// Numbas version: finer_feedback_settings
{"name": "Electronic circuit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Electronic circuit", "tags": [], "metadata": {"description": "<p>Simultaneous equation problem as circuit analysis to find unknown voltages. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>We need to solve \\begin{align} \\simplify[unitFactor]{-{a}V_2 + {b}V_1} &amp;= 0\\\\ \\simplify[unitFactor]{{c}V_1 - {d}V_2 + {f}} &amp;=0\\end{align} which can be written as \\begin{align} \\simplify[unitFactor]{{b}V_1-{a}V_2} &amp;= 0\\quad (1)\\\\ \\simplify[unitFactor]{{c}V_1 - {d}V_2} &amp;=\\simplify{-{f}}\\quad (2)\\end{align}</p>\n<p>Using the method of elimination to eliminate \\(V_2\\) we multiply equation \\((1)\\) by \\(\\var{factor2}\\) and equation \\((2)\\) by \\(\\var{factor1}\\) to get \\begin{align}\\simplify[unitFactor]{{b*factor2}V_1-{a*factor2}V_2} &amp;= 0\\quad (3)\\\\ \\simplify[unitFactor]{{c*factor1}V_1 - {d*factor1}V_2} &amp;=\\simplify{-{f*factor1}}\\quad (4)\\end{align}</p>\n<p>Taking \\((3)-(4)\\) we obtain \\[\\simplify{({b*factor2}-{c*factor1})V_1={f*factor1}}\\]</p>\n<p>and hence \\[V_1=\\simplify{{a*f/(b*d-a*c)}}\\]</p>\n<p>Substituting this into \\((1)\\) gives us \\[\\simplify[unitFactor]{-{a}V_2 + {b*a*f/(b*d-a*c)}} = 0\\] and hence \\[V_2=\\simplify{{b*f/(b*d-a*c)}}\\]</p>\n<p>Thus the voltages are \\(V_1=\\simplify{{a*f/(b*d-a*c)}}\\) volts and \\(V_2=\\simplify{{b*f/(b*d-a*c)}}\\) volts.</p>\n<p>(Note that this problem could also be solved by eliminating \\(V_1\\) instead of \\(V_2\\) or by the method of substitution, however the final answers will be the same.)</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "<p>Coefficent of V_1 in equation 2, random integer between 2 and 10</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>negative of coefficent of V_2 in equation 1, random integer between 1 and 10</p>", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "<p>Coefficient of V_1 iin equation 1, random value between 1 and 9</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>Negative coefficient of V_2 in equation 2, random integer between 1 and 10</p>", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(5..15)", "description": "<p>constant term in equation 2, random value between 5 and 15</p>", "templateType": "anything", "can_override": false}, "factor1": {"name": "factor1", "group": "Ungrouped variables", "definition": "a/gcf(a,d)", "description": "<p>factor used to multiply equation 2 by in advice showing solution by elimiation method</p>", "templateType": "anything", "can_override": false}, "factor2": {"name": "factor2", "group": "Ungrouped variables", "definition": "d/gcf(a,d)", "description": "<p>factor used to multiply equation 1 by in advice showing solution by elimiation method</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "b*d-a*c<>0", "maxRuns": 100}, "ungrouped_variables": ["c", "a", "b", "d", "f", "factor1", "factor2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>Analysis of a particular electronic circuit shows that the voltage drops across two sections of the circuit must satisfy the equations \\begin{align} \\simplify[unitFactor]{-{a}V_2 + {b}V_1} &amp;= 0\\\\ \\simplify[unitFactor]{{c}V_1 - {d}V_2 + {f}} &amp;=0 \\end{align} Find the values of \\(V_1\\) and \\(V_2\\). Write your final answer in the box below and show full working on your handwritten notes. (Note: Leave answers in fraction form. For example to enter the fraction \\(\\frac32\\) type <code>3/2</code>.)</p>\n<p>\\(V_1=\\)[[0]] V</p>\n<p>\\(V_2=\\)[[1]] V</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "\\(V_1\\)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a*f/(b*d-a*c)", "maxValue": "a*f/(b*d-a*c)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "\\(V_2\\)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b*f/(b*d-a*c)", "maxValue": "b*f/(b*d-a*c)", "correctAnswerFraction": true, "allowFractions": true, "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", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Hanh Vo", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12984/"}]}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Hanh Vo", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12984/"}]}