Find the equivalent resistance for the circuit in the figure.

In summary, the conversation discusses a circuit with resistors in parallel and series, and the goal is to find the equivalent resistance. The conversation suggests using a Δ - Y transformation or circuit analysis methods involving KCL and KVL equations to find the total current and then calculating the resistance using Vemf/I. Another method mentioned is using the Wheatstone bridge method.
  • #1
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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  • #2
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.
 
  • #3
you can also use http://en.wikipedia.org/wiki/Wheatstone_bridge" method ... its quite simpler than Δ - Y, KCL, KVL
 
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1. What is the purpose of finding the equivalent resistance in a circuit?

The equivalent resistance in a circuit is used to simplify complex circuits and make it easier to calculate the overall resistance of the circuit. It allows for easier analysis and understanding of the circuit's behavior.

2. How is the equivalent resistance calculated?

The equivalent resistance is calculated by using Ohm's law and Kirchhoff's laws. It involves finding the total resistance in series and parallel parts of the circuit and combining them using specific equations.

3. Why is it important to find the equivalent resistance?

Finding the equivalent resistance is important because it allows us to determine the overall resistance of a circuit and how much current will flow through it. This information is crucial in designing and troubleshooting circuits.

4. Can the equivalent resistance be different from the total resistance in a circuit?

Yes, the equivalent resistance can be different from the total resistance in a circuit. This is because the equivalent resistance takes into account the overall resistance of the circuit, while the total resistance may only consider a specific part of the circuit.

5. How does the arrangement of resistors affect the equivalent resistance?

The arrangement of resistors, whether in series or in parallel, can greatly affect the equivalent resistance of a circuit. In series, the equivalent resistance is the sum of all the resistors, while in parallel, it is calculated using a specific equation that takes into account the inverse of each resistor's value.

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