the capacitor fully and then connect the LED and 220 ohm resistor across it to show the fade-out over a few seconds.
What you should see
Smooth exponential charging and discharging curves with the 63 percent time close to the R C value for each resistor (about 47, 22 and 10 seconds), and a straight-line log plot for the discharge.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What is the time constant of an RC circuit?
tau = R C, the time to charge to 63 percent or discharge to 37 percent of the starting voltage.
2Why does the charging current fall with time?
As the capacitor voltage rises, the voltage across the resistor and hence the current falls.
3How is energy stored in a charged capacitor?
In the electric field between its plates, E = half C V squared.
4Why is the log plot of the discharge a straight line?
Because the discharge is exponential, ln V = ln V0 minus t / RC.
Take it further
Use the discharge curve to measure an unknown resistor, or an unlabelled capacitor, from the measured time constant.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
Science projects
Investigatory Projects for Class 11 and 12
Topics, method and report structure for physics, chemistry and biology