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MATHEMATICS PATHWAYS STAGE 1 Folio Task ELECTROTECHNOLOGY THE REFRIGERATION MECHANIC Suggested weighting: % Approximate duration: Created by: Robert Boyd (October ’09) Glossop High School - . Notes to the teacher A suggested approach to introduce and prepare students for this task The scenario of a refrigeration mechanic needing to understand how a compressor starts up so they can work out what’s wrong with one, should be discussed. A local refrigeration mechanic (e.g. the ones who service the school’s air conditioners) could be invited to talk to the class about this aspect of their work. The instruction on the Mathematical Skills contained in this activity (addition of positive whole numbers, fractions, inverting fractions and deduction reasoning) should follow this setting of the scenario . C level: complete questions 1 – 4 B level: complete questions 1 – 4 and either question 5 or question 7 A level: complete questions 1 – 7 Mathematical skills which may be required to complete this task. Fractions Decimals Integers Scientific Notation Equations Indices Algebraic Expressions Algebraic Fractions Formulae Units of measurement Introduction A refrigerator mechanic needs to understand the operation of a refrigerator and to use mathematics to correctly diagnose and repair faults. Task description The addition of resistors in series and parallel enables the student to understand how current flows through the motor that drives the refrigerator compressor. This involves addition of positive whole numbers, fractions and inverting fractions. The use of Ohms Law involves simple algebra. The Positive Temperature Coefficient (PTC) resistor use in providing extra starting torque on the compressor is the endpoint of the exercise. This is a draft, unauthorised working document. Feedback is appreciated. To achieve at a higher level the student also needs to perform the algebraic calculations as well as demonstrate a reasoned understanding of the PTC resistor’s change in value and its effect on the current flow in the motor’s windings. Specific Tasks 1. (a) Calculate the equivalent resistance for the series resistors in figure one. figure one __________________________________________________________________ __________________________________________________________________ _______________________________________________________ 1 mark (b) Calculate the current in the 16 resistor in figure one if the potential difference between A and B is 12V. __________________________________________________________________ __________________________________________________________________ _______________________________________________________ 2 marks 2. (a) Show that equivalent resistance for the parallel resistors in figure two is 0.5 . figure two This is a draft, unauthorised working document. Feedback is appreciated. __________________________________________________________________ __________________________________________________________________ _______________________________________________________ 2 marks (b) Calculate the current in the 6 resistor in figure two if the potential difference between A and B is 12V. __________________________________________________________________ __________________________________________________________________ _______________________________________________________ 2 marks Single Phase compressor motors require greater torque when starting than running for the rest of the time. For this reason some compressor motors have two sets of windings; one for normal running and one to provide the extra torque at startup. A picture of a typical refrigerator compressor and start pack is shown in figure three. figure three Source: Texas Instruments Product Bulletin - MCKS010 Reprinted 01/2004, Rev. A Figure four shows a circuit diagram of the two windings in the motor and the PTC resistor in series with the start winding. figure four This is a draft, unauthorised working document. Feedback is appreciated. A Positive Temperature Coefficient (PTC) resistor is used to ensure that the startup winding operates only for the time needed for the compressor to come up to operating speed. When power is first applied to the compressor, the PTC resistor is in the low resistance state. The actual value of resistance varies depending on the actual compressor. Typical values for the Texas Instruments Klixon SP series are shown in table one. table one SP Series 14CX 15CX 17CX Application Voltage 120 120 240 Vmax / Imax 180 / 12 200 / 12 300 / 7 Nominal Resistance (Ohms) 5.0 20% 6.8 20% 10 20% Heat Capacity MCP 1.40 1.40 1.40 Consider the equivalent resistive circuit shown in figure five. figure five This is a draft, unauthorised working document. Feedback is appreciated. Questions 3 and 4 provide set the scenario for the use of the PTC resistor. 3. Calculate the equivalent resistance between points C and D in figure five. __________________________________________________________________ __________________________________________________________________ _______________________________________________________ 1 mark The current flow through the PTC resistor causes self-heating and it switches to the high resistance state with a resistance of the order of 100,000 . Consider the equivalent resistive circuit shown in figure six. figure six 4. Calculate the new equivalent resistance between points C and D in figure six. 2 marks ___________________________________________________________________________________ 5. Let the potential difference applied to points A and B be 240 volts. (a) Calculate the current that flows through the PTC resistor and the 5 start winding in figure five. 2 marks (b) Calculate the current that flows through the PTC resistor and the 5 start winding in figure six. This is a draft, unauthorised working document. Feedback is appreciated. 2 marks Extension questions 6. Use your current values calculated above to explain how the PTC resistor in series with the start winding in the compressor’s motor provides extra starting power and ensures that the compressor uses less power when running than starting. 7. Determine the model of refrigerator at home, the compressor specifications and the type of method used by the compressor for start up. (it may be a magnetic relay or a PTC resister) Check that you have: Clarified: Modelled: Solved: Interpreted: Checked Reported: Evaluated: Fully explained your scenario and problem, including any assumptions and boundaries. Formed a mathematical model or strategy which closely investigates your problem. Used mathematical tools and methods to find a possible answer to the problem. Interpreted your solution by comparing it to real life situation. Is the solution around the mark? Checked your solution against your original scenario using an alternative method, or measurement. Discuss how appropriate your solution is to the work situation. Reported clearly and in detail, on all considerations, research, data, issues, and areas of extension, mathematical determinations conclusions and possible constraints. Reflected on your solution and determine areas where there could be improvement, refinement or development. Generalised the solution or methodology to other similar situations. This is a draft, unauthorised working document. Feedback is appreciated.