What it shows
A cell delivers the most power to a load when the load resistance equals the cell’s own internal resistance. The power curve rises, peaks and falls as the load is changed.
The science
A real cell behaves like an emf E in series with an internal resistance r. For a load R the current is I = E / (R + r) and the power in the load is P = E²R / (R + r)². Differentiating shows P is largest when R = r, and then P = E² / 4r. For small R most of the voltage is lost inside the cell, and for large R the current is too small, so the power falls on both sides of the peak.
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.
- Two AA cells in a holder (new, all of the same brand)
- About ten fixed resistors from 0.5 ohm to 47 ohm (shop, or old electronics)
- A multimeter used as a voltmeter
- Crocodile clips or a small breadboard
- Graph paper
- A calculator
Safety
For this project: An adult must supervise the low-ohm resistors, which can warm up; keep the circuit connected only while reading the meter.
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
7 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 E of the two-cell pack with the voltmeter and write it down.
Connect the 47 ohm resistor across the pack and read the voltage V across the terminals; the power in the load is V² / R.
Repeat with each resistor in turn (22, 10, 4.7, 2.2, 1, 0.5 ohm and others) and take each reading quickly, then disconnect.
Compute P = V² / R for every resistor and fill a table with R, V and P.
Estimate the internal resistance from any one reading using r = R (E − V) / V and average your values.
Plot P (vertical) against R (horizontal) and draw a smooth curve through the points.
Mark the load at which the curve peaks and compare it with the r you calculated.
What you should see
The power curve peaks when the load resistance is close to the internal resistance of the pack, typically between 0.5 and 2 ohm for two AA cells. At that point the load receives about half the cell’s total power.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What does the maximum power transfer theorem state?
Maximum power goes to the load when the load resistance equals the source’s internal resistance.
2What is the efficiency at maximum power?
Fifty percent, because the internal resistance uses as much power as the load.
3Why is a big load resistance not the best choice for power?
The current becomes very small, so V times I is small even though the terminal voltage is high.
4How do you find r from one reading?
r = R (E − V) / V, where V is the terminal voltage across the load R.
Take it further
Repeat the experiment with a half-used pack and show that its internal resistance, and so the power peak position, has moved.
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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