// Numbas version: finer_feedback_settings
{"name": "DC Machines - Practice", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "40", "showQuestionGroupNames": false, "showstudentname": false, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", "", "", ""], "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": "<p>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 $\\var{IF}\\ A$.</p>\n<p>Its intrinsic resistances are:</p>\n<p>Field Resistance:&nbsp;$R_F = \\var{RF}\\ \\Omega&nbsp;$</p>\n<p>Armature Resistance:&nbsp;$R_A = \\var{RA}\\&nbsp; \\Omega&nbsp;$&nbsp;</p>\n<p>The machine is then connected as a series generator to supply a load with a current of&nbsp;$\\var{IF}\\ A$ when running at a speed of $\\var{N}\\ rpm$ .</p>", "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": "<p>What is the magnetism on the machine?</p>\n<p>$k_a \\phi = $ [[0]]</p>", "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": "<ul>\n<li>Convert the testing speed from $N$ in rpm to $\\omega$ in rad/s.</li>\n<li>Fill all testing values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$ at the given current.</li>\n</ul>"}], "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": "<p>What is the torque on the shaft?</p>\n<p>$T$ =&nbsp;[[0]] $ Nm $</p>", "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": "<ul>\n<li>Find the torque from $T=k_a\\phi I_A$.</li>\n</ul>"}], "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": "<p>What is the output voltage to the load?</p>\n<p>$V_L$&nbsp;=&nbsp;[[0]] $ V $</p>\n<p>What is the load resistance?</p>\n<p>$R_L$ =&nbsp;[[1]] $\\Omega$</p>", "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": "<ul>\n<li>Calcuate the voltage, $e_a$, from $e_a=k_a\\phi \\omega$.</li>\n<li>Find the output voltage from Kirchhoff's Voltage Law.</li>\n<li>Find the load resistance from Ohm's Law.</li>\n</ul>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Voltage", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "VL*0.95", "maxValue": "VL*1.05", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Resistance", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "RL*0.95", "maxValue": "RL*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": "<p>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:</p>\n<p></p>\n<table border=\"1\" height=\"167\" style=\"margin-left: auto; margin-right: auto; width: 1020px;\">\n<tbody>\n<tr>\n<td style=\"width: 90.5556px;\">\n<p><strong>Field Current</strong></p>\n<p><strong>IF [A]</strong></p>\n</td>\n<td style=\"text-align: center; width: 58.3333px;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center; width: 61.6667px;\">\n<p>0.1</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.2</p>\n</td>\n<td style=\"text-align: center; width: 71.6667px;\">\n<p>0.3</p>\n</td>\n<td style=\"text-align: center; width: 66.1111px;\">\n<p>0.4</p>\n</td>\n<td style=\"text-align: center; width: 66.1111px;\">\n<p>0.5</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.6</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.7</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.8</p>\n</td>\n<td style=\"text-align: center; width: 65px;\">\n<p>0.9</p>\n</td>\n<td style=\"text-align: center; width: 77.2222px;\">\n<p>1.0</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 90.5556px;\">\n<p><strong>Armature Voltage</strong></p>\n<p><strong>VA [V]</strong></p>\n</td>\n<td style=\"width: 58.3333px; text-align: center;\">{VA[0]}</td>\n<td style=\"width: 61.6667px; text-align: center;\">{VA[1]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[2]}</td>\n<td style=\"width: 71.6667px; text-align: center;\">{VA[3]}</td>\n<td style=\"width: 66.1111px; text-align: center;\">{VA[4]}</td>\n<td style=\"width: 66.1111px; text-align: center;\">{VA[5]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[6]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[7]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[8]}</td>\n<td style=\"width: 65px; text-align: center;\">{VA[9]}</td>\n<td style=\"width: 77.2222px; text-align: center;\">{VA[10]}</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>\n<p>The&nbsp;intrinsic resistances are:</p>\n<p>Field Resistance:&nbsp;$R_F = \\var{RF}\\ \\Omega&nbsp;$</p>\n<p>Armature Resistance:&nbsp;$R_A = \\var{RA}\\&nbsp; \\Omega&nbsp;$&nbsp;</p>\n<p>The machine is then connected as a shunt generator to supply $\\var{VL}\\ V$ to a $\\var{RL}\\ \\Omega$ load.</p>", "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 .. 