// Numbas version: exam_results_page_options
{"name": "Electrical Energy Systems Exam", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "40", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": false, "question_groups": [{"name": "DC", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"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": {}, "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"}, {"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"}, {"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"}]}, {"name": "Transformers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Transformers", "extensions": [], "custom_part_types": [], "resources": [["question-resources/tranny.svg", "/srv/numbas/media/question-resources/tranny.svg"]], "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": "<p><img src=\"resources/question-resources/tranny.svg\"/></p>\n<p>A&nbsp; {V1} / {V2} V, {S} VA, 50 Hz single-phase transformer gave the following test results:</p>\n<p></p>\n<p>Open circuit test on LV side:&nbsp; $Ioc = \\var{Ioc}\\ A,\\ Poc =&nbsp;\\var{Poc}\\&nbsp;W$</p>\n<p>Short circuit test on HV side:&nbsp;$Vsc =\\var{Vsc}\\ V,\\ Psc =&nbsp;\\var{Psc} \\ W$</p>\n<p></p>\n<p>A {RL} $\\Omega$ resistive load is connected to the LV side with rated voltage on the HV side.</p>\n<p></p>", "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": "<p>Rated Voltage</p>", "templateType": "randrange", "can_override": false}, "RC": {"name": "RC", "group": "Impedances", "definition": "(Ratio^2)*(V2^2/Poc)", "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": "sqrt(Zsc^2-RW^2)", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Ratings", "definition": "round(random(5..50)*V1/100)", "description": "<p>Phase Voltage</p>", "templateType": "anything", "can_override": false}, "Poc": {"name": "Poc", "group": "Measurements", "definition": "round(random(50..90)*(Ioc*V2)/100)", "description": "<p>50-90% of total power</p>", "templateType": "anything", "can_override": false}, "Psc": {"name": "Psc", "group": "Measurements", "definition": "round(random(50..90)*(Vsc*I1)/100)", "description": "<p>50-90% of total power</p>", "templateType": "anything", "can_override": false}, "Vsc": {"name": "Vsc", "group": "Measurements", "definition": "round(random(10..20)*V1/100)", "description": "<p>5-10% of rated voltage</p>", "templateType": "anything", "can_override": false}, "Ioc": {"name": "Ioc", "group": "Measurements", "definition": "precround(random(10..20)*I2/100,2)", "description": "<p>5-10% of rated current</p>", "templateType": "anything", "can_override": false}, "ILHV": {"name": "ILHV", "group": "Currents", "definition": "V1/(RW + XL*i + RL')", "description": "", "templateType": "anything", "can_override": false}, "IL": {"name": "IL", "group": "Currents", "definition": "Ratio*ILHV", "description": "", "templateType": "anything", "can_override": false}, "S": {"name": "S", "group": "Ratings", "definition": "random(200 .. 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", "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+ILHV", "description": "", "templateType": "anything", "can_override": false}, "IMoc": {"name": "IMoc", "group": "Ungrouped variables", "definition": "sqrt(Ioc^2-ICoc^2)", "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(ILHV)^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}, "Zsc": {"name": "Zsc", "group": "Impedances", "definition": "Vsc/I1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "Ioc > 0", "maxRuns": 100}, "ungrouped_variables": ["ICoc", "IMoc", "VW", "VXL", "Ploss", "Pc", "PW", "efficiency", "PS", "PL"], "variable_groups": [{"name": "Ratings", "variables": ["V1", "V2", "S", "I1", "I2", "Ratio"]}, {"name": "Impedances", "variables": ["RL", "RC", "XM", "RW", "XL", "RL'", "Zsc"]}, {"name": "Measurements", "variables": ["Ioc", "Vsc", "Poc", "Psc"]}, {"name": "Currents", "variables": ["ILHV", "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": "<p>Find the approximate equivalent circuit for this transformer applied to the HV side.&nbsp;&nbsp;</p>\n<p>$R_C&nbsp; = $&nbsp;[[0]]$\\&nbsp; k\\Omega $</p>\n<p>$X_M = $ [[1]]$\\ k\\Omega $</p>\n<p>$R_W = $ [[2]]$\\ \\Omega $</p>\n<p>$X_L&nbsp; = $ [[3]]$\\ \\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>Use Complex Numbers throughout.</li>\n<li>Use P to get R.</li>\n<li>Use Ohm's Law to get Z.</li>\n<li>Use circuit theory to get X.