Download ELECTROTECHNOLOGY How does a refrigeration mechanic use

MATHEMATICS PATHWAYS STAGE 1 Folio Task
ELECTROTECHNOLOGY
THE REFRIGERATION MECHANIC
Suggested weighting: %
Approximate duration:
Created by: Robert Boyd (October ’09)
Glossop High School
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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
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1 mark
(b) Calculate the current in the 16 resistor in figure one if the potential difference between A
and B is 12V.
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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.
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2 marks
(b) Calculate the current in the 6 resistor in figure two if the potential difference between A
and B is 12V.
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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.
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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
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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.