What it shows
The terminal voltage of a cell falls as it supplies more current because of its internal resistance, following V = E minus I r. A graph of V against I is a straight line whose intercept is the emf E and whose slope is minus r.
The science
A real cell behaves like an ideal source of emf E in series with a small internal resistance r. When a current I flows, a voltage I r is lost inside the cell and the terminals show only V = E minus I r. Measuring V across a set of known load resistors and the current through each gives several (I, V) points; the best straight line has y-intercept E (open-circuit voltage) and gradient minus r. A used cell shows a much larger r, which is why old cells light a torch dimly even though their open-circuit voltage looks nearly normal.
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.
- One fresh and one used AA or D cell
- Five resistors: 4.7, 10, 22, 47 and 100 ohm (1 W or 2 W, from an electronics shop)
- A digital multimeter
- Crocodile clip leads
- Graph paper
Safety
For this project: Never short the cell directly with a wire; it heats fast. Keep each reading under ten seconds so the cell does not warm up or run down during the experiment.
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.
Measure the open-circuit voltage of the fresh cell with no load; this is close to E.
Connect the 100 ohm resistor across the cell with the meter in series on milliamps, record I, then move the meter across the cell terminals and record V.
Repeat for 47, 22, 10 and 4.7 ohm, keeping each connection brief, and record a table of R, I and V.
Plot V on the y-axis against I on the x-axis and draw the best straight line through the points.
Read the intercept on the V axis as E and compute r as minus the slope, in ohms.
Repeat the full set for the used cell and plot both lines on the same axes.
Calculate r a second way from any two points using r = (V1 minus V2) / (I2 minus I1) and compare with the slope.
Write a short discussion on why the used cell has a larger r (dried electrolyte and used-up electrodes) and how this limits the current it can give.
What you should see
A fresh AA cell gives E of about 1.5 to 1.6 V and r of about 0.1 to 0.5 ohm; a used cell gives a similar E but r of several ohms, seen as a much steeper line.
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 difference between emf and terminal voltage?
Emf is the voltage with no current drawn; terminal voltage is lower by I r when current flows.
2When does the cell deliver maximum power to a load?
When the load resistance equals the internal resistance.
3Why does an old cell still read 1.5 V on a voltmeter?
A voltmeter draws almost no current, so the I r drop is negligible and it reads nearly the emf.
4What is the slope of the V-I graph?
Minus the internal resistance.
Take it further
Measure r of two cells in series and in parallel and compare with the expected 2r and r/2.
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
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