# Are the second and third circuits same as the first one?

• B
• donaldparida
In summary, the conversation discusses the equivalence of three circuits with resistors of resistance r connected in parallel. The first circuit is simplified to the second and third circuits, and the equivalent resistance is the same for all three circuits. The question is raised about which circuit is equivalent and why. The answer is that all three circuits are equivalent because the resistors are all connected to the same nodes. The conversation also mentions the use of colours to distinguish between different nodes and the concept of topologically equivalent circuits. Finally, a challenge is given to calculate the resistance between two diagonally furthest apart corners of a cube with 12 ohm resistors on each edge.
donaldparida
It seems at first sight of the first circuit that all the resistors of resistance r are connected in parallel and i have thus simplified it to the second circuit. But then on numbering the nodes and redrawing the circuit i got the third circuit.
I got the same equivalent resistance for all the three circuits which i think is a coincidence because i do not not know why the second circuit is equivalent to the first one (i drew that way because the in the first circuit it seems that all the resistors are in parallel).
I basically have two questions:Is the first circuit equivalent to the second circuit or the third circuit or both? Why is the second circuit equivalent to the first one if it is so?

donaldparida said:
It seems at first sight of the first circuit that all the resistors of resistance r are connected in parallel and i have thus simplified it to the second circuit. But then on numbering the nodes and redrawing the circuit i got the third circuit.
I got the same equivalent resistance for all the three circuits which i think is a coincidence because i do not not know why the second circuit is equivalent to the first one (i drew that way because the in the first circuit it seems that all the resistors are in parallel).
I basically have two questions:Is the first circuit equivalent to the second circuit or the third circuit or both? Why is the second circuit equivalent to the first one if it is so?
Yes, they are the same. All of the resistors are in parallel. Each resistor connects to the same two nodes.

Colour all wires connected to the (+)ve terminal red.
Colour all wires connected to the (–)ve terminal black.
Note that every resistor now has different coloured wire at each terminal.
If a component had a wire that was not coloured, then it would be connected to a third “node” in the circuit and you would need another colour. You do not need colours if you number the nodes wherever they connect to a component.

Two circuits are topologically the same if the components are the same and are connected to the same nodes.If you can work out the resistance of a network try this one. Imagine a cube with nodes at the corner points. Place a 12 ohm resistor on each edge to connect with the ends of two other edge resistors. Draw the cube of resistors. There will be 8 corner nodes and 12 edge resistors.
Pick two of the diagonally furthest apart corners of the eight resistor cube. Find the resistance between them.

donaldparida

## 1. Are the second and third circuits identical to the first one?

No, the second and third circuits are not necessarily identical to the first one. While they may have similar components and functions, they can also have key differences in design and purpose.

## 2. Can the second and third circuits be interchanged with the first one?

It depends on the specific circuits and their compatibility. In some cases, the second and third circuits may be interchangeable with the first one, but in others, they may not be suitable replacements.

## 3. Do the second and third circuits have the same capabilities as the first one?

Not necessarily. The second and third circuits may have different capabilities and limitations compared to the first one. It is important to carefully consider the specifications and functions of each circuit before use.

## 4. Are the second and third circuits connected to the first one?

It depends on the overall circuit design. In some cases, the second and third circuits may be connected to the first one, while in others, they may be completely separate systems.

## 5. Do the second and third circuits have the same input and output as the first one?

Again, it depends on the specific circuits and their design. While they may share some inputs and outputs, they can also have unique inputs and outputs that differ from the first circuit.

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