// Numbas version: finer_feedback_settings
{"name": "Electrical Energy Systems 2.1 Final Exam", "metadata": {"description": "TU705 (DT009) year 2 Final Exam
", "licence": "None specified"}, "duration": 0, "percentPass": "40", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": false, "question_groups": [{"name": "DC Machines", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "DC Series Generator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "In testing, a separately excited DC machine, operating at a speed of $\\var{Ntest}\\ rpm$, produces $\\var{Vtest}\\ V$ with an open circuit armature, when operated at a fixed field current of $\\var{IF}\\ A$.
\nIts intrinsic resistances are:
\nField Resistance: $R_F = \\var{RF}\\ \\Omega $
\nArmature Resistance: $R_A = \\var{RA}\\ \\Omega $
\nThe machine is then connected as a series generator to supply a load with a current of $\\var{IF}\\ A$ when running at a speed of $\\var{N}\\ rpm$ .
", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Ntest": {"name": "Ntest", "group": "Test Data", "definition": "random(1000 .. 2000#100)", "description": "", "templateType": "randrange", "can_override": false}, "RF": {"name": "RF", "group": "Operation", "definition": "random(10 .. 50#5)", "description": "", "templateType": "randrange", "can_override": false}, "RA": {"name": "RA", "group": "Operation", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "VL": {"name": "VL", "group": "Operation", "definition": "random(100 .. 500#1)", "description": "", "templateType": "randrange", "can_override": false}, "IF": {"name": "IF", "group": "Operation", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "N": {"name": "N", "group": "Operation", "definition": "round(60*omega/(2*pi))", "description": "", "templateType": "anything", "can_override": false}, "magnetism": {"name": "magnetism", "group": "Test Data", "definition": "Vtest/(2*pi*Ntest/60)", "description": "", "templateType": "anything", "can_override": false}, "omega": {"name": "omega", "group": "Operation", "definition": "ea/magnetism", "description": "", "templateType": "anything", "can_override": false}, "T": {"name": "T", "group": "Operation", "definition": "magnetism*IF", "description": "", "templateType": "anything", "can_override": false}, "ea": {"name": "ea", "group": "Operation", "definition": "VL + IF*(RA+RF)", "description": "", "templateType": "anything", "can_override": false}, "Vtest": {"name": "Vtest", "group": "Test Data", "definition": "random(100 .. 500#50)", "description": "", "templateType": "randrange", "can_override": false}, "RL": {"name": "RL", "group": "Operation", "definition": "VL/IF", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "RL > 0", "maxRuns": "1000"}, "ungrouped_variables": [], "variable_groups": [{"name": "Test Data", "variables": ["Ntest", "Vtest", "magnetism"]}, {"name": "Operation", "variables": ["IF", "RF", "RA", "VL", "T", "ea", "omega", "N", "RL"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Magnetism", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the magnetism on the machine?
\n$k_a \\phi = $ [[0]]
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Convert the testing speed from $N$ in rpm to $\\omega$ in rad/s.
\n- Fill all testing values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$ at the given current.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Magnetism", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "magnetism*0.99", "maxValue": "magnetism*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Torque", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the torque on the shaft?
\n$T$ = [[0]] $ Nm $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Find the torque from $T=k_a\\phi I_A$.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Torque", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "T*0.99", "maxValue": "T*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Voltage", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the output voltage to the load?
\n$V_L$ = [[0]] $ V $
\nWhat is the load resistance?
\n$R_L$ = [[1]] $\\Omega$
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Calcuate the voltage, $e_a$, from $e_a=k_a\\phi \\omega$.
\n- Find the output voltage from Kirchhoff's Voltage Law.
\n- Find the load resistance from Ohm's Law.
\n
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\nIts intrinsic resistances are:
\nField Resistance: $R_F = \\var{RF}\\ \\Omega $
\nArmature Resistance: $R_A = \\var{RA}\\ \\Omega $
\nThe machine is then connected as a series motor to a supply providing $\\var{VS}\\ V$. It is found to draw the same current of $\\var{IF}\\ A$.
