Effective resistance between two points problem

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SUMMARY

The forum discussion centers on calculating the effective resistance between two points in a circuit with nodes labeled T, M, L, and Q. The original poster attempted to use symmetry arguments but incorrectly removed resistors LM and QM, leading to confusion about the current flow. The correct approach involves recognizing that if the voltage at nodes T and M is the same, the resistor between them does not affect the overall resistance, allowing for simplification using the delta-star transformation. Ultimately, the effective resistance between points A and B is determined to be 8R/11.

PREREQUISITES
  • Understanding of circuit theory, specifically series and parallel resistor combinations.
  • Familiarity with delta-star (Δ-Y) transformation techniques.
  • Knowledge of symmetry in electrical circuits and its implications on voltage and current.
  • Basic concepts of Wheatstone bridges and their analysis.
NEXT STEPS
  • Study the delta-star transformation in detail to simplify complex resistor networks.
  • Learn about Wheatstone bridge circuits and how to analyze them for effective resistance.
  • Explore symmetry arguments in circuit analysis to identify redundant components.
  • Practice problems involving effective resistance calculations in various circuit configurations.
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing and simplifying resistor networks in electrical circuits.

  • #31
Jahnavi said:
This is exactly how I got the answer first time in post#24 :smile:
No . I had actually employed the strategy as suggested by you when I wrote the answer in post#24 . After getting the right answer , then I tried applying Star Delta approach .

Your approach is quite admirable !

Please help me understand one thing i.e how could the middle line drawn ( to exploit symmetry ) coincide with the resistor between T and M .

I am still unsure how we could remove resistor between T and M .

Please reflect a little more on this symmetry aspect .
If the voltage is the same at T and M, then there is no current and no voltage drop across the resistor between them. So removing the resistor will not change any voltages or currents anywhere else in the circuit. Therefore, the effective resistance between A and B is the same with or without it.
 
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  • #32

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