60#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(VA[8]/IF)", "description": "", "templateType": "anything", "can_override": false}, "RA": {"name": "RA", "group": "Test Data", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "VL": {"name": "VL", "group": "Operation", "definition": "round(RF*IF)", "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": "60*omega/(2*pi)", "description": "", "templateType": "anything", "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": "ea/magnetism", "description": "", "templateType": "anything", "can_override": false}, "IA": {"name": "IA", "group": "Operation", "definition": "IL+IF", "description": "", "templateType": "anything", "can_override": false}, "ea": {"name": "ea", "group": "Operation", "definition": "VL+(IA*RA)", "description": "", "templateType": "anything", "can_override": false}, "IL": {"name": "IL", "group": "Operation", "definition": "VL/RL", "description": "", "templateType": "anything", "can_override": false}, "RL": {"name": "RL", "group": "Operation", "definition": "random(10 .. 100#10)", "description": "", "templateType": "randrange", "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", "RL", "VL", "IL", "magnetism", "IA", "ea", "omega", "N"]}], "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": "<p>What is the magnetism on the machine?</p>\n<p>$k_a \\phi = $ [[0]]</p>", "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": "<ul>\n<li>Find the field current, $I_F$, using Ohm's Law.</li>\n<li>Find the speed and voltage during testing from the data at this field current.</li>\n<li>Convert the speed from $N$ in rpm to $\\omega$ in rad/s.</li>\n<li>Fill these values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$.</li>\n</ul>"}], "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": "<p>How much current is it flowing in the armature conductors?</p>\n<p>$I_A$ =&nbsp;[[0]] $ A $</p>", "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": "<ul>\n<li>Calcuate the field current, $I_F$, as before using Ohm's Law.</li>\n<li>Calcuate the load current, $I_L$, using Ohm's Law.</li>\n<li>Get the armature current from Kirchhoff's Current Law.</li>\n</ul>"}], "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": "<p>At what speed is it running?</p>\n<p>N =&nbsp;[[0]] $ rpm $</p>", "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": "<ul>\n<li>Calcuate the voltage, $e_a$, from Kirchhoff's Voltage Law.</li>\n<li>Find the&nbsp;speed from $e_a=k_a\\phi \\omega$.</li>\n<li>Convert this to rpm.</li>\n</ul>"}], "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": "<p>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:</p>\n<p></p>\n<table border=\"1\" height=\"167\" style=\"margin-left: auto; margin-right: auto; width: 1020px;\">\n<tbody>\n<tr>\n<td style=\"width: 90.5556px;\">\n<p><strong>Field Current</strong></p>\n<p><strong>IF [A]</strong></p>\n</td>\n<td style=\"text-align: center; width: 58.3333px;\">\n<p>0</p>\n</td>\n<td style=\"text-align: center; width: 61.6667px;\">\n<p>0.1</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.2</p>\n</td>\n<td style=\"text-align: center; width: 71.6667px;\">\n<p>0.3</p>\n</td>\n<td style=\"text-align: center; width: 66.1111px;\">\n<p>0.4</p>\n</td>\n<td style=\"text-align: center; width: 66.1111px;\">\n<p>0.5</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.6</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.7</p>\n</td>\n<td style=\"text-align: center; width: 67.2222px;\">\n<p>0.8</p>\n</td>\n<td style=\"text-align: center; width: 65px;\">\n<p>0.9</p>\n</td>\n<td style=\"text-align: center; width: 77.2222px;\">\n<p>1.0</p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 90.5556px;\">\n<p><strong>Armature Voltage</strong></p>\n<p><strong>VA [V]</strong></p>\n</td>\n<td style=\"width: 58.3333px; text-align: center;\">{VA[0]}</td>\n<td style=\"width: 61.6667px; text-align: center;\">{VA[1]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[2]}</td>\n<td style=\"width: 71.6667px; text-align: center;\">{VA[3]}</td>\n<td style=\"width: 66.1111px; text-align: center;\">{VA[4]}</td>\n<td style=\"width: 66.1111px; text-align: center;\">{VA[5]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[6]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[7]}</td>\n<td style=\"width: 67.2222px; text-align: center;\">{VA[8]}</td>\n<td style=\"width: 65px; text-align: center;\">{VA[9]}</td>\n<td style=\"width: 77.2222px; text-align: center;\">{VA[10]}</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"></p>\n<p>The&nbsp;intrinsic resistances are:</p>\n<p>Field Resistance:&nbsp;$R_F = \\var{RF}\\ \\Omega&nbsp;$</p>\n<p>Armature Resistance:&nbsp;$R_A = \\var{RA}\\&nbsp; \\Omega&nbsp;$&nbsp;</p>\n<p>The machine is then connected as a shunt motor to a&nbsp;supply providing $\\var{VS}\\ V$.