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{"name": "Potential Dividers", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Ks_second_law_question_2.png", "/srv/numbas/media/question-resources/Ks_second_law_question_2.png"], ["question-resources/pot_div_ques_2.png", "/srv/numbas/media/question-resources/pot_div_ques_2.png"], ["question-resources/pot_div_ques_2_MeUnlAB.png", "/srv/numbas/media/question-resources/pot_div_ques_2_MeUnlAB.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Potential Dividers", "tags": [], "metadata": {"description": "<p>Basic potential divider questions</p>", "licence": "All rights reserved"}, "statement": "<p>Using Kirchoff's second law, determine the unknown quantities in the potential dividers below.</p>", "advice": "<p>a) The total e.m.f = 4 V = 3 mA$\\times$ 1 k$\\Omega$ + 3 mA $\\times$ R = total p.d. at the resistors</p>\n<p>3 R mA= 1 V&nbsp; $\\Rightarrow$ R = $\\frac{1}{3}$ = 0.33 k $\\Omega$.&nbsp;</p>\n<p>The p.d. across the resistor is: V = 4 - 3 mA $\\times$ 1 k$\\Omega$ = 1 V.&nbsp;</p>\n<p>b) The combined resistance of the bulb and 2 k$\\Omega$ resistor is: $\\frac{1}{2} + \\frac{1}{2} = 1\\,\\text{k}\\Omega$.&nbsp;</p>\n<p>The ratio of resistance across the combined resistance of the bulb and 2 k$\\Omega$ resistor to the total resistance of the circuit should be: \\[\\frac{1}{1+R} = \\frac{4}{5}\\\\4R + 4=5\\\\R=\\frac{1}{4}=0.25 \\text{k}\\Omega\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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><img src=\"resources/question-resources/Ks_second_law_question_2.png\"/></p>\n<p>What is the value of R?&nbsp;</p>\n<p>[[0]]k$\\Omega$</p>\n<p>What is potential difference across R?</p>\n<p>[[1]] V</p>", "gaps": [{"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": "0.33", "maxValue": "0.33", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision (2 decimal places).&nbsp;", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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><img src=\"resources/question-resources/pot_div_ques_2_MeUnlAB.png\"/></p>\n<p>What should be the value of R for the potential difference across the bulb to be 4V?</p>\n<p>[[0]]k$\\Omega$&nbsp;</p>", "gaps": [{"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": "0.25", "maxValue": "0.25", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision (2 decimal places).", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Madhava Krishna Prasad", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11576/"}]}]}], "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Madhava Krishna Prasad", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/11576/"}]}