Internal Resistance

Electricity and Magnetism

## Internal resistance of a shoe box cell

Practical Activity for 14-16

**Class practical**

Finding an internal resistance of a supply from the power dissipated by a load resistance.

Apparatus and Materials

*For each student group*

- Digital multimeters, 2
- Leads, 4 mm, 5
- Cells, 1.5 V type C, 4
- Resistors of a range of values from 10 ohms to 100 ohms
- Crocodile clips, 10 pairs

Health & Safety and Technical Notes

Read our standard health & safety guidance

Procedure

- The shoe box cell contains a 6 V supply with an unknown resistor in series. The unknown resistor acts as the internal resistance in the shoe box cell. Your challenge is to find the value of the internal resistance without opening the box!
- Choose a value for the load resistance
*R*and set up the circuit as shown. Record the current and potential difference values.*E*is the e.m.f. of the equivalent perfect cell of internal resistance*r*. - Change the load resistance and once again record the values of current and potential difference values.
- Repeat this process for about ten values of load resistance.

**Analysis**

- Calculate the power dissipated by the load resistance by using the equation
*P*=*I**V*. - Plot a graph of power dissipated against load resistance.
- The power dissipated by the load resistance is a maximum value when it equals the ‘internal resistance’ of the shoe box cell. Use this fact to estimate the resistance in the box.
- The cells in the box have a total internal resistance of about 4 ohms. How does this fact change your answer?

Teaching Notes

- The resistance in the box needs to be about 50 ohms if a clear peak is to be found when the load resistance varies between about 10 ohms and 100 ohms. This will give a minimum current of about 40 mA. using 4 x 1.5 V cells.
- Resistors can be labelled and clipped together to give a good range of total resistance values.
- Students familiar with
*V*=*ε*–*I**r*should be able to interpret the data in terms of the internal resistance of the shoe box cell. This experiment can also be interpreted as an example of a potential divider. The internal and external resistances are in series, so the e.m.f. is divided between them. - Some students will be able to complete the analysis more quickly using a spreadsheet.

*This experiment submitted by Lawrence Herklots, King Edward VI School, Southampton.*

*This experiment was safety-tested in April 2006*