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{"name": "Wheatstone Bridge", "extensions": [], "custom_part_types": [], "resources": [["question-resources/wheatstone_bridge_ques.png", "/srv/numbas/media/question-resources/wheatstone_bridge_ques.png"], ["question-resources/wheatstone_bridge_ques_2.png", "/srv/numbas/media/question-resources/wheatstone_bridge_ques_2.png"], ["question-resources/wheatstone_bridge_ques_3.png", "/srv/numbas/media/question-resources/wheatstone_bridge_ques_3.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Wheatstone Bridge", "tags": [], "metadata": {"description": "<p>Basic questions on the Wheatstone Bridge</p>", "licence": "All rights reserved"}, "statement": "<p>The following circuit shows a Wheatstone Bridge with an unknown resistance.&nbsp;</p>", "advice": "<p>a) The unknown resistance in a wheatstone bridge is equal to: $R_x = \\frac{R_1\\,R_4}{R_2} = \\frac{3\\,\\text{k}\\Omega\\times2\\,\\text{k}\\Omega}{5\\,\\text{k}\\Omega} = 1.2\\,\\text{k}\\Omega$. Where $R_1 = 3\\,\\text{k}\\Omega,\\;R_2=5\\,\\text{k}\\Omega,\\;R_4=2\\,\\text{k}\\Omega$.</p>\n<p>b) Rearranging the same formula, \\[R_2 \\times R_3 = R_1 \\times R_x\\\\R_x = \\frac{5\\,\\text{k}\\Omega\\times 2\\,\\text{k}\\Omega}{3\\,\\text{k}\\Omega} = 3.33\\,\\text{k}\\Omega\\]</p>\n<p>c) When the Wheatstone bridge is balanced, $I_A = 0$.</p>\n<p>d) The ratio of the resistances determine whether the bridge remains balanced, the source voltage does not affect the bridge. Therefore, the bridge remains balanced.&nbsp;</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/wheatstone_bridge_ques_2.png\"/></p>\n<p>Given that the bridge is balanced, what is the value of the unknown resistance R<sub>x</sub>?</p>\n<p>[[0]]k$\\Omega$</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": "1.2", "maxValue": "1.2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision (1 decimal place).", "strictPrecision": true, "showPrecisionHint": 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/wheatstone_bridge_ques_3.png\"/></p>\n<p>What should the value of the variable resistance R<sub>x</sub> be for the bridge to be balanced?</p>\n<p>[[0]] k$\\Omega$</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": "3.33", "maxValue": "3.33", "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).", "strictPrecision": true, "showPrecisionHint": 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>When the bridge is&nbsp;<strong>balanced</strong>, the value of I<sub>A</sub> is [[0]].</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", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "1_n_2", "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>If the batter is replaced with another battery which can provide 4 times the e.m.f. will the bridge remain balanced?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Yes. The external voltage source does not affect the state of the bridge.", "No. A current will flow between nodes 3 and 4 and I<sub>A</sub> $\\neq 0$."], "matrix": ["1", 0], "distractors": ["", ""]}], "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/"}]}