</li>\n</ul>"}], "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": "0.99*(1/1000)*RC", "maxValue": "1.09*(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": "0.99*(1/1000)*XM", "maxValue": "1.01*(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": "<p>Calculate the current in the load:</p>\n<p>$I_L = $[[0]]$\\angle \\ $[[1]]$^o $ 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>Use Complex Numbers throughout.</li>\n<li>Transform the load to the HV side.</li>\n<li>Use Ohm's Law to get the current in this transformed load.</li>\n<li>Transform the current back to the LV side.</li>\n</ul>"}], "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": "<p>Calculate the current drawn from the supply:</p>\n<p>$I_S = $[[0]]$\\angle \\ $[[1]]&nbsp;$^o&nbsp;$ &nbsp;mA</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>Use Complex Numbers throughout.</li>\n<li>Use Ohm's Law to get the loss currents in RC and XM.</li>\n<li>Use Kirchhoff's Current Law to get the&nbsp;total current.</li>\n</ul>"}], "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*1000*abs(IS)", "maxValue": "1.01*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": "0.99*180*arg(IS)/pi", "maxValue": "1.01*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": "<p>Calculate the losses in the transformer:</p>\n<p>$Ploss = $[[0]]&nbsp;&nbsp;W</p>\n<p>What is the efficiency?</p>\n<p>$\\eta = $[[1]]&nbsp; %</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>Use Complex Numbers throughout.</li>\n<li>Use Power Equations to get losses in $R_C$ and $R_W$. Add these to get total $Ploss$.</li>\n<li>Calculate input power $P_S$ and output power $P_L$ to get efficiency, $\\eta$.</li>\n</ul>"}], "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"}]}, {"name": "Three Phase", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"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": "<p>A balanced, three phase, {VLINE} V system is supplying a load connected in delta.</p>\n<p>{image('resources/question-resources/DeltaCircuit_NBsNnJk.png')}</p>\n<p></p>\n<p>The loads are:</p>\n<p>$Z_1 = \\var{R1}+i\\&nbsp; \\var{X1}\\ \\Omega $</p>\n<p>$Z_2 = \\var{R2}+i\\&nbsp; \\var{X2}\\ \\Omega $&nbsp;</p>\n<p>$Z_3 = \\var{R3}+i\\ \\var{X3}\\ \\Omega $</p>\n<p></p>\n<p></p>\n<p></p>", "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": "<p>Rated Voltage</p>", "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": "<p>Phase Voltage</p>", "templateType": "anything", "can_override": false}, "IA": {"name": "IA", "group": "Currents", "definition": "I3-I2", "description": "<p>Line&nbsp;Current</p>", "templateType": "anything", "can_override": false}, "IB": {"name": "IB", "group": "Currents", "definition": "I1-I3", "description": "<p>Line&nbsp;Current</p>", "templateType": "anything", "can_override": false}, "IC": {"name": "IC", "group": "Currents", "definition": "I2-I1", "description": "<p>Line&nbsp;Current</p>", "templateType": "anything", "can_override": false}, "I1": {"name": "I1", "group": "Currents", "definition": "VBC/(R1+X1*i)", "description": "<p>Load Current</p>", "templateType": "anything", "can_override": false}, "I2": {"name": "I2", "group": "Currents", "definition": "VCA/(R2+X2*i)", "description": "<p>Load Current</p>", "templateType": "anything", "can_override": false}, "I3": {"name": "I3", "group": "Currents", "definition": "VAB/(R3+X3*i)", "description": "<p>Load Current</p>", "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": "<p>Using $V_A$ as the reference voltage, calculate the currents in each load:</p>\n<p>$I_1 = $[[0]]$\\angle$ [[1]]$^o$ A</p>\n<p>$I_2 = $[[2]]$\\angle$ [[3]]$^o$ A</p>\n<p>$I_3 = $[[4]]$\\angle$ [[5]]$^o$ 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>Use Complex Numbers throughout.</li>\n<li>Use Ohm's Law.</li>\n</ul>"}], "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": "<p>Determine the currents in each line:</p>\n<p>$I_A = $[[0]]$\\angle$ [[1]]$^o$ A</p>\n<p>$I_B = $[[2]]$\\angle$ [[3]]$^o$ A</p>\n<p>$I_C = $[[4]]$\\angle$ [[5]]$^o$ 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>Use Complex Numbers throughout.</li>\n<li>Use&nbsp;Kirchhoff's Current Law.</li>\n</ul>"}], "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": "<p>Determine the real power flowing in each line:</p>\n<p>$P_A = $[[0]]W</p>\n<p>$P_B = $[[1]]W</p>\n<p>$P_C = $[[2]]W</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>Use Complex Numbers throughout (but the final answer is real).</li>\n<li>Real power is the real part of the voltage times the current.