# Are there any general "rules of thumb" that one can follow when trying to find equivalent resistances in circuits?

Say I have a "confusing" circuit such as this one:

Where I want to find the equivalent resistance between terminals a and b. What are some tips and tricks to do this? I am asking because I find circuits like these quite confusing, it is difficult for me to spot what is in series and in parallel.

Another similar example is this circuit:

Get into the regular practice of re-drawing schematics. Also keep in mind that you can avoid some of the clutter of wires running around by selecting some convenient node as ground.

In your top schematic, I'd find this perhaps:

simulate this circuit – Schematic created using CircuitLab

I selected the wire that appeared to have the most connections (a) as ground, just because. Then I re-drew the schematic as shown above.

This allows a relatively quick check of parallel resistors.

(This re-drawing technique can be used as I did, above, to reduce clutter and more quickly see a way to get a numerical result. But it can also be used to aid in understanding more complex circuits where an author wrote a wiring diagram to aid construction rather than a schematic intended to be read well for meaning. So it's good practice to get into, just generally.)

You can also go back to your own image:

where I've circled a few items that match up, quickly.

Either way, you can more easily see that to get from a to b (or the reverse) there are three parallel paths: $$\R_3\$$, $$\R_4\$$, and $$\R_5+R_1\mid\mid R_2\$$.

As to the question about equivalent resistance, there are mathematical approaches that can be blindly applied in order to work that out. For example, you could measure the current through a short circuit across the terminals and then separately inject a $$\1\:\text{A}\$$ current and measure the voltage produced. But I don't think you were asking about that. So I'll leave it there.

The best tip I can give you is re-draw the circuit to remove the confusing diagonal lines: -

Then simplify: -

• 25 Ω is in parallel with 50 Ω
• 40 Ω is in parallel with 70 Ω

It's all about using your eyes and not getting confused by diagonal lines.

There is no general rule exactly, the important thing is to be imaginative! Or at least it can help a lot to redesign the circuit in equivalent ways. For the second example, they can be seen like this:

Resistors R1 and R3 (as well as R4 and R5) are in parallel because they both share their terminals.

"It is difficult for me to spot what is in series and in parallel."

That's your problem. You need practice visualizing series and parallel connections. Your trouble is pattern recognition and we need to give you some advice about it.

All of the previous answers gave you the same advice: redraw the circuit. That's good advice! But in the case of resistive networks, you need to redraw it with the goal of making the patterns obvious. So, here's some more advice:

1. If you haven't been introduced to it yet, allow me to introduce you to a basic engineering acronym:1 KISS! It stands for Keep it Simple, Stupid! That's not meant to be rude! It's meant to remind us2 that simple is a really good goal.

2. KISS! Whenever you see a line like the (a) line, where there are multiple connections that are spread out, but it's really all the same electrical point or connection, that should warn you that the picture has complexity that electrically doesn't exist. Learn to identify common nodes that have been spread out.

This is an important skill. Paper schematics are becoming a thing of the past, but they can teach you a thing or two! I have the schematic of an old electro-magnetic pinball machine that commonly uses straight lines that are (I kid you not...) several feet long. Along those lines hundreds of components are connected and they quite literally represent wires running all over the place connecting those components in the machine. You need to learn to recognize these common nodes for what they are: one electrically equivalent point.

1. KISS! While in real life you might find a circuit that's physically laid out with diagonal components, it'll happen a lot less than you might think. So your next task is to straighten everything out. This will help you see the patterns.

2. KISS! Look for a simple resistor pair (just two resistors) that is in a basic-series or basic-parallel configuration. Reduce the pair to a single resistor.

Examining your fist example, the 6Ω resistor doesn't appear to be paired with just one of anything, so we ignore it. If we redraw the diamond circuit so the symbols are all vertical rather than diagonal, you should be able to recognize the two parallel pairs: the 25Ω and 50Ω pair, and the 40Ω and 70Ω pair. Remember: Look for simple pairs.3

1. KISS! Reduce each pair to a single resistor, then re-examine the new schematic. In other words, repeat step #4 until all the basic pairs are gone.

After reducing the two parallel pairs, we're left with three resistors. Remember step #4! We're only looking for pairs! The simplified 40Ω/70Ω resistor is not paired with anything so we ignore it for now. On the other hand, the 6Ω resistor is in series with the combined 25Ω/50Ω resistor, so we reduce that pair.

What's left are two resistors, the 6Ω/25Ω/50Ω combined resistor and the 40Ω/70Ω combined resistor, and they're in parallel. So we invoke step #4 again and reduce them to a single resistance.

What's left over will be one of two things: either (a) it will be a single resistor or (b) what's left has no series or parallel combinations. But (b) is something to discuss in a later question.

Remember, the goal of my answer is to help you to learn how to more easily recognize basic-series and basic-parallel resistor pairs in a large(ish) circuit — like learning to see individual trees in a forest. Learn that, and no pretty picture will ever confuse you.

1Engineering is filled with quality acronyms and mnemonics like KISS! But they're not always... well... (*ahem*)... politically or socially correct. This is one of the better ones. How I was taught to remember the resistor color codes in high school would probably offend the socks off people today. But I've gotta admit... it's memorable....

2And believe me, we all need the reminder from time to time. The phrase "over-engineered" exists for a reason.

3If you don't have trouble recognizing basic-series and basic-parallel pairs, skip this footnote. If, on the other hand, you're having trouble remembering what a basic-series or basic-parallel pair looks like, open this page to remind yourself.