Practical: EMF and internal resistance
To measure the internal resistance of a battery the PD across the terminals needs to be measured as current flows, in this practical the current is varied by changing the length of a piece of nichrome resistance wire connected across the terminals.
The circuit can be represented by the diagram below, where R represents the resistance wire and r the internal resistance of the battery.
The equation for this circuit is ε = IR + Ir
Rearranging this gives R = ε/I - r
Alternatively we can write IR = -Ir + ε
This method assumes you only have one multimeter so can't measure the PD and current at the same time, however if you have 2 then you can adapt the method to save time.
- Attach a 30cm length of resistance wire to a plastic ruler with some sticky tape.
- Set the multimeter to measure resistance and measure the resistance of 30cm of the wire.
- Move one of the contacts 5cm along the wire and measure the resistance again, in this way fill in a table of resistance and length like the one below.
- Connect the circuit shown in the diagram above including the multimeter set to measure current to measure the current flowing through R.
- Measure the current flowing through for each length of the resistance wire. Enter the currents in your table.
- Disconnect the meter and connect it as a voltmeter to measure the PD across R.
- Measure the PD across R for each length of the wire. Again enter you values into the table. You should now have 4 columns.
- Estimate the uncertainties in each measurement and enter into the headers of the table.
According the the theory R = ε/I - r so a graph of R vs 1/I should be a straight line with gradient ε and intercept -r. Calculate values of 1/I in your spreadsheet then plot the relevant graph to find ε and r.
An alternative version of the equation is IR = -Ir + ε where IR = V, the PD across the resistance wire (also equal to the PD across the terminals of the battery). Plot a graph of V vs I to find ε and r.
Conclusion and evaluation
Compare the values obtained for each method. Which method gave the best value for each quantity?
What effect did the meters have on your measurements?