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\n$k_a \\phi = $ [[0]]
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Convert the testing speed from $N$ in rpm to $\\omega$ in rad/s.
\n- Fill all testing values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$ at the given current.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Magnetism", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "magnetism*0.99", "maxValue": "magnetism*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Torque", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the torque on the motor?
\n$T$ = [[0]] $ Nm $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Find the torque from $T=k_a\\phi I_A$.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Torque", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "T*0.99", "maxValue": "T*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Speed", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "At what speed is it running?
\nN = [[0]] $ rpm $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Calcuate the voltage, $e_a$, from Kirchhoff's Voltage Law.
\n- Find the speed from $e_a=k_a\\phi \\omega$.
\n- Convert this to rpm.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Speed", "marks": "15", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N*0.95", "maxValue": "N*1.05", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "DC Shunt Generator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "The following test data was measured for a separately excited DC machine operating at a speed of $\\var{Ntest}\\ rpm$ with an open circuit armature:
\n\n\n\n\n| \n Field Current \nIF [A] \n | \n\n 0 \n | \n\n 0.1 \n | \n\n 0.2 \n | \n\n 0.3 \n | \n\n 0.4 \n | \n\n 0.5 \n | \n\n 0.6 \n | \n\n 0.7 \n | \n\n 0.8 \n | \n\n 0.9 \n | \n\n 1.0 \n | \n
\n\n| \n Armature Voltage \nVA [V] \n | \n{VA[0]} | \n{VA[1]} | \n{VA[2]} | \n{VA[3]} | \n{VA[4]} | \n{VA[5]} | \n{VA[6]} | \n{VA[7]} | \n{VA[8]} | \n{VA[9]} | \n{VA[10]} | \n
\n\n
\n\nThe intrinsic resistances are:
\nField Resistance: $R_F = \\var{RF}\\ \\Omega $
\nArmature Resistance: $R_A = \\var{RA}\\ \\Omega $
\nThe machine is then connected as a shunt generator to supply $\\var{VL}\\ V$ to a $\\var{RL}\\ \\Omega$ load.
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\n$k_a \\phi = $ [[0]]
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Find the field current, $I_F$, using Ohm's Law.
\n- Find the speed and voltage during testing from the data at this field current.
\n- Convert the speed from $N$ in rpm to $\\omega$ in rad/s.
\n- Fill these values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Magnetism", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "magnetism*0.99", "maxValue": "magnetism*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "How much current is it flowing in the armature conductors?
\n$I_A$ = [[0]] $ A $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Calcuate the field current, $I_F$, as before using Ohm's Law.
\n- Calcuate the load current, $I_L$, using Ohm's Law.
\n- Get the armature current from Kirchhoff's Current Law.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Current", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "IA*0.95", "maxValue": "IA*1.05", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Speed", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "At what speed is it running?
\nN = [[0]] $ rpm $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Calcuate the voltage, $e_a$, from Kirchhoff's Voltage Law.
\n- Find the speed from $e_a=k_a\\phi \\omega$.
\n- Convert this to rpm.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Speed", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N*0.99", "maxValue": "N*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "DC Shunt Motor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "The following test data was measured for a separately excited DC machine operating at a speed of $\\var{Ntest}\\ rpm$ with an open circuit armature:
\n\n\n\n\n| \n Field Current \nIF [A] \n | \n\n 0 \n | \n\n 0.1 \n | \n\n 0.2 \n | \n\n 0.3 \n | \n\n 0.4 \n | \n\n 0.5 \n | \n\n 0.6 \n | \n\n 0.7 \n | \n\n 0.8 \n | \n\n 0.9 \n | \n\n 1.0 \n | \n
\n\n| \n Armature Voltage \nVA [V] \n | \n{VA[0]} | \n{VA[1]} | \n{VA[2]} | \n{VA[3]} | \n{VA[4]} | \n{VA[5]} | \n{VA[6]} | \n{VA[7]} | \n{VA[8]} | \n{VA[9]} | \n{VA[10]} | \n
\n\n
\n\nThe intrinsic resistances are:
\nField Resistance: $R_F = \\var{RF}\\ \\Omega $
\nArmature Resistance: $R_A = \\var{RA}\\ \\Omega $
\nThe machine is then connected as a shunt motor to a supply providing $\\var{VS}\\ V$. The motor is used to lift a weight which creates a torque of $\\var{T}\\ Nm$.
", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"Ntest": {"name": "Ntest", "group": "Test Data", "definition": "random(1000 .. 2000#100)", "description": "", "templateType": "randrange", "can_override": false}, "VAstep": {"name": "VAstep", "group": "Test Data", "definition": "random(20 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "VA": {"name": "VA", "group": "Test Data", "definition": "[VAstep,round(2*VAstep),round(3*VAstep),round(4*VAstep),round(5*VAstep),round(5.6*VAstep),round(6.2*VAstep),round(6.4*VAstep),round(6.5*VAstep),round(6.5*VAstep),round(6.5*VAstep)]", "description": "", "templateType": "anything", "can_override": false}, "RF": {"name": "RF", "group": "Test Data", "definition": "round(VS/IF)", "description": "", "templateType": "anything", "can_override": false}, "RA": {"name": "RA", "group": "Test Data", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "VS": {"name": "VS", "group": "Operation", "definition": "round(ea+(IA*RA))", "description": "", "templateType": "anything", "can_override": false}, "IF": {"name": "IF", "group": "Operation", "definition": "random(0.5 .. 1#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "N": {"name": "N", "group": "Operation", "definition": "random(200 .. 2000#50)", "description": "", "templateType": "randrange", "can_override": false}, "magnetism": {"name": "magnetism", "group": "Operation", "definition": "VA[IF*10]/(2*pi*Ntest/60)", "description": "", "templateType": "anything", "can_override": false}, "omega": {"name": "omega", "group": "Operation", "definition": "2*pi*N/60", "description": "", "templateType": "anything", "can_override": false}, "T": {"name": "T", "group": "Operation", "definition": "random(1 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "IA": {"name": "IA", "group": "Operation", "definition": "T/magnetism", "description": "", "templateType": "anything", "can_override": false}, "ea": {"name": "ea", "group": "Operation", "definition": "magnetism*omega", "description": "", "templateType": "anything", "can_override": false}, "IS": {"name": "IS", "group": "Operation", "definition": "IA+IF", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "N > 0", "maxRuns": "1000"}, "ungrouped_variables": [], "variable_groups": [{"name": "Test Data", "variables": ["Ntest", "VAstep", "VA", "RF", "RA"]}, {"name": "Operation", "variables": ["IF", "VS", "T", "magnetism", "IA", "ea", "omega", "N", "IS"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Magnetism", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is the magnetism on the machine?
\n$k_a \\phi = $ [[0]]
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Find the field current, $I_F$, using Ohm's Law.
\n- Find the speed and voltage during testing from the data at this field current.
\n- Convert the speed from $N$ in rpm to $\\omega$ in rad/s.
\n- Fill these values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Magnetism", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "magnetism*0.99", "maxValue": "magnetism*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "How much current is it drawing from the supply?
\n$I_S$ = [[0]] $ A $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Calcuate the field current, $I_F$, as before using Ohm's Law.
\n- Find the armature current from $T=k_a\\phi I_A$.
\n- Get the supply current from Kirchhoff's Current Law.
\n
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\nN = [[0]] $ rpm $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Calcuate the voltage, $e_a$, from Kirchhoff's Voltage Law.
\n- Find the speed from $e_a=k_a\\phi \\omega$.
\n- Convert this to rpm.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Speed", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N*0.99", "maxValue": "N*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "AC", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "OldTransformers", "extensions": [], "custom_part_types": [], "resources": [["question-resources/transformerCircuit.bmp", "/srv/numbas/media/question-resources/transformerCircuit.bmp"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "![](\"resources/question-resources/transformerCircuit.bmp\"/)
\n\nA {V1} / {V2} V, {S} VA, 50 Hz single-phase transformer gave the following test results:
\n\nOpen circuit test on LV side: $Ioc = \\var{Ioc}\\ A,\\ Poc = \\var{Poc}\\ W$
\nShort circuit test on HV side: $Vsc =\\var{Vsc}\\ V,\\ Psc = \\var{Psc} \\ W$
\n\nA {RL} $\\Omega$ load is connected to the LV side with rated voltage on the HV side.
