# How do I simplify and calculate the resistance of this circuit?

I am studying this circuit:

and I tried to simplify it like so:

I'm confused since there is a wire atop A surrounding the "square" wire. I calculated its maximum resistance as 63.77 ohms. Any help especially how to simplify it is greatly appreciated.

Edit: Thank you for all the responses! It's quite clear that I still am confused about the topologies of series and parallel, can anyone recommend videos for it so I can understand is better?

• Hint: What's the lowest resistance path from the 100 ohm resistor to A and B. How have you redrawn it? Does it still look right? What's the shortest distance from 90 ohms ..., from 12 ..., from ... There's a built-in schematic tool on the editor toolbar if it helps. Double-click to edit component properties. 'R' to rotate. Tip: Draw a horizontal rail across the top of your schematic for 'A' and one at the bottom for 'B'. Mar 19, 2021 at 14:34
• Your approach to simplify first - it is excellent. There are three resistors completely shorted out - you can eliminate those entirely from your solution. Mar 19, 2021 at 14:42
• I think you should finish your redrawn schematic. Label all nodes on both schematics. Label all resistors on both schematics. See if something doesn't pop out at you when you do that. Mar 19, 2021 at 14:48
• Yes, this is definitely a "puzzle" schematic to make sure students can understand parallel/series topologies, as well as identify "degenerate" components.
– W5VO
Mar 19, 2021 at 15:11

simulate this circuit – Schematic created using CircuitLab

Think you can work it out, now?

Always, always, always get into the practice of re-drawing schematics. Especially, when they look like yours.

It's a silly artificial puzzle question meant to teach you how schematics work.

The point A exists all along the line where it was drawn. As long as you can follow a line in a schematic without passing a component, you are still in the very same spot electrically. So for example the dot in the upper right corner is as much 'A' as the dot where the signal 'A' is connected. So we have:

simulate this circuit – Schematic created using CircuitLab

This means you also have B all over the schematic. The only resistors with any current passing through them are those who go between A to B. From there on, you can calculate the parallel resistance of those resistors that go between A and B. Those which don't are just there to confuse.

1/R1 + 1/R2 + ... 1/Rn = 1/Rp

Then you can replace the whole schematic with a single resistor between A and B.

There are only 3 nodes. The nodes 3, 18, 6 meeting are not connected to the current flowing path.