Equivalent Resistance: Simplifying Circuits with Symmetry

In summary, when solving for equivalent resistance, there are two approaches that can be used: setting up a system of node-voltage equations or simplifying the network using Y-Δ transformations. In this specific network, the nodes C and D can be combined into one node, as well as the nodes E and F, due to a plane of symmetry. After redrawing the network, it can be seen that the equivalent resistance is indeed 4/3 Ω.
  • #1
stardust006
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resistor-cube-kirt-2.GIF



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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  • #2
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.
 
  • #3
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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Related to Equivalent Resistance: Simplifying Circuits with Symmetry

1. What is equivalent resistance?

Equivalent resistance is the total resistance of a circuit when multiple resistors are connected in either series or parallel.

2. How is equivalent resistance calculated?

The equivalent resistance for resistors in series is calculated by adding the individual resistances. For resistors in parallel, it is calculated using the equation 1/Req = 1/R1 + 1/R2 +...+ 1/Rn, where Req is the equivalent resistance and R1, R2, etc. are the individual resistances.

3. Why is equivalent resistance important?

Equivalent resistance is important because it allows us to simplify complex circuits and make calculations easier. It also helps us understand how current flows through a circuit and how different components affect the overall resistance.

4. Can equivalent resistance be greater than the individual resistances?

Yes, equivalent resistance can be greater than the individual resistances. This is often the case in parallel circuits, where the equivalent resistance is less than any of the individual resistances. In series circuits, the equivalent resistance is equal to the sum of the individual resistances.

5. How does temperature affect equivalent resistance?

Temperature can affect equivalent resistance as the resistance of a material typically increases with temperature. This means that as the temperature increases, the equivalent resistance of a circuit may also increase. However, this effect may be negligible in some cases.

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