</li>\n</ul>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Line Power A", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*PA", "maxValue": "1.01*PA", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Power B", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*PB", "maxValue": "1.01*PB", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Line Power C", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*PC", "maxValue": "1.01*PC", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Load Power", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Determine the real power flowing in each load:</p>\n<p>$P_1 = $[[0]]W</p>\n<p>$P_2 = $[[1]]W</p>\n<p>$P_3 = $[[2]]W</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>Use Complex Numbers throughout (but the final answer is real).</li>\n<li>Real load power is used only in resistances.</li>\n</ul>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Load Power 1", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*P1", "maxValue": "1.01*P1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Power 2", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*P2", "maxValue": "1.01*P2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Load Power 3", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*P3", "maxValue": "1.01*P3", "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"}, {"name": "Three Phase Impedance", "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": "All rights reserved"}, "statement": "<p>A balanced, three-phase, $ \\var{VLINE} V $ system is supplying a balanced load connected in delta. A three-phase wattmeter (measuring total three-phase power) is connected to the supply and an ammeter is connected to one of the supply phases. Each load consists of a resistance in parallel with an inductive reactance.</p>\n<p></p>\n<p></p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"VLINE": {"name": "VLINE", "group": "Voltages", "definition": "random(50 .. 1000#50)", "description": "<p>Rated Voltage</p>", "templateType": "randrange", "can_override": false}, "W": {"name": "W", "group": "Power", "definition": "3*P", "description": "<p>Wattmeter reading</p>", "templateType": "anything", "can_override": false}, "P": {"name": "P", "group": "Power", "definition": "precround(0.1*random(1..10)*vph*A/1000,1)", "description": "<p>Power per phase in kW</p>", "templateType": "anything", "can_override": false}, "VPH": {"name": "VPH", "group": "Voltages", "definition": "VLINE/sqrt(3)", "description": "<p>Phase Voltage</p>", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Currents", "definition": "random(10 .. 50#5)", "description": "<p>Ammeter Reading</p>", "templateType": "randrange", "can_override": false}, "ILoad": {"name": "ILoad", "group": "Currents", "definition": "A/sqrt(3)", "description": "<p>Delta Current</p>", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Impedances", "definition": "Vline^2/(P*1000)", "description": "", "templateType": "anything", "can_override": false}, "Z": {"name": "Z", "group": "Impedances", "definition": "Vline/Iload", "description": "", "templateType": "anything", "can_override": false}, "X": {"name": "X", "group": "Impedances", "definition": "Vline/IX", "description": "", "templateType": "anything", "can_override": false}, "ps": {"name": "ps", "group": "Ungrouped variables", "definition": "3*Vph^2/(R*1000)", "description": "", "templateType": "anything", "can_override": false}, "is": {"name": "is", "group": "Ungrouped variables", "definition": "sqrt((vph/r)^2 + (vph/X)^2)", "description": "", "templateType": "anything", "can_override": false}, "IR": {"name": "IR", "group": "Currents", "definition": "Vline/R", "description": "", "templateType": "anything", "can_override": false}, "IX": {"name": "IX", "group": "Currents", "definition": "sqrt(ILoad^2-IR^2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "is = A/3", "maxRuns": 100}, "ungrouped_variables": ["ps", "is"], "variable_groups": [{"name": "Voltages", "variables": ["VLINE", "VPH"]}, {"name": "Power", "variables": ["P", "W"]}, {"name": "Currents", "variables": ["A", "ILoad", "IR", "IX"]}, {"name": "Impedances", "variables": ["R", "Z", "X"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Wattmeter", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the wattmeter reads $\\var{W} kW$, what is the resistance of each load?</p>\n<p>$R = $[[0]] $\\Omega $</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "R", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*R", "maxValue": "1.01*R", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Ammeter", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If the ammeter reads $\\var{A} A $ What is the impedance of each load?</p>\n<p>$Z = $ [[0]] $\\Omega$</p>\n<p>What is the reactance?