# Why are resistors that are shorted and connected to each other considered to be in parallel and not in series?

In the following image, we are finding the Thévenin equivalent resistance after shorting the voltage sources. Why are these two resistors considered to be in parallel? It seems they are connected both in series and in parallel.

• The ends are connected together on both sides so they're definitely in parallel. The way it's drawn is just putting you on the wrong foot. Redraw the image with the resistors on top of each other and it'll look more familiar with typical textbook examples. Commented Apr 2, 2023 at 3:41
• how many nodes are in the diagram? Commented Apr 2, 2023 at 5:15
• The Thevenin equivalent resistance of what? It matters! Label nodes please for this to make sense. Commented Apr 2, 2023 at 9:09
• "The way they're drawn is just putting you on the wrong foot" This is done intentionally in most textbooks, to confuse and obfuscate. One of the meta-skills you must learn to succeed in class is how to physically re-draw a diagram in a way that is electrically the same, so you can push things around and thus see what is then obvious. Whether this is lazy textbook writing, or teaching you an important lesson, I do not know. I'm sure cr*p like this causes many otherwise qualified people to wash out of school. Commented Apr 2, 2023 at 19:36
• I commend the OP for asking for clarification on a result that they have worked successfully. The diagram is the result of a Thevenin analysis. The OP has clearly realized that the resistors appear to be both in series and in parallel. I really don’t think their work is cr*p. This is a well presented question. Commented Apr 3, 2023 at 22:28

It depends on point of view. I suspect that the original circuit is something like this with the load across nodes a and b removed:

simulate this circuit – Schematic created using CircuitLab

For Thevenin analysis:

R1 and R2 are in series from the point of view of the sources while calculating the Thevenin voltage Vab.

As shown in other answers, they are in parallel from the point of view of calculating the Thevenin resistance Rab.

Because these are the same circuit:

simulate this circuit – Schematic created using CircuitLab

It seems to be they are connected in both series and parallel.

You are correct.

Amusingly, you are the only one to state that. No one else (as of my writing) has said what you have realized: they are connected in both series and parallel.

If you add a 3rd component across one of the resistors (e.g., an ohmmeter), then the resulting circuit becomes just parallel.

Slide each resistor around the corner so it is in the middle of a vertical part of net, and you will see that they are directly in parallel. If they were in series, as it looks like across the top of the drawing, the outside ends of the two resistors would not be connected together around the bottom of the drawing.

## Why the resistors are connected in parallel

Definitely the two resistors are connected in parallel and we can measure their equivalent resistance R1||R2 (in my schematics below) by connecting an ohmmeter in parallel to this network. So they are connected in parallel but with respect to the nodes A and B between which the ohmmeter is connected.

simulate this circuit – Schematic created using CircuitLab

## Why the resistors are not connected in series

If the two resistors were connected in series, we should be able to measure their equivalent resistance R1 + R2 by connecting the ohmmeter in series with this network... but it is shorted. So we have to break the connection and insert the ohmmeter between the two ends C and D. Thus the two resistors are connected in series but with respect to the nodes C and D between which the ohmmeter is connected, not with respect to the initial nodes A and B.

simulate this circuit

If you still want to say that they are connected in both configurations, then you can say it that way:

"The resistors are connected both in parallel (with respect to A and B) and in series (with respect to C and D)."

Note: Since CircuitLab does not have an ohmmeter, in the schematics above I have assembled it by connecting a 1mA current source and a voltmeter "in parallel":-) At this value of the current, [mV] corresponds to [ohm] and [V] to kohm. So just look at the voltmeter to read the equivalent resistance.

## Conclusion

We can talk about connecting in series or in parallel at least two loads to one source or at least two sources to one load (i.e. when there are at least three elements).

When there is only one source and one load (the simplest case), we can say that they are connected "both in series and in parallel"... but it does not make much sense. I prefer to say they are connected "to each other" or simply "connected".

The resistors are in series if the current flowing in them is the same and only 1 end is common for both resistors.

The resistors are in parallel if the voltage across them is the same and both ends of the resistors are shorted to each other.

Here, both resistor ends are shorted and voltage is the same hence they are in parallel. Connect a voltage source between the 2 terminals shown in your diagram and you will see that current in the 2 resistors is different (so, definitely not series). So, through which terminals you are looking at the circuit is critical.