// Numbas version: exam_results_page_options
{"name": "OldTransformers", "extensions": [], "custom_part_types": [], "resources": [["question-resources/transformerCircuit.bmp", "/srv/numbas/media/question-resources/transformerCircuit.bmp"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "OldTransformers", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p><img src=\"resources/question-resources/transformerCircuit.bmp\"/></p>\n<p></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} $\\Omega$ load is connected to the LV side with rated voltage on the HV side.</p>\n<p></p>\n<p></p>\n<p></p>", "advice": "", "rulesets": {}, "extensions": [], "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/ICoc)", "description": "", "templateType": "anything", "can_override": false}, "RW": {"name": "RW", "group": "Impedances", "definition": "Psc/(I1^2)", "description": "", "templateType": "anything", "can_override": false}, "XL": {"name": "XL", "group": "Impedances", "definition": "VXL/I1", "description": "", "templateType": "anything", "can_override": false}, "V2": {"name": "V2", "group": "Ratings", "definition": "round(V1/ApproxRatio)", "description": "<p>Phase Voltage</p>", "templateType": "anything", "can_override": false}, "Poc": {"name": "Poc", "group": "Measurements", "definition": "round(random(5..10)*S/100)", "description": "<p>5-10% of rated power</p>", "templateType": "anything", "can_override": false}, "Psc": {"name": "Psc", "group": "Measurements", "definition": "round(random(5..10)*S/100)", "description": "<p>5-10% of rated power</p>", "templateType": "anything", "can_override": false}, "ApproxRatio": {"name": "ApproxRatio", "group": "Ratings", "definition": "random(2 .. 44#2)", "description": "", "templateType": "randrange", "can_override": false}, "Vsc": {"name": "Vsc", "group": "Measurements", "definition": "round(sqrt(VW^2+VXL^2))", "description": "", "templateType": "anything", "can_override": false}, "Ioc": {"name": "Ioc", "group": "Measurements", "definition": "precround(sqrt(ICoc^2+IMoc^2),2)", "description": "", "templateType": "anything", "can_override": false}, "IL'": {"name": "IL'", "group": "Currents", "definition": "V1/(RW + XL*i + RL')", "description": "", "templateType": "anything", "can_override": false}, "IL": {"name": "IL", "group": "Currents", "definition": "Ratio*IL'", "description": "", "templateType": "anything", "can_override": false}, "S": {"name": "S", "group": "Ratings", "definition": "random(50 .. 1000#50)", "description": "", "templateType": "randrange", "can_override": false}, "I1": {"name": "I1", "group": "Ratings", "definition": "S/V1", "description": "", "templateType": "anything", "can_override": false}, "I2": {"name": "I2", "group": "Ratings", "definition": "S/V2", "description": "", "templateType": "anything", "can_override": false}, "RL": {"name": "RL", "group": "Impedances", "definition": "ceil(V2/I2)", "description": "", "templateType": "anything", "can_override": false}, "RL'": {"name": "RL'", "group": "Impedances", "definition": "Ratio^2*RL\n", "description": "", "templateType": "anything", "can_override": false}, "IC": {"name": "IC", "group": "Currents", "definition": "V1/RC", "description": "", "templateType": "anything", "can_override": false}, "IM": {"name": "IM", "group": "Currents", "definition": "V1/(XM*i)", "description": "", "templateType": "anything", "can_override": false}, "IS": {"name": "IS", "group": "Currents", "definition": "IC+IM+IL'", "description": "", "templateType": "anything", "can_override": false}, "IMoc": {"name": "IMoc", "group": "Ungrouped variables", "definition": "random(1..5)*ICoc", "description": "", "templateType": "anything", "can_override": false}, "ICoc": {"name": "ICoc", "group": "Ungrouped variables", "definition": "Poc/V2", "description": "", "templateType": "anything", "can_override": false}, "VW": {"name": "VW", "group": "Ungrouped variables", "definition": "I1*RW", "description": "", "templateType": "anything", "can_override": false}, "VXL": {"name": "VXL", "group": "Ungrouped variables", "definition": "random(1..5)*VW", "description": "", "templateType": "anything", "can_override": false}, "Ploss": {"name": "Ploss", "group": "Ungrouped variables", "definition": "Pc + Pw", "description": "", "templateType": "anything", "can_override": false}, "Pc": {"name": "Pc", "group": "Ungrouped variables", "definition": "V1^2/RC", "description": "", "templateType": "anything", "can_override": false}, "PW": {"name": "PW", "group": "Ungrouped variables", "definition": "abs(IL')^2*Rw", "description": "", "templateType": "anything", "can_override": false}, "efficiency": {"name": "efficiency", "group": "Ungrouped variables", "definition": "100*PL/PS", "description": "", "templateType": "anything", "can_override": false}, "PS": {"name": "PS", "group": "Ungrouped variables", "definition": "re(V1*conj(IS))", "description": "", "templateType": "anything", "can_override": false}, "PL": {"name": "PL", "group": "Ungrouped variables", "definition": "abs(IL)^2*RL", "description": "", "templateType": "anything", "can_override": false}, "Ratio": {"name": "Ratio", "group": "Ratings", "definition": "V1/V2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ICoc", "IMoc", "VW", "VXL", "Ploss", "Pc", "PW", "efficiency", "PS", "PL"], "variable_groups": [{"name": "Ratings", "variables": ["ApproxRatio", "V1", "V2", "Ratio", "S", "I1", "I2"]}, {"name": "Impedances", "variables": ["RC", "XM", "RW", "XL", "RL", "RL'"]}, {"name": "Measurements", "variables": ["Poc", "Psc", "Ioc", "Vsc"]}, {"name": "Currents", "variables": ["IL'", "IL", "IC", "IM", "IS"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Equivalent Circuit", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<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": "0.95*(1/1000)*RC", "maxValue": "1.05*(1/1000)*RC", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Xm", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.95*(1/1000)*XM", "maxValue": "1.05*(1/1000)*XM", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Rw", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*RW", "maxValue": "1.01*RW", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Xl", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.99*XL", "maxValue": "1.01*XL", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Load Current", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<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": "0.95*1000*abs(IS)", "maxValue": "1.05*1000*abs(IS)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Angle", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "0.95*180*arg(IS)/pi", "maxValue": "1.05*180*arg(IS)/pi", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Efficiency", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<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", "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}]}]}], "contributors": [{"name": "Jane Courtney", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2154/"}]}