</p>\n<p>$X = $ [[1]] $\\Omega$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Z", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*Z", "maxValue": "1.01*Z", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "X", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*X", "maxValue": "1.01*X", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Star", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If this load was instead connected in star, what would the new readings be? Verify your answer.</p>\n<p>$P = $[[0]] $kW$</p>\n<p>$I = $[[1]] $A$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Wattmeter", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*PS", "maxValue": "1.01*PS", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Ammeter", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(IS)", "maxValue": "1.01*abs(IS)", "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"}, {"name": "Three Phase Balanced", "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": "All rights reserved"}, "statement": "<p>A balanced, three-phase, four-wire, $ \\var{VLINE} V $ system is supplying a balanced load connected in star with $Z = \\var{R}+i\\&nbsp; \\var{X}\\ \\Omega $&nbsp; per phase. A three-phase wattmeter (measuring total three-phase power) is connected to the supply and an ammeter is connected to one of the phases.</p>\n<p></p>\n<p></p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"VLINE": {"name": "VLINE", "group": "Voltages", "definition": "random(200 .. 1000#50)", "description": "<p>Rated Voltage</p>", "templateType": "randrange", "can_override": false}, "R": {"name": "R", "group": "Impedances", "definition": "random(10 .. 80#5)", "description": "", "templateType": "randrange", "can_override": false}, "X": {"name": "X", "group": "Impedances", "definition": "random(10 .. 80#5)", "description": "", "templateType": "randrange", "can_override": false}, "VPH": {"name": "VPH", "group": "Voltages", "definition": "VLINE/sqrt(3)", "description": "<p>Phase Voltage</p>", "templateType": "anything", "can_override": false}, "IS": {"name": "IS", "group": "Currents", "definition": "VPH/(R+X*i)", "description": "<p>Star Current</p>", "templateType": "anything", "can_override": false}, "IDLoad": {"name": "IDLoad", "group": "Currents", "definition": "VLINE/(R+X*i)", "description": "<p>Delta Current</p>", "templateType": "anything", "can_override": false}, "PS": {"name": "PS", "group": "Power", "definition": "3*abs(IS)^2*R/1000", "description": "", "templateType": "anything", "can_override": false}, "PD": {"name": "PD", "group": "Power", "definition": "3*abs(IDLoad)^2*R/1000", "description": "", "templateType": "anything", "can_override": false}, "ID": {"name": "ID", "group": "Currents", "definition": "sqrt(3)*IDload", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Voltages", "variables": ["VLINE", "VPH"]}, {"name": "Impedances", "variables": ["R", "X"]}, {"name": "Currents", "variables": ["IS", "IDLoad", "ID"]}, {"name": "Power", "variables": ["PS", "PD"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Ammeter", "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 reading on the ammeter?</p>\n<p>$I = $[[0]] $A$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "IS", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(IS)", "maxValue": "1.01*abs(IS)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Wattmeter", "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 reading on the wattmeter?</p>\n<p>$P = $[[0]] $kW$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "PS", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*PS", "maxValue": "1.01*PS", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Delta", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If this load was instead connected in delta, what would the new readings be? Verify your answer.</p>\n<p>$P = $[[0]] $kW$</p>\n<p>$I = $[[1]] $A$</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Wattmeter", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*PD", "maxValue": "1.01*PD", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Ammeter", "marks": "5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*abs(ID)", "maxValue": "1.01*abs(ID)", "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"}]}, {"name": "Power Systems Studies", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Power Systems Studies", "extensions": [], "custom_part_types": [], "resources": [["question-resources/PSScircuit.png", "/srv/numbas/media/question-resources/PSScircuit.