Problem 53775. Total resistance of a network of resistors in series and parallel

Created by Mark Posen

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>What is the total resistance of a network of resistors in series and in parallel?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A matrix R contains the resistances (in Ohm) of resistors, which are connected in series and in parallel:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"145\"/><w:attr w:name=\"width\" w:val=\"222\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The network consists of one or more 'strings' of resistors in series, each of which is connected in parallel with the others. Each row of the matrix contains the resistances of the resistors in that 'string', and all rows of resistors are connected in parallel. An input matrix may thus be represented as:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[R = [120 200 1500 50;\n     500 50 NaN NaN;\n     3000 NaN NaN NaN;\n     460 180 900 NaN]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Since there must be as many columns in the matrix as the maximum number of resistors in any 'string', NaNs are used to 'pad out' any row in which that string has fewer resistors.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The simple case in the figure above would be represented as:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[R = [R1 R2; R3 NaN]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Your function should take the matrix R as its input and return the total resistance (in Ohm) of the network of resistors.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Hint: see </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Resistor#Series_and_parallel_resistors\"><w:r><w:t>https://en.wikipedia.org/wiki/Resistor#Series_and_parallel_resistors</w:t></w:r></w:hyperlink></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.png","relationshipId":"rId1"}]},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 547.917px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 273.958px; transform-origin: 407px 273.958px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 237.658px 7.75px; transform-origin: 237.658px 7.75px; unicode-bidi: normal; "><span style="">What is the total resistance of a network of resistors in series and in parallel?</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 318.567px 7.75px; transform-origin: 318.567px 7.75px; unicode-bidi: normal; "><span style="">A matrix R contains the resistances (in Ohm) of resistors, which are connected in series and in parallel:</span></span></div><div style="block-size: 150.75px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 75.375px; text-align: left; transform-origin: 384px 75.375px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 222px;height: 145px" src="data:image/png;base64,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" data-image-state="image-loaded" width="222" height="145"></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373.733px 7.75px; transform-origin: 373.733px 7.75px; unicode-bidi: normal; "><span style="">The network consists of one or more 'strings' of resistors in series, each of which is connected in parallel with the others. Each row of the matrix contains the resistances of the resistors in that 'string', and all rows of resistors are connected in parallel. An input matrix may thus be represented as:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 81.7333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 40.8667px; transform-origin: 404px 40.8667px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80.85px 8.25px; tab-size: 4; transform-origin: 80.85px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">R = [120 200 1500 50;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 77px 8.25px; tab-size: 4; transform-origin: 77px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">     500 50 NaN NaN;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84.7px 8.25px; tab-size: 4; transform-origin: 84.7px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">     3000 NaN NaN NaN;</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80.85px 8.25px; tab-size: 4; transform-origin: 80.85px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">     460 180 900 NaN]</span></span></div></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.442px 7.75px; transform-origin: 376.442px 7.75px; unicode-bidi: normal; "><span style="">Since there must be as many columns in the matrix as the maximum number of resistors in any 'string', NaNs are used to 'pad out' any row in which that string has fewer resistors.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 191px 7.75px; transform-origin: 191px 7.75px; unicode-bidi: normal; "><span style="">The simple case in the figure above would be represented as:</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 73.15px 8.25px; tab-size: 4; transform-origin: 73.15px 8.25px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">R = [R1 R2; R3 NaN]</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361.067px 7.75px; transform-origin: 361.067px 7.75px; unicode-bidi: normal; "><span style="">Your function should take the matrix R as its input and return the total resistance (in Ohm) of the network of resistors.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5583px 7.75px; transform-origin: 29.5583px 7.75px; unicode-bidi: normal; "><span style="">Hint: see </span></span><a target='_blank' href = "https://en.wikipedia.org/wiki/Resistor#Series_and_parallel_resistors"><span style=""><span style="">https://en.wikipedia.org/wiki/Resistor#Series_and_parallel_resistors</span></span></a></div></div></div>

What is the total resistance of a network of resistors in series and in parallel?
A matrix R contains the resistances (in Ohm) of resistors, which are connected in series and in parallel:

The network consists of one or more 'strings' of resistors in series, each of which is connected in parallel with the others. Each row of the matrix contains the resistances of the resistors in that 'string', and all rows of resistors are connected in parallel. An input matrix may thus be represented as:
R = [120 200 1500 50;
     500 50 NaN NaN;
     3000 NaN NaN NaN;
     460 180 900 NaN]
Since there must be as many columns in the matrix as the maximum number of resistors in any 'string', NaNs are used to 'pad out' any row in which that string has fewer resistors.
The simple case in the figure above would be represented as:
R = [R1 R2; R3 NaN]
Your function should take the matrix R as its input and return the total resistance (in Ohm) of the network of resistors.
Hint: see https://en.wikipedia.org/wiki/Resistor#Series_and_parallel_resistors

Solve

Solution Stats

27 Solutions
20 Solvers

Last Solution submitted on Aug 28, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers20

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 53775. Total resistance of a network of resistors in series and parallel

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers20

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Problem 53775. Total resistance of a network of resistors in series and parallel

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers20

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

Players