Find the equivalent resistance of this circuit

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SUMMARY

The discussion focuses on calculating the equivalent resistance of a circuit composed entirely of 1Ω resistors. The initial calculation yielded an equivalent resistance of 7/12Ω, while the correct answer is 4/5Ω, as stated in the referenced textbook. Participants emphasized the importance of recognizing the symmetry in the circuit and the necessity of formulating independent equations for the currents through the resistors. Ultimately, the correct approach involves using Kirchhoff's Voltage Law (KVL) and matrix methods to solve the system of equations accurately.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with circuit analysis techniques, including symmetry considerations
  • Proficiency in solving systems of equations, particularly using matrix methods
  • Basic knowledge of equivalent resistance calculations in series and parallel circuits
NEXT STEPS
  • Study advanced circuit analysis techniques using Thevenin and Norton transformations
  • Learn about using software tools like Maple for solving complex circuit equations
  • Explore the concept of symmetry in electrical circuits and its applications
  • Investigate methods for simplifying circuit networks before applying KCL and KVL
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing complex resistor networks will benefit from this discussion.

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  • #32
Deli Zhang said:
This article https://delizhang.blogspot.com/2015/04/the-formula-for-equicalent-resistance.html gives a formula for calculating the equivalent resistance of an arbitrarily complex circuit, and you can get the answer by following it without having to think about it.
Very neat, but in the context of the problem in post #1, wouldn’t it be computationally more arduous than using symmetry?
 

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