Basic Series/Parallel connection understanding

Question

I am just starting out with electronics and I have understood that there is something fundemental I just cant seem to figure out about parallel and series connections. I am having a lot of trouble figuring out the connection type between resistors in some circuits.

Here is the example from which I base my question:

After too much time I figured it might be correct to redraw said network as such:

which then is clear as per which connections are parallel and which in series.

So my question is:

• Have I made any mistakes in re-drawing my network?
• Is there any foolproof way of telling which connections are in parallel and which in series in any given network?

Answer 1

Have I made any mistakes in re-drawing my network?

Yes. You left R2 out of the re-drawn network entirely.

Is there any foolproof way of telling which connections are in parallel and which in series in any given network?

If two components are end-to-end so that all the current flowing out of one must flow into the other, then they are in series.

If two components are connected at both ends, so that the exact same voltage must appear across both components then they are in parallel.

Sometimes you will find that neither situation applies, and then you will have to use more complicated analysis methods that you will probably learn shortly.

Answer 2

It's easier to comprehend when the resistor network is redrawn this way.

R3 and R5 are in parallel. The equivalent of R3 and R5 in parallel is in series with R2.

And so on.