Internal Resistance of a Battery, and Equivalent Resistance of a Network
Every battery resists the current flowing through it, and that internal resistance is why the usable voltage drops the moment you draw current. With the switch open no current flows, nothing is lost inside the battery, and a voltmeter across it reads the full emf. Close the switch and some of that emf is spent pushing charge through the battery itself, so the terminal voltage is lower. The difference between those two readings, divided by the current, is the internal resistance. This is a prescribed formal assessment for CAPS Physical Sciences, Grade 12, Term 3.
Where this fits in the curriculum
| Subject | Physical Sciences |
|---|---|
| Grade | 12 |
| Term | 3 |
| Topic | Electric circuits, electricity and magnetism |
| Status | Prescribed experiment for formal assessment (SBA) |
| Time needed | 90 minutes, one double period |
Two parts, both assessed. Part 1 finds the internal resistance of a battery. Part 2 builds a series-parallel network and compares the measured resistance against the calculated one.
The physics behind it
With the switch open, the voltmeter reads the emf. With it closed, it reads the terminal voltage, which is lower because some of the emf is now being used inside the battery:
emf = Vterminal + Ir
Rearranged, that gives you the internal resistance from three measurements:
r = (emf − Vterminal) ÷ I
The gap between the two voltmeter readings is called the lost volts. The voltage is not really lost, it is just used up inside the battery rather than in the circuit you can see.
Part 1: internal resistance of a battery
Apparatus
A 1,5 V cell and holder, a resistor of less than 5 Ω, a switch, a voltmeter, an ammeter (or a multimeter), and five connecting leads.
Method
- Connect the battery, switch, ammeter and resistor in series. Leave the switch open.
- Draw the circuit diagram before taking any readings.
- With the switch still open, connect the voltmeter in parallel across the battery, just long enough to take the reading. This is the emf.
- Close the switch and read the current on the ammeter.
- With the switch still closed, read the voltmeter across the battery. This is the terminal voltage. Open the switch.
- Explain why the two voltmeter readings are different.
- Calculate the internal resistance: r = (emf − Vterminal) ÷ I
Using a multimeter instead? Connect it in series to measure current and in parallel to measure voltage, and move the dial to the right setting each time. Leaving the dial on current with the probes in parallel puts a short circuit across the battery.
Part 2: equivalent resistance of a series-parallel circuit
Apparatus
A 1,5 V cell and holder, a switch, at least three resistors of 10 Ω or more with different known values, an ammeter, a voltmeter (or multimeter), and at least seven connecting leads.
Method
- Build a circuit with the battery, a switch, and one resistor in series with a parallel network of two more.
- Connect the ammeter in series with the battery and the voltmeter in parallel across it.
- Draw the circuit diagram, marking clearly which terminal of each meter is positive and which is negative.
- Close the switch and measure the current through the battery and the voltage across it.
- Measured resistance of the load: R = V ÷ I
- Calculated resistance: 1/Rparallel = 1/R2 + 1/R3, then Rtotal = R1 + Rparallel
- Compare the two values.
What you should see
Part 1: the terminal voltage is noticeably lower than the emf once the switch closes. With a tired carbon-zinc cell expect a drop of a few tenths of a volt and an internal resistance somewhere around 0,5 to 2 Ω.
Part 2: the measured and calculated values will not match exactly, and that is exactly what the question is testing. The calculation ignores the internal resistance of the battery and the resistance of the connecting leads.
Choose the right cell, or this will not work
This one decision decides whether the practical succeeds.
Use a carbon-zinc cell, and an older one beats a fresh one. A new alkaline cell has an internal resistance of a fraction of an ohm. The terminal voltage barely drops when the switch closes, the difference between your two readings is almost nothing, and the arithmetic falls apart.
A cell that has been sitting in a drawer has a much higher internal resistance, gives a clear measurable drop, and produces a number a learner can work with. Test one before the lesson. If the two voltmeter readings look nearly identical, find an older cell.
What you need
A digital multimeter can stand in for either meter. Analogue moving coil meters are easier for learners to read a trend from, a multimeter is more accurate.
You supply
A 1,5 V carbon-zinc cell. Older ones work better, see above.
If it does not work
| What you see | What caused it |
|---|---|
| emf and terminal voltage almost identical | The cell is too fresh. Swap alkaline for an older carbon-zinc cell |
| Readings drift while you work | The switch is being left closed. It heats the battery and changes the thing you are measuring. Close, read, open |
| Ammeter reads nothing | Ammeter wired in parallel instead of series, or the switch is open |
| A needle goes backwards | Leads reversed on that meter |
| The resistor gets hot | Switch held closed too long. A low value resistor on a 1,5 V cell dissipates about 0,4 W, which is more than a standard quarter watt resistor is rated for. Take the reading and open the switch |
| Part 2 measured value far too high | The parallel pair is wired in series. Check that branch |
| Multimeter reads nothing sensible | Dial on the wrong setting. Series for current, parallel for voltage |
If your task asks for a graph instead
Some versions of this assessment ask for five sets of readings and a graph of V against I, reading the internal resistance off the gradient rather than calculating it from a single pair. That version needs a way to vary the current, either a rheostat or simply a set of different resistors swapped in between readings.
The physics is the same. On that graph the gradient is negative and equals −r, and the y-intercept is the emf, because that is the voltage when no current flows.
Check which version your school has been set before the lesson. Five different resistors will do the job perfectly well in place of a rheostat.
Safety
Low voltage cells cannot give a dangerous shock, but a short circuit across a battery gets hot quickly. Never let bare connecting leads touch. Check the ammeter is in series before closing the switch, because an ammeter across a battery is a short circuit.
Do not leave the switch closed between readings. Flat or leaking cells go to battery recycling, not general waste.
Free worksheet and marking memo
Both free, no sign up. Coming shortly for this experiment. In the meantime the method above covers everything the practical requires.
Buy this experiment
We are putting together a complete Internal Resistance Kit for Grade 12 with the meters, switch, resistors and leads in one box. Coming shortly.
In the meantime every instrument in the table above is sold separately, and the meters in particular are items a school keeps for years rather than replaces.