&nbsp;The motor is used to lift a weight which creates a torque of $\\var{T}\\ Nm$.</p>", "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": "<p>What is the magnetism on the machine?</p>\n<p>$k_a \\phi = $ [[0]]</p>", "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": "<ul>\n<li>Find the field current, $I_F$, using Ohm's Law.</li>\n<li>Find the speed and voltage during testing from the data at this field current.</li>\n<li>Convert the speed from $N$ in rpm to $\\omega$ in rad/s.</li>\n<li>Fill these values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$.</li>\n</ul>"}], "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": "<p>How much current is it drawing from the supply?</p>\n<p>$I_S$ =&nbsp;[[0]] $ A $</p>", "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": "<ul>\n<li>Calcuate the field current, $I_F$, as before using Ohm's Law.</li>\n<li>Find the armature current from $T=k_a\\phi I_A$.</li>\n<li>Get the supply current from Kirchhoff's Current Law.</li>\n</ul>"}], "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": "IS*0.95", "maxValue": "IS*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": "<p>At what speed is it running?</p>\n<p>N =&nbsp;[[0]] $ rpm $</p>", "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": "<ul>\n<li>Calcuate the voltage, $e_a$, from Kirchhoff's Voltage Law.</li>\n<li>Find the&nbsp;speed from $e_a=k_a\\phi \\omega$.</li>\n<li>Convert this to rpm.</li>\n</ul>"}], "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 Series 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": "<p>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 $\\var{IF}\\ A$.</p>\n<p>Its intrinsic resistances are:</p>\n<p>Field Resistance:&nbsp;$R_F = \\var{RF}\\ \\Omega&nbsp;$</p>\n<p>Armature Resistance:&nbsp;$R_A = \\var{RA}\\&nbsp; \\Omega&nbsp;$&nbsp;</p>\n<p>The machine is then connected as a series motor to a&nbsp;supply providing $\\var{VS}\\ V$.&nbsp;It is found to draw the same current of&nbsp;$\\var{IF}\\ A$.</p>", "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": "Test Data", "definition": "random(10 .. 50#5)", "description": "", "templateType": "randrange", "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+IF*(RA+RF))", "description": "", "templateType": "anything", "can_override": false}, "IF": {"name": "IF", "group": "Test Data", "definition": "random(1 .. 10#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": "Vtest/(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": "magnetism*IF", "description": "", "templateType": "anything", "can_override": false}, "ea": {"name": "ea", "group": "Operation", "definition": "magnetism*omega", "description": "", "templateType": "anything", "can_override": false}, "Vtest": {"name": "Vtest", "group": "Test Data", "definition": "random(100 .. 500#50)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "VS > 0", "maxRuns": "1000"}, "ungrouped_variables": [], "variable_groups": [{"name": "Test Data", "variables": ["Ntest", "Vtest", "IF", "RF", "RA"]}, {"name": "Operation", "variables": ["magnetism", "VS", "T", "ea", "omega", "N"]}], "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": "<p>What is the magnetism on the machine?</p>\n<p>$k_a \\phi = $ [[0]]</p>", "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": "<ul>\n<li>Convert the testing speed from $N$ in rpm to $\\omega$ in rad/s.</li>\n<li>Fill all testing values into $e_a=k_a\\phi\\omega$ to get the magnetism, $k_a\\phi$ at the given current.</li>\n</ul>"}], "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": "<p>What is the torque on the motor?</p>\n<p>$T$ =&nbsp;[[0]] $ Nm $</p>", "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": "<ul>\n<li>Find the torque from $T=k_a\\phi I_A$.</li>\n</ul>"}], "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": "<p>At what speed is it running?</p>\n<p>N =&nbsp;[[0]] $ rpm $</p>", "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": "<ul>\n<li>Calcuate the voltage, $e_a$, from Kirchhoff's Voltage Law.</li>\n<li>Find the&nbsp;speed from $e_a=k_a\\phi \\omega$.</li>\n<li>Convert this to rpm.</li>\n</ul>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Speed", "marks": "15", "scripts": {}, 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