Solve Thevenin Resistance at Node 2: 10k || 10k

[Will15]

For the following circuit:
http://imagizer.imageshack.us/v2/640x480q90/674/aBkkRU.png

I'm solving for the Rth at node 2. In the solution guide, it shows that the Rth = (10k || 10k). I don't understand how this is so, by following the resistence equivalent rules, these two resistance should be in series.

I'd appreciation for the clarification.

 

[Baluncore]

The fixed 10V ideal source has zero dv/di = zero resistance, so the two resistors are actually in parallel.
If it was a fixed current source, it would be treated as an infinite resistance element.

 

[jrive]

When computing the Thevenin resistance, voltage sources become short circuits and current sources become open circuits. In your example, when the voltage source is shorted, the 10k resistors are in parallel

 

[NascentOxygen]

I'm solving for the Rth at node 2. In the solution guide, it shows that the Rth = (10k || 10k). I don't understand how this is so, by following the resistence equivalent rules, these two resistance should be in series.

I'd appreciation for the clarification.

For Thévenin analysis, we first replace the voltage source with a short circuit. Then examine what we are left with.

To get from node 2 to ground, an electron can go via a path through one of the 10k resistors to ground, OR through the other 10k resistor to ground, but no path to ground takes it through both resistors. That's the characteristic of parallel paths: you can take one path OR the other, and don't go through both in sequence.

If one path leads inevitably through the other, then and only then, are they are in series.

 

[rezeew]

I would like to clarify that the solution guide is correct in stating that the Thevenin resistance at node 2 in this circuit is (10k || 10k). This is because the two 10k resistors are connected in parallel, not in series.

In a parallel circuit, the total resistance is calculated by taking the reciprocal of each resistance and adding them together, and then taking the reciprocal of the result. In this case, the reciprocal of 10k is 1/10k, and adding two of them together gives 2/10k. Taking the reciprocal of 2/10k gives a total resistance of 10k.

I understand that this may be confusing, as the resistors are physically connected in a straight line, but the key here is to look at how they are connected in the circuit. In this case, they are connected at both ends, creating a parallel connection.

I hope this clarification helps in your understanding of Thevenin resistance and parallel circuits. As scientists, it is important to carefully analyze how components are connected in a circuit to accurately determine the equivalent resistance.