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urt 1: a) The power (P) dissipated in a resistor (R) which is subjected to a voltage (V) across its terminals is given by the well-known formula; R

urt 1: a) The power (P) dissipated in a resistor (R) which is subjected to a voltage (V) across its terminals is given by the well-known formula; R

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Scenario: You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions, She has asked you to undertake a series of such evaluations. Activity: Part 1: a) The power (P) dissipated in a resistor (R) which is subjected to a voltage (V) across its terminals is given by the well-known formula; P = R Since you are new to the company your new Line Manager is unsure of your capabilities, and has asked you to use the dimensions of P and V to determine the dimensions of R. b) A guitar string, made by your Musical Instruments division, has mass (m), length (I) and tension (F). It is proposed by one of your junior colleagues that a formula for the period of vibration (t) of the string might be; t = 2n Use dimensional analysis to show your colleague that this formula is incorrect. c) An analogue-to-digital converter (ADC), manufactured by your Signals division, takes 20 voltage sam- ples of a ramp waveform, measured in mv, as follows... 2, 4, 6, 8, 10 ..40 Your Test colleague has asked you to assist by using a formula to calculate the sum of these 20 voltage samples.
Transcribed Image Text:Scenario: You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions, She has asked you to undertake a series of such evaluations. Activity: Part 1: a) The power (P) dissipated in a resistor (R) which is subjected to a voltage (V) across its terminals is given by the well-known formula; P = R Since you are new to the company your new Line Manager is unsure of your capabilities, and has asked you to use the dimensions of P and V to determine the dimensions of R. b) A guitar string, made by your Musical Instruments division, has mass (m), length (I) and tension (F). It is proposed by one of your junior colleagues that a formula for the period of vibration (t) of the string might be; t = 2n Use dimensional analysis to show your colleague that this formula is incorrect. c) An analogue-to-digital converter (ADC), manufactured by your Signals division, takes 20 voltage sam- ples of a ramp waveform, measured in mv, as follows... 2, 4, 6, 8, 10 ..40 Your Test colleague has asked you to assist by using a formula to calculate the sum of these 20 voltage samples.
d) A digital chip, made by your Microelectronics division, counts continuously in the sequence: 1024, 2048, 4096, 8192, ... You have been asked to use a formula to calculate the 9h count of the chip. e) A series electrical circuit which you are testing features a capacitor (C) charging via a 1MQ resistor (R) and a 12V dc supply (V.). The voltage across the capacitor (Va) may be described by the equation.. Ve =v, (1-e hc) where t represents time. Assuming that Vc is 2V after a time of 4 seconds, detemine the approximate value of the capacitor. f) One of your commonly-used laboratory instantaneous test signal voltages (v.) is described by the equation... v, = 6sin 27 ft- where f = 1MHZ and t represents time. Make time (t) the subject of this formula, and hence determine the first point in time when the instantaneous signal voltage has a magnitude of +3V. Note: A colleague has reminded you that you need to have your calculator in radians mode (RAD) for this calculation, because the angle is given in radians (i.e. T is featured). Use suitable software to draw at least two cycles of this signal, and annotate the drawing so that non- technical colleagues may understand it. 9) The curve assumed by a heavy power cable, manufactured by your Power division, is described by the equation... y = 60 cosh 60 where x and y are horizontal and vertical positions respectively. Calculate; () The value of y when x is 104. (ii) The value of x when y is 180. h) You are testing a decorative clock, to possibly be manufactured by your Consumer Electronics divi- sion, and attach a mass (m) to a string of length (1) to form a simple pendulum. Assuming that the ac- celeration due to gravity (g) of the earth may have an influence on the period (t) of the pendulum swing, use dimensional analysis to find a formula for t which could possibly involve m, l, and g. i) You are testing a prototype loudspeaker for your Audio division, which may possibly be used in smoke-filled environments when nuclear reactor emergencies occur. A senior colleague has asked you to use dimensional analysis to predict how the speed of sound (u) in a gas may be influenced by the gas pressure (p), gas density (r) and acceleration due to gravity (g).
Transcribed Image Text:d) A digital chip, made by your Microelectronics division, counts continuously in the sequence: 1024, 2048, 4096, 8192, ... You have been asked to use a formula to calculate the 9h count of the chip. e) A series electrical circuit which you are testing features a capacitor (C) charging via a 1MQ resistor (R) and a 12V dc supply (V.). The voltage across the capacitor (Va) may be described by the equation.. Ve =v, (1-e hc) where t represents time. Assuming that Vc is 2V after a time of 4 seconds, detemine the approximate value of the capacitor. f) One of your commonly-used laboratory instantaneous test signal voltages (v.) is described by the equation... v, = 6sin 27 ft- where f = 1MHZ and t represents time. Make time (t) the subject of this formula, and hence determine the first point in time when the instantaneous signal voltage has a magnitude of +3V. Note: A colleague has reminded you that you need to have your calculator in radians mode (RAD) for this calculation, because the angle is given in radians (i.e. T is featured). Use suitable software to draw at least two cycles of this signal, and annotate the drawing so that non- technical colleagues may understand it. 9) The curve assumed by a heavy power cable, manufactured by your Power division, is described by the equation... y = 60 cosh 60 where x and y are horizontal and vertical positions respectively. Calculate; () The value of y when x is 104. (ii) The value of x when y is 180. h) You are testing a decorative clock, to possibly be manufactured by your Consumer Electronics divi- sion, and attach a mass (m) to a string of length (1) to form a simple pendulum. Assuming that the ac- celeration due to gravity (g) of the earth may have an influence on the period (t) of the pendulum swing, use dimensional analysis to find a formula for t which could possibly involve m, l, and g. i) You are testing a prototype loudspeaker for your Audio division, which may possibly be used in smoke-filled environments when nuclear reactor emergencies occur. A senior colleague has asked you to use dimensional analysis to predict how the speed of sound (u) in a gas may be influenced by the gas pressure (p), gas density (r) and acceleration due to gravity (g).
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