\n\n\n", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"XM": {"name": "XM", "group": "Impedances", "definition": "(Ratio^2)*(V2/IMoc)", "description": "", "templateType": "anything", "can_override": false}, "V1": {"name": "V1", "group": "Ratings", "definition": "random(100 .. 1000#20)", "description": "Rated Voltage
", "templateType": "randrange", "can_override": false}, "RC": {"name": "RC", "group": "Impedances", "definition": "(Ratio^2)*(V2/ICoc)", "description": "", "templateType": "anything", "can_override": false}, "RW": {"name": "RW", "group": "Impedances", "definition": "Psc/(I1^2)", "description": "", "templateType": "anything", "can_override": false}, "XL": {"name": "XL", "group": "Impedances", "definition": "VXL/I1", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Ratings", "definition": "round(V1/ApproxRatio)", "description": "Phase Voltage
", "templateType": "anything", "can_override": false}, "Poc": {"name": "Poc", "group": "Measurements", "definition": "round(random(5..10)*S/100)", "description": "5-10% of rated power
", "templateType": "anything", "can_override": false}, "Psc": {"name": "Psc", "group": "Measurements", "definition": "round(random(5..10)*S/100)", "description": "5-10% of rated power
", "templateType": "anything", "can_override": false}, "ApproxRatio": {"name": "ApproxRatio", "group": "Ratings", "definition": "random(2 .. 44#2)", "description": "", "templateType": "randrange", "can_override": false}, "Vsc": {"name": "Vsc", "group": "Measurements", "definition": "round(sqrt(VW^2+VXL^2))", "description": "", "templateType": "anything", "can_override": false}, "Ioc": {"name": "Ioc", "group": "Measurements", "definition": "precround(sqrt(ICoc^2+IMoc^2),2)", "description": "", "templateType": "anything", "can_override": false}, "IL'": {"name": "IL'", "group": "Currents", "definition": "V1/(RW + XL*i + RL')", "description": "", "templateType": "anything", "can_override": false}, "IL": {"name": "IL", "group": "Currents", "definition": "Ratio*IL'", "description": "", "templateType": "anything", "can_override": false}, "S": {"name": "S", "group": "Ratings", "definition": "random(50 .. 1000#50)", "description": "", "templateType": "randrange", "can_override": false}, "I1": {"name": "I1", "group": "Ratings", "definition": "S/V1", "description": "", "templateType": "anything", "can_override": false}, "I2": {"name": "I2", "group": "Ratings", "definition": "S/V2", "description": "", "templateType": "anything", "can_override": false}, "RL": {"name": "RL", "group": "Impedances", "definition": "ceil(V2/I2)", "description": "", "templateType": "anything", "can_override": false}, "RL'": {"name": "RL'", "group": "Impedances", "definition": "Ratio^2*RL\n", "description": "", "templateType": "anything", "can_override": false}, "IC": {"name": "IC", "group": "Currents", "definition": "V1/RC", "description": "", "templateType": "anything", "can_override": false}, "IM": {"name": "IM", "group": "Currents", "definition": "V1/(XM*i)", "description": "", "templateType": "anything", "can_override": false}, "IS": {"name": "IS", "group": "Currents", "definition": "IC+IM+IL'", "description": "", "templateType": "anything", "can_override": false}, "IMoc": {"name": "IMoc", "group": "Ungrouped variables", "definition": "random(1..5)*ICoc", "description": "", "templateType": "anything", "can_override": false}, "ICoc": {"name": "ICoc", "group": "Ungrouped variables", "definition": "Poc/V2", "description": "", "templateType": "anything", "can_override": false}, "VW": {"name": "VW", "group": "Ungrouped variables", "definition": "I1*RW", "description": "", "templateType": "anything", "can_override": false}, "VXL": {"name": "VXL", "group": "Ungrouped variables", "definition": "random(1..5)*VW", "description": "", "templateType": "anything", "can_override": false}, "Ploss": {"name": "Ploss", "group": "Ungrouped variables", "definition": "Pc + Pw", "description": "", "templateType": "anything", "can_override": false}, "Pc": {"name": "Pc", "group": "Ungrouped