// Numbas version: finer_feedback_settings
{"name": "Voltage drop formula", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Voltage drop formula", "tags": [], "metadata": {"description": "<p>Students are asked to rearrane the formula giving the voltage drop across a resistor in terms of emf of battery, resistance of resistor and internal resistance of battery to make the internal resistance the subject. They are then asked to calculate the internal resistance given values for the other variables (randomised).</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A battery with emf \\(E\\) and internal resistance \\(r\\) is connected across an external resistor of resistance \\(R\\). The voltage drop across the resistor can be shown to be \\(\\displaystyle{V=\\frac{ER}{R+r}}\\).</p>", "advice": "<p>For the first part we have \\begin{align}V&amp;=\\frac{ER}{R+r}\\quad\\text{multiply both sides by }(R+r)\\\\V(R+r)&amp;=ER\\quad\\text{expand brackets}\\\\VR+Vr&amp;=ER\\quad\\text{subtract }VR\\text{ from both sides}\\\\Vr&amp;=ER-VR\\quad\\text{factorise RHS}\\\\Vr&amp;=R(E-V)\\quad\\text{divide both sides by }V\\\\r&amp;=\\frac{R(E-V)}{V}\\end{align}</p>\n<p>Substituting \\(E=\\var{E}\\) volts, \\(V=\\var{V}\\) volts and \\(R=\\var{R}\\) ohms into the above formula gives \\begin{align}r&amp;=\\frac{R(E-V)}{V}\\\\&amp;=\\frac{\\var{R}(\\var{E}-\\var{V})}{\\var{V}}\\\\&amp;=\\frac{\\var{R*(E-V)}}{\\var{V}}\\\\&amp;\\approx\\simplify{{precround(R*(E-V)/V,2)}}\\end{align}</p>\n<p>Hence \\(r\\) is \\(\\simplify{{precround(R*(E-V)/V,2)}}\\) ohms (correct to two decimal places).</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": false, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"E": {"name": "E", "group": "Ungrouped variables", "definition": "random(5..12)", "description": "<p>Battery emf in volts, random integer from 5 to 12</p>", "templateType": "anything", "can_override": false}, "V": {"name": "V", "group": "Ungrouped variables", "definition": "random(3..E-1)", "description": "<p>Voltage drop across resistor in volts, random from 3 to E-1.</p>", "templateType": "anything", "can_override": false}, "R": {"name": "R", "group": "Ungrouped variables", "definition": "random(10..80 #10)", "description": "<p>Resistance in ohms.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["E", "V", "R"], "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>Rearrange the formula to make \\(r\\) the subject. (Note: to enter a fraction such as \\(\\frac{a}{b}\\), type <code>a/b</code>.)</p>\n<p>\\(r=\\)[[0]] (You must xhow full working on your handwritten working for this part to get full marks)</p>\n<p>If \\(E=\\var{E}\\) volts, \\(V=\\var{V}\\) volts and \\(R=\\var{R}\\) ohms, what is the value of \\(r\\)?</p>\n<p>\\(r=\\)[[1]] ohms (answer to 2 decimal places)</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(E*R-V*R)/V", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": true, "caseSensitive": false, "valuegenerators": [{"name": "e", "value": ""}, {"name": "r", "value": ""}, {"name": "v", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "({E}*{R}-{V}*{R})/{V}", "maxValue": "({E}*{R}-{V}*{R})/{V}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "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": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}, {"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": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}, {"name": "Hanh Vo", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12984/"}]}