// Numbas version: finer_feedback_settings
{"name": "motors and generators", "metadata": {"description": "", "licence": "None specified"}, "duration": 5400, "percentPass": "40", "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "DC Shunt motor", "extensions": [], "custom_part_types": [], "resources": [["question-resources/DC_Shunt.png", "/srv/numbas/media/question-resources/DC_Shunt.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Doyle", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1649/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A DC shunt motor has an armature circuit resistance (R<sub>a</sub>) of $\\var c$&Omega; and a shunt field resistance (R<sub>f</sub>) of $\\var d$&Omega;. The motor is connected to a $\\var V$V supply. On no-load the input current is $\\var f$A at a speed of $\\var N$rpm. On full-load the the input current is $\\var g$A. Calculate the back emf (E) generated and the speed of the motor at full-load.</p>\n<p><img src=\"resources/question-resources/DC_Shunt.png\" width=\"283\" height=\"147\"/></p>", "advice": "", "rulesets": {}, "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(0.3 .. 0.7#0.05)", "description": "<p>Ra</p>", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(100 .. 300#1)", "description": "<p>Rf</p>", "templateType": "randrange"}, "V": {"name": "V", "group": "Ungrouped variables", "definition": "random(200 .. 250#10)", "description": "", "templateType": "randrange"}, "N": {"name": "N", "group": "Ungrouped variables", "definition": "random(1200 .. 1800#60)", "description": "", "templateType": "randrange"}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "N/60", "description": "", "templateType": "anything"}, "If": {"name": "If", "group": "Ungrouped variables", "definition": "V/d", 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"originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>At no-load&nbsp;</p>\n<p>Rotor speed (n) =&nbsp;[[0]]rps</p>\n<p>Field Current (I<sub>f</sub>) =&nbsp;[[1]]A</p>\n<p>Armature current (Ia) =&nbsp;[[2]]A</p>\n<p>Back emf (E) =&nbsp;[[3]]V</p>\n<p>Constant (k&phi;) =&nbsp;[[4]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "n1*a", "maxValue": "n1*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], 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[], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Ia1*a", "maxValue": "Ia1*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "E1*a", "maxValue": "E1*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k*a", "maxValue": "k*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>At full load</p>\n<p>Armature current (I<sub>a</sub>) =&nbsp;[[0]]A</p>\n<p>Back emf (E) =&nbsp;[[1]]V</p>\n<p>Rotor speed (n) =&nbsp;[[2]]rps</p>\n<p>Rotor speed (N) =&nbsp;[[3]]rpm</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Ia2*a", "maxValue": "Ia2*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "E2*a", "maxValue": "E2*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "n2*a", "maxValue": "n2*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N3*a", "maxValue": "N3*b", "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 Motor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Doyle", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1649/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A $\\var a$V, $\\var b$-pole, $\\var c$Hz, 3-phase, $\\var d$HP, star connected induction motor has a no load slip of $\\var f$% and a full load slip of $\\var g$%. Find the following</p>\n<ul>\n<li>Synchronous speed</li>\n<li>No-load speed</li>\n<li>Full-load speed</li>\n<li>Frequency of rotor current at full load</li>\n<li>Full load torque</li>\n</ul>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(400 .. 440#1)", "description": "<p>V</p>", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2 .. 8#2)", "description": "<p>p</p>", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(50 .. 60#10)", "description": "<p>f</p>", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(5 .. 12#0.5)", "description": "<p>HP</p>", "templateType": "randrange"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(0.8 .. 2#0.1)", "description": "<p>Sol</p>", "templateType": "randrange"}, "g": {"name": "g", "group": 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"ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>Synchronous speed = [[0]]rpm</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "h*0.99", "maxValue": "h*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>No load speed =[[0]]rpm</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "j*0.99", "maxValue": "j*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>Full load speed = [[0]]rpm</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k*0.99", "maxValue": "k*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>Rotor current frequency = [[0]]Hz</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "l*0.99", "maxValue": "l*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>Motor kW= [[0]]kW</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "m*0.99", "maxValue": "m*1.01", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>Full load Torque=[[0]]Nm</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "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 Generator", "extensions": [], "custom_part_types": [], "resources": [["question-resources/DC_generator.png", "/srv/numbas/media/question-resources/DC_generator.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "David Doyle", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1649/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A DC shunt generator supplies a $\\var a$kW load at $\\var b$V through cables of resistance, R= $\\var c$m&Omega;. If the field winding resistance, Rf =$\\var f$&Omega; and the armature resistance, Ra =$\\var d$m&Omega;, determine</p>\n<ul>\n<li>the terminal voltage,</li>\n<li>the e.m.f. generated in the armature.</li>\n</ul>\n<p><img src=\"resources/question-resources/DC_generator.png\" width=\"353\" height=\"196\"/></p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(12 .. 20#0.1)", "description": "<p>Power</p>", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(200 .. 240#1)", "description": "<p>Vload</p>", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(80 .. 200#1)", "description": "<p>R</p>", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(30 .. 50#1)", "description": "<p>Ra</p>", "templateType": "randrange"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(40 .. 60#1)", "description": "<p>Rf</p>", "templateType": "randrange"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(a*1000)/b", "description": "<p>Iload</p>", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "g*c/1000\n", "description": "<p>Vdrop</p>", "templateType": "anything"}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "b+h", "description": "<p>Vt</p>", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "j/f", "description": "<p>If</p>", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "g+k", "description": "<p>Ia</p>", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "j+(l*d/1000)", "description": "<p>E</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", 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An additional synchronous motor is added having an input power of $\\var c$kW and a maximum power factor of $\\var d$leading. 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