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1 of 31 © Boardworks Ltd 2009 2 of 31 © Boardworks Ltd 2009 The effect of temperature on resistance Resistance is a characteristic of all materials. Some materials (e.g. air) have a high resistance. Other materials (e.g. gold) have a very small resistance. Electrical resistance is similar to friction, in that it is a resistance to movement. Electrons drift slowly through a conductor when a voltage is put across the ends. The metal’s atoms interfere with the motion of the electrons, causing resistance. electron 3 of 31 metal atom The higher the temperature, the faster the metal atoms vibrate, and the more likely they are to impede electron flow, hence increasing resistance. © Boardworks Ltd 2009 Ohm’s Law Ohm’s Law states that: The current in an ohmic conductor is proportional to the voltage across it, provided that the temperature and other physical conditions are kept constant. We can write ‘voltage is proportional to current’ in symbols as: VI If R is a constant: V=R×I R is the resistance, measured in ohms (Ω). 4 of 31 © Boardworks Ltd 2009 Finding resistance from a graph Compare the equation for an ohmic conductor to the general equation for a straight line: V = RI y = mx + c V If a graph is plotted with voltage on the y axis and current on the x axis, it can be seen that the gradient (m) is the resistance. The y intercept (c) is 0. gradient = R I Voltage–current graphs are often drawn with the axes the other way around. In this case, the gradient = 1/R and R = 1/gradient. 5 of 31 © Boardworks Ltd 2009 Plotting voltage–current graphs 6 of 31 © Boardworks Ltd 2009 How well do you understand graphs? 7 of 31 © Boardworks Ltd 2009 Which symbol and which graph? 8 of 31 © Boardworks Ltd 2009 Ohm’s Law summary 9 of 31 © Boardworks Ltd 2009 10 of 31 © Boardworks Ltd 2009 Equivalent resistance R2 R1 R3 R4 R5 R6 RT R7 When designing or analysing circuits, complex combinations of resistors are common. To perform calculations, for example to find a suitable fuse to protect the circuit, it is easier to use a value for the total resistance of the circuit, RT. RT can be called the equivalent resistance because it is the single resistor that is equivalent to the complex combination. 11 of 31 © Boardworks Ltd 2009 Resistors in series To work out the equivalent resistance of resistors in series, the resistor values can just be added together: 10 Ω 20 Ω 15 Ω equivalent resistance = 10 + 20 + 15 = 45 Ω In general for a number of resistors, n: RT = R1 + R2 + … + Rn 12 of 31 © Boardworks Ltd 2009 Resistors in parallel To work out the equivalent resistance for resistors in parallel, a more complex equation must be applied: 1 1 1 1 = + + … + RT R1 R2 Rn For example: 10 Ω 20 Ω 15 Ω 13 of 31 1 1 1 1 = + + RT 10 20 15 1 6+3+4 = RT 60 1 = 13 RT 60 RT 60 = Ω = 4.62 Ω 13 © Boardworks Ltd 2009 Resistor combinations 14 of 31 © Boardworks Ltd 2009 15 of 31 © Boardworks Ltd 2009 What is resistivity? Which of the four examples below has the largest resistance, and which has the smallest? The resistance depends on the size and shape of the material (its crosssectional area and length) and the material itself. copper silver silicon plastic 16 of 31 The measure of how much a particular material opposes electron flow is called the resistivity of the material. © Boardworks Ltd 2009 Introducing the resistivity equation Resistivity is usually given the symbol r (the Greek letter rho). Resistivity is calculated using the following equation: resistance × cross-sectional area resistivity = length RA r= L The units of resistivity are ohm metres (Ωm). Resistivity for a particular material varies with temperature, so it is usually quoted for a particular temperature. This is because resistivity depends on resistance, and resistance varies with temperature. 17 of 31 © Boardworks Ltd 2009 Using the resistivity equation 18 of 31 © Boardworks Ltd 2009 Resistivity calculation 19 of 31 © Boardworks Ltd 2009 Effect of temperature on resistivity 20 of 31 © Boardworks Ltd 2009 Investigating the effect of temperature 21 of 31 © Boardworks Ltd 2009 Resistivity of different materials 22 of 31 © Boardworks Ltd 2009 23 of 31 © Boardworks Ltd 2009 E.m.f. and internal resistance 24 of 31 © Boardworks Ltd 2009 Using the e.m.f. equations 25 of 31 © Boardworks Ltd 2009 Finding e.m.f. and internal resistance 26 of 31 © Boardworks Ltd 2009 E.m.f. summary 27 of 31 © Boardworks Ltd 2009 28 of 31 © Boardworks Ltd 2009 Glossary 29 of 31 © Boardworks Ltd 2009 What’s the keyword? 30 of 31 © Boardworks Ltd 2009 Multiple-choice quiz 31 of 31 © Boardworks Ltd 2009