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": "None specified"}, "statement": "<p style=\"text-align: center;\">In the system shown in <strong>Figure 1</strong>, the transformers&nbsp;are connected star-star with both star points grounded and the generator is connected in star with&nbsp;its star points grounded. The per unit&nbsp;impedances of each element on a {SBASE} MVA base are given in <strong>Table 1</strong>&nbsp;and the&nbsp;voltage levels are given in&nbsp;<strong>Table 2</strong>.</p>\n<p style=\"text-align: center;\">{image('resources/question-resources/PSScircuit.png')}</p>\n<p style=\"text-align: center;\"><strong><em>Figure 1: A section of the distribution system</em></strong></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto;\" width=\"786\" height=\"79\">\n<tbody>\n<tr>\n<td style=\"text-align: center; width: 139px;\">\n<p>&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 140px;\">\n<p><strong>Generator</strong></p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p><strong>Transformer T1</strong></p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p style=\"text-align: center;\"><strong>Line</strong></p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p style=\"text-align: center;\"><strong>Transformer T2</strong></p>\n</td>\n</tr>\n<tr>\n<td style=\"text-align: center; width: 139px;\">\n<p><strong>Z&nbsp; &nbsp;[p.u.]</strong></p>\n</td>\n<td style=\"text-align: center; width: 140px;\">\n<p>{RG} + j {XG}&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p>{RT1} + j {XT1}&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p>{RL} + j {XL}&nbsp;</p>\n</td>\n<td style=\"text-align: center; width: 142px;\">\n<p>{RT2} + j {XT2}&nbsp;</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong></strong></em><em><strong>&nbsp;Table 1: Sequence impedances (p.u. on {SBASE} MVA base)</strong></em></p>\n<p style=\"text-align: center;\"><em><strong></strong></em></p>\n<table border=\"1\" cellpadding=\"1\" style=\"margin-left: auto; margin-right: auto; width: 486px;\" height=\"122\">\n<tbody>\n<tr style=\"height: 44px;\">\n<td style=\"height: 44px; width: 115.5px;\">\n<p>&nbsp;</p>\n</td>\n<td style=\"height: 44px; text-align: center; width: 116.5px;\">\n<p><strong>Generator</strong></p>\n</td>\n<td style=\"height: 44px; text-align: center; width: 93px;\">\n<p><strong>Line</strong></p>\n</td>\n<td style=\"height: 44px; text-align: center; width: 96px;\">\n<p><strong>Load</strong></p>\n</td>\n</tr>\n<tr style=\"height: 52.2118px;\">\n<td style=\"height: 52.2118px; width: 115.5px;\">\n<p><strong>V&nbsp;<sub>BASE</sub></strong>&nbsp;&nbsp;<strong>[kV]</strong></p>\n</td>\n<td style=\"height: 52.2118px; text-align: center; width: 116.5px;\">\n<p>{VG}</p>\n</td>\n<td style=\"width: 93px; text-align: center;\">\n<p>{VLine}</p>\n</td>\n<td style=\"width: 96px; text-align: center;\">\n<p>{VLoad}</p>\n</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: center;\"><em><strong>Table 2: Voltage bases&nbsp;</strong></em><strong>(kV)</strong></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"XG": {"name": "XG", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "XL": {"name": "XL", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "XT1": {"name": "XT1", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.2#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "SBASE": {"name": "SBASE", "group": "Ungrouped variables", "definition": "random(10 .. 100#10)", "description": "", "templateType": "randrange", "can_override": false}, "IkA": {"name": "IkA", "group": "Calculated", "definition": "precround(Ipu*IBASE,3)", "description": "", "templateType": "anything", "can_override": false}, "XT2": {"name": "XT2", "group": "Ungrouped variables", "definition": "random(0.05 .. 0.1#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "V1": {"name": "V1", "group": "Calculated", "definition": "1-(RG+i*XG)*IL", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Calculated", "definition": "V1-(RT1+i*XT1)*IL", "description": "", "templateType": "anything", "can_override": false}, "V3": {"name": "V3", "group": "Calculated", "definition": "V2-(RL+i*XL)*IL", "description": "", "templateType": "anything", "can_override": false}, "V4": {"name": "V4", "group": "Calculated", "definition": "V3-(RT2+i*XT2)*IL", "description": "", "templateType": "anything", "can_override": false}, "delta1": {"name": "delta1", "group": "Calculated", "definition": "180*arg(V1)/pi", "description": "", "templateType": "anything", "can_override": false}, "delta2": {"name": "delta2", "group": "Calculated", "definition": "180*arg(V2)/pi", "description": "", "templateType": "anything", "can_override": false}, "delta3": {"name": "delta3", "group": "Calculated", "definition": "180*arg(V3)/pi", "description": "", "templateType": "anything", "can_override": false}, "RG": {"name": "RG", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "RT1": {"name": "RT1", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "RL": {"name": "RL", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "RT2": {"name": "RT2", "group": "Ungrouped variables", "definition": "random(0.01 .. 