Find the equivalent resistance for the circuit in the figure.

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SUMMARY

The discussion focuses on calculating the equivalent resistance of a circuit involving multiple resistors. The participants clarify that the leftmost and rightmost resistors are not in parallel due to the presence of a central resistor. They recommend using circuit analysis methods such as Kirchhoff's Current Law (KCL) or Kirchhoff's Voltage Law (KVL) to find the total current and subsequently the equivalent resistance using the formula Vemf/I. Additionally, they suggest considering the symmetry of the circuit to simplify the analysis.

PREREQUISITES
  • Understanding of basic circuit theory
  • Familiarity with Kirchhoff's Current Law (KCL)
  • Knowledge of Kirchhoff's Voltage Law (KVL)
  • Concept of Delta-Y transformation
NEXT STEPS
  • Research Delta-Y transformation for resistor networks
  • Learn how to apply Kirchhoff's Current Law (KCL) in circuit analysis
  • Study Kirchhoff's Voltage Law (KVL) for voltage calculations
  • Explore the Wheatstone bridge method for simplifying resistor circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing or designing electrical circuits will benefit from this discussion.

Patdon10
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Homework Statement


Find the equivalent resistance for the circuit in the figure. (Use the following as necessary: Vemf, R.)

Homework Equations


V=IR


The Attempt at a Solution



This problem isn't that hard, but I'm having trouble trying to visualize how to combine the resistors. The 2 most left Resistors are in parallel, as are the 2 most right ones. Those 4 are all in series with the middle resistor. How can you split it? I can't visualize it. Can anyone give me a hint?
 

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Patdon10 said:
This problem isn't that hard, but I'm having trouble trying to visualize how to combine the resistors. The 2 most left Resistors are in parallel, as are the 2 most right ones. Those 4 are all in series with the middle resistor. How can you split it? I can't visualize it. Can anyone give me a hint?

The two most left resistors are not in parallel. Neither are the two rightmost resistors. In order to be in parallel, each end of each resistor in a pair must be directly tied together, with no other components in between. In the diagram, the central resistor is between one end of the "paired" resistors.

You can approach this problem either by employing a Δ - Y transformation (look up Delta-Y transformation), or by using one of several circuit analysis methods involving KCL or KVL equations to find the total current, I, drawn from the voltage source. The resistance of the circuit would then be Vemf/I.

If you're clever you might be able to conclude something about the voltage potential across the central resistor (symmetry of the circuit helps), then draw a further conclusion about the current flowing through it and what it implies about its affect on the overall circuit. Certain obvious simplifications would then make your life much easier :smile:.

Probably best to start with the basic circuit analysis methods and then see how the results jibe with an 'intuitive' approach.
 
you can also use http://en.wikipedia.org/wiki/Wheatstone_bridge" method ... its quite simpler than Δ - Y, KCL, KVL
 
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