// Numbas version: exam_results_page_options
{"name": "Transformers - Practice", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": false, "question_groups": [{"name": "Group", "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"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": false, "browse": false, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "warnifunattempted", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "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, "results_options": {"printquestions": true, "printadvice": 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/tranny.svg", "/srv/numbas/media/question-resources/tranny.svg"]]}