{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":44701,"title":"Nodal Voltage of Resistor Ladder Network","description":"* You have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.\r\n* Create a ladder network as follows.\r\n* Connect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.\r\n* Connect the node at one end to the positive terminal of the battery and the negative terminal to the ground.\r\n* Connect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors. \r\n* Starting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.\r\n\r\nNote: This problem illustrates an application of Number Theory in circuit analysis. \r\n ","description_html":"\u003cul\u003e\u003cli\u003eYou have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.\u003c/li\u003e\u003cli\u003eCreate a ladder network as follows.\u003c/li\u003e\u003cli\u003eConnect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.\u003c/li\u003e\u003cli\u003eConnect the node at one end to the positive terminal of the battery and the negative terminal to the ground.\u003c/li\u003e\u003cli\u003eConnect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors.\u003c/li\u003e\u003cli\u003eStarting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eNote: This problem illustrates an application of Number Theory in circuit analysis.\u003c/p\u003e","function_template":"function reading = LadderVolt(N,R,V)\r\n  reading = tf*V;\r\nend","test_suite":"1\t\r\n%% Simple voltage divider circuit.\r\nN=2; R=100; V=1;\r\nreading_correct = [1 1/2];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n2\t\r\n%%\r\nN=4; R=10; V=15;\r\nreading_correct = [15 6 3];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n3\t\r\n%%\r\nN=6; R=1000; V=130;\r\nreading_correct = [130 50 20 10];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n4\r\n%%\r\nN=8; R=1; V=3.4;\r\nreading_correct = [3.4 1.3 0.5 0.2 0.1];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n5\r\n%%\r\nN=10; R=5000; V=267;\r\nreading_correct = [267  102  39  15  6  3];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n6\r\n%%\r\nN=14; R=3500; V=122;\r\nreading_correct = [122  46.6  17.8  6.8  2.6  1.0  0.4  0.2];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-07-26T21:15:46.000Z","updated_at":"2026-05-30T00:33:01.000Z","published_at":"2018-07-26T21:22:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a ladder network as follows.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConnect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConnect the node at one end to the positive terminal of the battery and the negative terminal to the ground.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConnect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStarting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: This problem illustrates an application of Number Theory in circuit analysis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"problems":[{"id":44701,"title":"Nodal Voltage of Resistor Ladder Network","description":"* You have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.\r\n* Create a ladder network as follows.\r\n* Connect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.\r\n* Connect the node at one end to the positive terminal of the battery and the negative terminal to the ground.\r\n* Connect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors. \r\n* Starting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.\r\n\r\nNote: This problem illustrates an application of Number Theory in circuit analysis. \r\n ","description_html":"\u003cul\u003e\u003cli\u003eYou have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.\u003c/li\u003e\u003cli\u003eCreate a ladder network as follows.\u003c/li\u003e\u003cli\u003eConnect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.\u003c/li\u003e\u003cli\u003eConnect the node at one end to the positive terminal of the battery and the negative terminal to the ground.\u003c/li\u003e\u003cli\u003eConnect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors.\u003c/li\u003e\u003cli\u003eStarting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eNote: This problem illustrates an application of Number Theory in circuit analysis.\u003c/p\u003e","function_template":"function reading = LadderVolt(N,R,V)\r\n  reading = tf*V;\r\nend","test_suite":"1\t\r\n%% Simple voltage divider circuit.\r\nN=2; R=100; V=1;\r\nreading_correct = [1 1/2];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n2\t\r\n%%\r\nN=4; R=10; V=15;\r\nreading_correct = [15 6 3];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n3\t\r\n%%\r\nN=6; R=1000; V=130;\r\nreading_correct = [130 50 20 10];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n4\r\n%%\r\nN=8; R=1; V=3.4;\r\nreading_correct = [3.4 1.3 0.5 0.2 0.1];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n5\r\n%%\r\nN=10; R=5000; V=267;\r\nreading_correct = [267  102  39  15  6  3];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n\r\n6\r\n%%\r\nN=14; R=3500; V=122;\r\nreading_correct = [122  46.6  17.8  6.8  2.6  1.0  0.4  0.2];\r\nreading = LadderVolt(N,R,V);\r\nassert(norm(reading-reading_correct)\u003c100*eps)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-07-26T21:15:46.000Z","updated_at":"2026-05-30T00:33:01.000Z","published_at":"2018-07-26T21:22:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have a bunch (an even number N) of identical resistors (each R ohms), a good battery (V volts) and a high impedance voltmeter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a ladder network as follows.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConnect N/2 of the resistors in series to each other (not a loop) giving N/2 + 1 node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConnect the node at one end to the positive terminal of the battery and the negative terminal to the ground.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConnect each of the remaining N/2 nodes to the ground through one resistor from the other N/2 remaining resistors.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eStarting from the node at the battery, use the voltmeter to measure the readings with reference to the ground at each of the N/2 + 1 node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: This problem illustrates an application of Number Theory in circuit analysis.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"transfer function\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}