variables", "definition": "V1^2/RC", "description": "", "templateType": "anything", "can_override": false}, "PW": {"name": "PW", "group": "Ungrouped variables", "definition": "abs(IL')^2*Rw", "description": "", "templateType": "anything", "can_override": false}, "efficiency": {"name": "efficiency", "group": "Ungrouped variables", "definition": "100*PL/PS", "description": "", "templateType": "anything", "can_override": false}, "PS": {"name": "PS", "group": "Ungrouped variables", "definition": "re(V1*conj(IS))", "description": "", "templateType": "anything", "can_override": false}, "PL": {"name": "PL", "group": "Ungrouped variables", "definition": "abs(IL)^2*RL", "description": "", "templateType": "anything", "can_override": false}, "Ratio": {"name": "Ratio", "group": "Ratings", "definition": "V1/V2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ICoc", "IMoc", "VW", "VXL", "Ploss", "Pc", "PW", "efficiency", "PS", "PL"], "variable_groups": [{"name": "Ratings", "variables": ["ApproxRatio", "V1", "V2", "Ratio", "S", "I1", "I2"]}, {"name": "Impedances", "variables": ["RC", "XM", "RW", "XL", "RL", "RL'"]}, {"name": "Measurements", "variables": ["Poc", "Psc", "Ioc", "Vsc"]}, {"name": "Currents", "variables": ["IL'", "IL", "IC", "IM", "IS"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Equivalent Circuit", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Find the approximate equivalent circuit for this transformer applied to the HV side.
\n$R_C = $ [[0]]$\\ k\\Omega $
\n$X_M = $ [[1]]$\\ k\\Omega $
\n$R_W = $ [[2]]$\\ \\Omega $
\n$X_L = $ [[3]]$\\ \\Omega $
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout.
\n- Use P to get R.
\n- Use Ohm's Law to get Z.
\n- Use circuit theory to get X.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Rc", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.95*(1/1000)*RC", "maxValue": "1.05*(1/1000)*RC", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Xm", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.95*(1/1000)*XM", "maxValue": "1.05*(1/1000)*XM", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Rw", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*RW", "maxValue": "1.01*RW", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Xl", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*XL", "maxValue": "1.01*XL", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Load Current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the current in the load:
\n$I_L = $[[0]]$\\angle \\ $[[1]]$^o $ A
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout.
\n- Transform the load to the HV side.
\n- Use Ohm's Law to get the current in this transformed load.
\n- Transform the current back to the LV side.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Magnitude", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(IL)", "maxValue": "1.01*abs(IL)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Angle", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*180*arg(IL)/pi", "maxValue": "1.01*180*arg(IL)/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Supply Current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the current drawn from the supply:
\n$I_S = $[[0]]$\\angle \\ $[[1]] $^o $ mA
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout.
\n- Use Ohm's Law to get the loss currents in RC and XM.
\n- Use Kirchhoff's Current Law to get the total current.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Magnitude", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.95*1000*abs(IS)", "maxValue": "1.05*1000*abs(IS)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Angle", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.95*180*arg(IS)/pi", "maxValue": "1.05*180*arg(IS)/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Efficiency", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the losses in the transformer:
\n$Ploss = $[[0]] W
\nWhat is the efficiency?
\n$\\eta = $[[1]] %
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout.
\n- Use Power Equations to get losses in $R_C$ and $R_W$. Add these to get total $Ploss$.