0.04#0.01)", "description": "", "templateType": "randrange", "can_override": false}, "VG": {"name": "VG", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "Vline": {"name": "Vline", "group": "Ungrouped variables", "definition": "random(5 .. 50#5)", "description": "", "templateType": "randrange", "can_override": false}, "Vload": {"name": "Vload", "group": "Ungrouped variables", "definition": "random(1 .. 9#1)", "description": "", "templateType": "randrange", "can_override": false}, "IBASE": {"name": "IBASE", "group": "Calculated", "definition": "SBASE/(sqrt(3)*VLoad)", "description": "", "templateType": "anything", "can_override": false}, "Ipu": {"name": "Ipu", "group": "Calculated", "definition": "random(0.1 .. 0.9#0.01)", "description": "<p>percentage of full load on bus 4</p>", "templateType": "randrange", "can_override": false}, "loading": {"name": "loading", "group": "Calculated", "definition": "IkA/IBASE", "description": "", "templateType": "anything", "can_override": false}, "theta_rad": {"name": "theta_rad", "group": "Calculated", "definition": "-arccos(pf/100)", "description": "", "templateType": "anything", "can_override": false}, "pf": {"name": "pf", "group": "Ungrouped variables", "definition": "random(86 .. 99#2)", "description": "", "templateType": "randrange", "can_override": false}, "theta": {"name": "theta", "group": "Calculated", "definition": "180*theta_rad/pi", "description": "", "templateType": "anything", "can_override": false}, "IL": {"name": "IL", "group": "Calculated", "definition": "Ipu*cos(theta_rad)+i*Ipu*sin(theta_rad)", "description": "", "templateType": "anything", "can_override": false}, "delta4": {"name": "delta4", "group": "Calculated", "definition": "180*arg(V4)/pi", "description": "", "templateType": "anything", "can_override": false}, "V1m": {"name": "V1m", "group": "Calculated", "definition": "abs(V1)", "description": "", "templateType": "anything", "can_override": false}, "V4m": {"name": "V4m", "group": "Calculated", "definition": "abs(V4)", "description": "", "templateType": "anything", "can_override": false}, "V2m": {"name": "V2m", "group": "Calculated", "definition": "abs(V2)", "description": "", "templateType": "anything", "can_override": false}, "V3m": {"name": "V3m", "group": "Calculated", "definition": "abs(V3)", "description": "", "templateType": "anything", "can_override": false}, "P1": {"name": "P1", "group": "Calculated", "definition": "re(SBASE*1*conj(IL))", "description": "", "templateType": "anything", "can_override": false}, "P4": {"name": "P4", "group": "Calculated", "definition": "re(SBASE*V4*conj(IL))", "description": "", "templateType": "anything", "can_override": false}, "efficiency": {"name": "efficiency", "group": "Calculated", "definition": "100*P4/P1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["XG", "RG", "XT1", "RT1", "XL", "RL", "XT2", "RT2", "VG", "Vline", "Vload", "SBASE", "pf"], "variable_groups": [{"name": "Calculated", "variables": ["IkA", "V1", "V2", "V3", "V4", "delta1", "delta2", "delta3", "delta4", "IBASE", "Ipu", "loading", "theta_rad", "theta", "IL", "V1m", "V2m", "V3m", "V4m", "P1", "P4", "efficiency"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "<p>A load current of {IkA} kA is flowing with a lagging power factor of {pf} %. Convert this to a current vector in per-unit.</p>\n<p>$ I_L $ = [[0]]$\\angle$ [[1]]$^o $&nbsp; &nbsp;p.u.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ipu", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*Ipu", "maxValue": "1.01*Ipu", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "theta", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], 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"correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "V3", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*V3m", "maxValue": "1.01*V3m", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "delta3", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*delta3", "maxValue": "1.01*delta3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "V4", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*V4m", "maxValue": "1.01*V4m", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, 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