// Numbas version: exam_results_page_options
{"name": "Three Phase - Practice", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": "40", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": false, "question_groups": [{"name": "Group", "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"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": false, "browse": false, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": false, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": false, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}], "extensions": [], "custom_part_types": [], "resources": [["question-resources/DeltaCircuit_NBsNnJk.png", "/srv/numbas/media/question-resources/DeltaCircuit_NBsNnJk.png"]]}