\n- Calculate input power $P_S$ and output power $P_L$ to get efficiency, $\\eta$.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ploss", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*Ploss", "maxValue": "1.01*Ploss", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Efficiency", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*efficiency", "maxValue": "1.01*efficiency", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Three Phase Delta", "extensions": [], "custom_part_types": [], "resources": [["question-resources/DeltaCircuit_NBsNnJk.png", "/srv/numbas/media/question-resources/DeltaCircuit_NBsNnJk.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "A balanced, three phase, {VLINE} V system is supplying a load connected in delta.
\n{image('resources/question-resources/DeltaCircuit_NBsNnJk.png')}
\n\nThe loads are:
\n$Z_1 = \\var{R1}+i\\ \\var{X1}\\ \\Omega $
\n$Z_2 = \\var{R2}+i\\ \\var{X2}\\ \\Omega $
\n$Z_3 = \\var{R3}+i\\ \\var{X3}\\ \\Omega $
\n\n\n", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"R3": {"name": "R3", "group": "Impedances", "definition": "random(0 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "R2": {"name": "R2", "group": "Impedances", "definition": "random(0 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "VLINE": {"name": "VLINE", "group": "Voltages", "definition": "random(50 .. 1000#50)", "description": "Rated Voltage
", "templateType": "randrange", "can_override": false}, "R1": {"name": "R1", "group": "Impedances", "definition": "random(0 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "X1": {"name": "X1", "group": "Impedances", "definition": "random(0 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "X2": {"name": "X2", "group": "Impedances", "definition": "random(0 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "X3": {"name": "X3", "group": "Impedances", "definition": "random(0 .. 100#5)", "description": "", "templateType": "randrange", "can_override": false}, "VPH": {"name": "VPH", "group": "Voltages", "definition": "VLINE/sqrt(3)", "description": "Phase Voltage
", "templateType": "anything", "can_override": false}, "IA": {"name": "IA", "group": "Currents", "definition": "I3-I2", "description": "Line Current
", "templateType": "anything", "can_override": false}, "IB": {"name": "IB", "group": "Currents", "definition": "I1-I3", "description": "Line Current
", "templateType": "anything", "can_override": false}, "IC": {"name": "IC", "group": "Currents", "definition": "I2-I1", "description": "Line Current
", "templateType": "anything", "can_override": false}, "I1": {"name": "I1", "group": "Currents", "definition": "VBC/(R1+X1*i)", "description": "Load Current
", "templateType": "anything", "can_override": false}, "I2": {"name": "I2", "group": "Currents", "definition": "VCA/(R2+X2*i)", "description": "Load Current
", "templateType": "anything", "can_override": false}, "I3": {"name": "I3", "group": "Currents", "definition": "VAB/(R3+X3*i)", "description": "Load Current
", "templateType": "anything", "can_override": false}, "PA": {"name": "PA", "group": "Power", "definition": "re(conj(IA)*VA)", "description": "", "templateType": "anything", "can_override": false}, "VBC": {"name": "VBC", "group": "Voltages", "definition": "VB-VC", "description": "", "templateType": "anything", "can_override": false}, "VCA": {"name": "VCA", "group": "Voltages", "definition": "VC-VA", "description": "", "templateType": "anything", "can_override": false}, "VAB": {"name": "VAB", "group": "Voltages", "definition": "VA-VB", "description": "", "templateType": "anything", "can_override": false}, "VA": {"name": "VA", "group": "Voltages", "definition": "VPH", "description": "", "templateType": "anything", "can_override": false}, "VB": {"name": "VB", "group": "Voltages", "definition": "VPH*(cos(-2*pi/3)+i*sin(-2*pi/3))", "description": "", "templateType": "anything", "can_override": false}, "VC": {"name": "VC", "group": "Voltages", "definition": "VPH*(cos(2*pi/3)+i*sin(2*pi/3))", "description": "", "templateType": "anything", "can_override": false}, "PB": {"name": "PB", "group": "Power", "definition": "re(conj(IB)*VB)", "description": "", "templateType": "anything", "can_override": false}, "PC": {"name": "PC", "group": "Power", "definition": "re(conj(IC)*VC)", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Power", "definition": "re(conj(I1)*VBC)", "description": "", "templateType": "anything", "can_override": false}, "P2": {"name": "P2", "group": "Power", "definition": "re(conj(I2)*VCA)", "description": "", "templateType": "anything", "can_override": false}, "P3": {"name": "P3", "group": "Power", "definition": "re(conj(I3)*VAB)", "description": "", "templateType": "anything", "can_override": false}, "PLine": {"name": "PLine", "group": "Power", "definition": "PA+PB+PC", "description": "", "templateType": "anything", "can_override": false}, "PLoad": {"name": "PLoad", "group": "Power", "definition": "P1+P2+P3", "description": "", "templateType": "anything", "can_override": false}, "I1angle": {"name": "I1angle", "group": "Currents", "definition": "180*arg(I1)/pi", "description": "", "templateType": "anything", "can_override": false}, "I2angle": {"name": "I2angle", "group": "Currents", "definition": "180*arg(I2)/pi", "description": "", "templateType": "anything", "can_override": false}, "I3angle": {"name": "I3angle", "group": "Currents", "definition": "180*arg(I3)/pi", "description": "", "templateType": "anything", "can_override": false}, "IAangle": {"name": "IAangle", "group": "Currents", "definition": "180*arg(IA)/pi", "description": "", "templateType": "anything", "can_override": false}, "IBangle": {"name": "IBangle", "group": "Currents", "definition": "180*arg(IB)/pi", "description": "", "templateType": "anything", "can_override": false}, "ICangle": {"name": "ICangle", "group": "Currents", "definition": "180*arg(IC)/pi", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Voltages", "variables": ["VLINE", "VPH", "VA", "VB", "VC", "VBC", "VCA", "VAB"]}, {"name": "Impedances", "variables": ["R1", "R2", "R3", "X1", "X2", "X3"]}, {"name": "Currents", "variables": ["I1", "I2", "I3", "IA", "IB", "IC", "I1angle", "I2angle", "I3angle", "IAangle", "IBangle", "ICangle"]}, {"name": "Power", "variables": ["PA", "PB", "PC", "P1", "P2", "P3", "PLine", "PLoad"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Load Currents", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Using $V_A$ as the reference voltage, calculate the currents in each load:
\n$I_1 = $[[0]]$\\angle$ [[1]]$^o$ A
\n$I_2 = $[[2]]$\\angle$ [[3]]$^o$ A
\n$I_3 = $[[4]]$\\angle$ [[5]]$^o$ A
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout.
\n- Use Ohm's Law.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Load Current 1 magnitude", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(I1)", "maxValue": "1.01*abs(I1)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Current 1 angle", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*I1angle", "maxValue": "1.01*I1angle", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Current 2 magnitude", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(I2)", "maxValue": "1.01*abs(I2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Current 2 angle", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*I2angle", "maxValue": "1.01*I2angle", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Current 3 magnitude", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(I3)", "maxValue": "1.01*abs(I3)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Current 3 angle", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*I3angle", "maxValue": "1.01*I3angle", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Supply Currents", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Determine the currents in each line:
\n$I_A = $[[0]]$\\angle$ [[1]]$^o$ A
\n$I_B = $[[2]]$\\angle$ [[3]]$^o$ A
\n$I_C = $[[4]]$\\angle$ [[5]]$^o$ A
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout.
\n- Use Kirchhoff's Current Law.
\n
"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Line Current A magnitude", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(IA)", "maxValue": "1.01*abs(IA)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Current A angle", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IAangle", "maxValue": "1.01*IAangle", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Current B magnitude", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(IB)", "maxValue": "1.01*abs(IB)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Current B angle", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*IBangle", "maxValue": "1.01*IBangle", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Current C magnitude", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(IC)", "maxValue": "1.01*abs(IC)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Current C angle", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*ICangle", "maxValue": "1.01*ICangle", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Supply Power", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Determine the real power flowing in each line:
\n$P_A = $[[0]]W
\n$P_B = $[[1]]W
\n$P_C = $[[2]]W
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "\n- Use Complex Numbers throughout (but the final answer is real).
\n- Real power is the real part of the voltage times the current.
\n
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\n$P_3 = $[[2]]W
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\n
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