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A –Level Physics: Electrical Quantities: Resistance and Resistivity Objectives: 36. be able to derive the equations for combining resistances in series and parallel using the principles of charge and energy conservation, and be able to use these equations 39. be able to use the equation for resistivity 41. be able to use I = nqvA to explain the large range of resistivities of different materials Additional skills gained: • Practical Planning • Integrating GCSE content Starter: Resistance is futile… For the following resistor combinations, calculate the total resistance and the voltmeter reading for each assuming a total EMF of 24V You have 10mins Conduction and Resistance In pairs, discuss and create a definition of ‘conduction’ and ‘resistance’ and write them on a whiteboard Resistance quantifies how strongly a component opposes the flow of charge carriers (current) Conduction is the movement of charged particles or propagation of energy through a material Conduction A metal consists of positive metal ions with free electrons that move with random motion as they collide with the ions. If a source of emf is connected across a metal, the electric field set up have a tendency to push the electrons toward the positive end of the metal. This ‘crawling’ motion towards the positive terminal is known as the drift velocity Drift Velocity (transport equation) This time I will show you the equation, and you’ll tell me how it’s derived! The diagram to the left will help! We consider the shape of a wire to be a cylinder, the current that is flowing by can be calculated with the formula: 𝐼 = 𝑛𝐴𝑣𝑞 With ‘v’ being the drift velocity and ‘n’ the number density of electrons Using the diagram to help, prove how this equation was derived 10m Drift Velocity Practice 1. How fast would the drift velocity be for electrons in a copper wire which has a diameter of 0.22mm and carries a current of 0.50A? The number density of electrons for copper (n) = 8.5x1028m-3 2. For an aluminium wire (at room temp) with a diameter of 0.4mm, calculate the drift velocity when a current of 2.2A passes through the wire. The number density for aluminium is 18.2x1028m-3 Models In pairs you will need to develop a model to help explain conduction and resistance in metals. Your explanation should include reference to at least the following ideas: • Movement of charge carriers • Fixed lattice ions • Collisions between ions and charge carriers • Increased vibrations of fixed lattice ions with temperature • Evaluation of the strengths and weaknesses of your model Resistivity Resistivity is similar to resistance with the exception that it’s an inherent characteristic of the material itself, i.e. “ a quantification of a material’s ability to resist the flow of electric current” So this means that it is a feature of the type of metal for example, rather than anything to do with the dimensions of this metal in a wire. 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒(Ω) = 𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 Ω𝑚 × 𝑆𝑎𝑚𝑝𝑙𝑒 𝑙𝑒𝑛𝑔𝑡ℎ(𝑚) 𝐶𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐴𝑟𝑒𝑎 (𝑚2 𝜌𝑙 𝑅= 𝐴 What is the resistance of a copper fuse wire (resistivity of 1.7x10-8 Ωm ) with a diameter of 0.4mm and 2cm in length? SILVER 1. Taking the resistivity of platinoid as 3.3 x 10-7 m, find the resistance of 7.0 m of platinoid wire of average diameter 0.14 cm. 2. The resistance of the ohm is very approximately that of a column of mercury 1.06 m long and of uniform cross-section of one hundredth of a cm2. Find the resistivity of mercury. 3. What length of German silver wire, diameter 0.050 cm, is needed to make a 28 resistor, if the resistivity of German silver is 2.2 x 10-7 m? 4. The maximum allowable resistance for an underwater cable is one hundredth of an ohm per metre. If the resistivity of copper is 1.54x10-8m, find the smallest diameter of a copper cable that could be used. 5. A block of carbon, 1.0 cm by 2.0 cm by 5.0 cm, has a resistance of 0.015 between its two smaller faces. What is the resistivity of carbon? 6. A uniform strip of eureka (resistivity 5-0 x 10-7 m) has a resistance of 0.80 per metre and is 0.25 cm wide. What is its thickness? 7. A wire of uniform cross-section has a resistance of R . What would be the resistance of a similar wire, made of the same material, but twice as long and of twice the diameter? 8. A wire of uniform cross-section has a resistance of R . If it is drawn to three times the length, but the volume remains constant, what will be its resistance? GOLD Complete the following practice questions. Show all values before answering: BRONZE Differentiated Q Independent Study Research the following and write half a page (each) on how they function: • Potential Divider (Rheostat) • Semiconductor Diode Due: Monday 20th March