Practical: EMF and internal resistance

Introduction

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.

Theory

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

Method

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.

If you are wondering why there is a 28 in the table then join the club, I am wondering too. Maybe 25 cm might have been more logical.

  • 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.

Analysis

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?

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