# Electric Kettle

Explore the relationship between resistance and temperature

## Problem

The diagram shows a simple circuit: the cell provides energy, *V* volts, which causes a current, *I* amps, to flow around the circuit. There is also a resistance, *R* ohms.

Image

This circuit provides a simple model for what happens in an electric kettle: a resistance converts electrical energy into heat energy by impeding the flow of electrons around the circuit.

The table shows data collected from a circuit like this.

Resistance (ohms) |
Temperature (degrees Celsius) |

5 | 44.9 |

6 | 50 |

7 | 55.1 |

8 | 59.9 |

9 | 65 |

10 | 70.1 |

- Draw a graph of this data, with the resistance on the horizontal axis, putting a straight line through the points.
- Find the gradient of the line.
- Find the equation of the line.

Once you have found the equation, discuss these questions:

- What resistance would you need to heat water to 100 C °?
- What would the temperature be if the resistance was zero?
- Do you think that in practice, any circuit can have zero resistance?

## Student Solutions

The equation of the line is $T = 5R +20$, so your gradient should be close to 5.

To heat water to 100 C you need $R = \frac{100 - 20}{5} = 16$ ohms. If the resistance is zero then $T = 20$C. In practice it is really hard to have a circuit with zero resistance. You need special conditions such as a low temperature.

## Teachers' Resources

It is not envisaged that this problem would be used as a class problem. It is more appropriate for an enthusiastic student or small group of students looking for a challenge to work on independently.