7456 /www/nrich/html/content/id/7456/ 1 2011-06-15T12:53:46 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/6603">Warm-up</a></li> <li><a href="http://nrich.maths.org/7278">Try this next</a></li> <li><a href="http://nrich.maths.org/7677">Think higher</a></li> <li><a href="http://plus.maths.org/content/making-grade">Read: mathematics</a></li> <li><a href="http://nrich.maths.org/6652">Read: science</a></li> <li><a href="http://motivate.maths.org/content/LiquidNitrogenShowMathsLowTemperaturePhysics/Resistance">Explore further</a></li> </ul> <div> </div> <br></br> <p>The diagram shows a simple circuit: the cell provides energy, <em>V</em> volts, which causes a current, <em>I</em> amps, to flow around the circuit. There is also a resistance, <em>R</em> ohms.<br></br>  <mdo:image alt="circuit diagram" height="148" src="kettlecircuit-small.png" width="178"></mdo:image><br></br>  <br></br> 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.<br></br> <br></br> The table shows data collected from a circuit like this.<br></br>  </p> <table style="" border="1"> <tbody align="center"> <tr> <td><strong>Resistance (ohms)</strong></td> <td><strong>Temperature (degrees Celsius)</strong></td> </tr> <tr> <td>5</td> <td>44.9</td> </tr> <tr> <td>6</td> <td>50</td> </tr> <tr> <td>7</td> <td>55.1</td> </tr> <tr> <td>8</td> <td>59.9</td> </tr> <tr> <td>9</td> <td>65</td> </tr> <tr> <td>10</td> <td>70.1</td> </tr> </tbody> </table> <br></br> <br></br> <ul> <li>Draw a graph of this data, with the resistance on the horizontal axis, putting a straight line through the points.</li> <li>Find the gradient of the line.</li> <li>Find the equation of the line.</li> </ul> <br></br> <br></br> <p>Once you have found the equation, discuss these questions:<br></br>  </p> <ul> <li>What resistance would you need to heat water to 100 C°?</li> <li>What would the temperature be if the resistance was zero?</li> <li>Do you think that in practice, any circuit can have zero resistance?</li> </ul> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">It is not envisaged that <a href="http://nrich.maths.org/7456">this problem</a> 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.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p style="text-align: justify;"> </p> <p>The equation of the line is $T = 5R +20$, so your gradient should be close to 5.<br></br> <br></br> 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.</p></mdoxml> 2 3 0 0 0 1 0 Explore the relationship between resistance and temperature Applications Maths Supporting SET Applications STEM - physical world Admin Individual Sequences, Functions and Graphs Graphs Sequences, Functions and Graphs Gradients STEM mapping STEM - Scientific Calculation STEM mapping STEM Physical World STEM mapping STEM - Textiles STEM mapping STEM - Real World STEM mapping STEM - Units STEM mapping STEM - Graphs STEM mapping STEM - Equations And Formulae