Solving the Physics Riddle: A Current Across a Single Resistor

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Discussion Overview

The discussion revolves around a physics riddle involving an infinite grid of resistors, each with a resistance of 1 ohm, and the effect of connecting a battery that supplies a current of one amp through a single resistor. Participants explore the implications of the riddle, the interpretation of the current and resistance, and the calculations involved.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the answer to the riddle is 2/pi, indicating a specific calculation related to the effective resistance of the grid.
  • Another participant argues that the wording of the riddle implies that the current across the single resistor is one amp, as the battery is configured to supply that current directly.
  • A later reply questions the clarity of the original phrasing regarding the current and proposes that a more interesting interpretation would involve the battery supplying one volt instead, which could lead to a different calculation of effective resistance.
  • There is a mention of confusion regarding the interpretation of the current and resistance across the nodes of the grid, with one participant seeking to clarify the question posed by the teacher.

Areas of Agreement / Disagreement

Participants express differing interpretations of the riddle, with some asserting that the current is one amp while others propose that the effective resistance of the grid leads to a different conclusion. The discussion remains unresolved with multiple competing views.

Contextual Notes

There are unresolved assumptions regarding the configuration of the battery and the interpretation of the current and resistance in the context of the infinite grid. The phrasing of the riddle is also noted as potentially confusing.

Tom McCurdy
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Today in physics lecture our physics teacher left us with a riddle.

If you had an infinite grid of resistors say with 1 ohm of resistance set up between every node of the grid and then you connected a battery that supplies a current of one amp through across a single resistor, what would be the current across that single resistor.
 
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Is this like that question game on "Whose Line Is It Anyway?"
 
Swiper no swiping!
 
by the way the answer is 2/pi i believe
 
Tom McCurdy said:
Today in physics lecture our physics teacher left us with a riddle.

If you had an infinite grid of resistors say with 1 ohm of resistance set up between every node of the grid and then you connected a battery that supplies a current of one amp through across a single resistor, what would be the current across that single resistor.
You do that by calling the effective resistance R and each resistor r.
Then (R+2r) and r in parallel equal R. (Draw a picture to see that.)
This gives 1/R=1/r+1/(R+2r), and I get R=(sqrt{3}-1) ohm.
Your phrase "a current of one amp through across a single resistor, what would be the current across that single resistor" is too confusing to determine what you mean by the current.
 
Achuz, I don't think your reasoning is correct.

Tom McCurdy said:
... a battery that supplies a current of one amp through across a single resistor, what would be the current across that single resistor[?]

Clearly, the answer to the teacher's question (as posed, a riddle) is "one amp" (notice the battery is specifically configured to supply one amp across "that" resistor -- wording implies in situ!).

A more interesting question is to interpret that the battery instead provides one volt (ie. one amp across the one ohm in isolation), that is, asking how to calculate the effective resistance of the infinite grid - in which case a factor of pi in the result wouldn't sound unreasonable.
 
cesiumfrog said:
Achuz, I don't think your reasoning is correct.



Clearly, the answer to the teacher's question (as posed, a riddle) is "one amp" (notice the battery is specifically configured to supply one amp across "that" resistor -- wording implies in situ!).

A more interesting question is to interpret that the battery instead provides one volt (ie. one amp across the one ohm in isolation), that is, asking how to calculate the effective resistance of the infinite grid - in which case a factor of pi in the result wouldn't sound unreasonable.

I thought it was one amp as well... but its not... I am going to try and find out if he meant the resistance across one set of nodes which Is 2/pi
 

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