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FrontierScience / 239c543b-7543-445a-b492-89c994b9ba7c / Consider an infinite two-dimensional plane of nodes arranged in a uniform…

Problem

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problem

Consider an infinite two-dimensional plane of nodes arranged in a uniform triangular lattice. Each node is connected to each of its 6 nearest neighbors by a resistor with resistance `

R

`. Find an equation for `

R_{eq}

,` the equivalent resistance between two neighbouring grid points in terms of `

R

`. Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.

Plain-text mathematical notation (without MathML)

Consider an infinite two-dimensional plane of nodes arranged in a uniform triangular lattice. Each node is connected to each of its 6 nearest neighbors by a resistor with resistance `R`. Find an equation for `R_(eq),` the equivalent resistance between two neighbouring grid points in terms of `R`.

Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.

Original LaTeX notation

Consider an infinite two-dimensional plane of nodes arranged in a uniform triangular lattice. Each node is connected to each of its 6 nearest neighbors by a resistor with resistance `\(R\)`. Find an equation for `\(R_{eq}\),` the equivalent resistance between two neighbouring grid points in terms of `\(R\)`.

Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.

subject

physics

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Source and history

upstream_id / Original problem ID: 239c543b-7543-445a-b492-89c994b9ba7c
task_id: 1cada8eb-4480-5ce4-95ac-9c6d5f7b0b5c
task_key: olympiad--test--239c543b~2d7543~2d445a~2db492~2d89c994b9ba7c
task_revision_id: 1
config / split: olympiad / test

Official source

initial import