Equivalent Resistance: Simplifying Circuits with Symmetry

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SUMMARY

The discussion focuses on calculating equivalent resistance in a circuit with symmetrical nodes. The user initially assumes resistor values of R = 2 Ω and current I = 3 A, questioning the method to determine voltage for equivalent resistance calculation. The solution involves using node-voltage equations or simplifying the network through Y-Δ transformations, leveraging the symmetry of the circuit. The final equivalent resistance is confirmed to be Req = 4/3 Ω.

PREREQUISITES
  • Understanding of node-voltage analysis in circuit theory
  • Familiarity with Y-Δ transformations for circuit simplification
  • Knowledge of electrical resistance and Ohm's Law
  • Basic skills in solving systems of equations
NEXT STEPS
  • Study node-voltage analysis techniques in electrical circuits
  • Learn about Y-Δ transformations and their applications in circuit simplification
  • Explore methods for solving systems of equations in circuit analysis
  • Investigate the impact of symmetry in electrical networks on simplifying calculations
USEFUL FOR

Electrical engineers, circuit designers, and students studying circuit analysis who are looking to enhance their understanding of equivalent resistance and circuit simplification techniques.

stardust006
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how can i solve the equivalent resistance?

I assume R = 2 and I = 3, I know I in node A will be divided. It's just that I don't know what direction I will go to solve for Voltage so I can solve the equivalent resistance.

Is Req = 4/3 Ω ?
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There are a couple ways you might attack this. One is to set up a system of node-voltage equations like you would for any circuit network. That will guarantee that you can solve it, although it will involve 8 equations in 8 unknowns, so you better have your calculator handy.

The other solution is to try and simplify the network. Since this one is made up entirely of nodes with three edges coming into each one, you might try using Y-Δ transformations on it.
 
The network has got a plane of symmetry: The yellow plane in the figure attached. The symmetric nodes (C,D) and (E,F) are at equal potential. The nodes which are at equal potential can be shorted (connected with a wire), it does not change the currents and voltages in the network. Connecting the equivalent nodes, C and D become a single node, and E, F also. Redraw the network.

Req=4/3 Ω is correct.

ehild
 

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