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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.
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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. The higher the temperature, the faster the metal atoms vibrate, and the more likely they are to impede electron flow, hence increasing resistance. metalatom electron
The current in an ohmic conductor is proportional to the voltage across it, provided that the temperature and other physical conditions are kept constant. VµI V = R × I Ohm’s Law Ohm’s Law states that: We can write ‘voltage is proportional to current’ in symbols as: If R is a constant: R is the resistance, measured in ohms (Ω).
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.
Equivalent resistance R2 R3 R4 R1 R5 RT R6 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.
RT = R1 + R2 + … + Rn Resistors in series To work out the equivalent resistance of resistors in series, the resistor values can just be added together: 10Ω 20Ω 15Ω equivalent resistance = 10 + 20 + 15 = 45Ω In general for a number of resistors, n:
1 1 1 1 1 = + + … + RT RT R1 R2 Rn 1 1 1 20 15 10 1 1 6 + 3 + 4 RT RT 60 13 60 60 13 Resistors in parallel To work out the equivalent resistance for resistors in parallel, a more complex equation must be applied: For example: = + + 10Ω = = 20Ω RT = Ω = 4.62Ω 15Ω
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 cross-sectional area and length) and the material itself. copper silver The measure of how much a particular material opposes electron flow is called the resistivity of the material. silicon plastic
resistance × cross-sectional area length resistivity = RAL r = Introducing the resistivity equation Resistivity is usually given the symbol r (the Greek letter rho). Resistivity is calculated using the following equation: 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.
