Get the latest tech news
Ohmaps: your image montage is a resistor network
Occasionally there’s a lovely moment when I’m working on a problem and I realise I’m also looking at some other thing that seems completely unrelated. It’s like a metaphor made flesh. These ‘isomorphism moments’ can be powerful because the two seemingly unrelated things can give you insights into each other. Their commonality encourages you think about the essential thread running through them both. This post details one of these moments I had recently.
The growing or shrinking of the rect for \(\text{R}_1\) in order to join it to \(\text{R}_0\) is preserving the dimension at the vertical edge, which is current in this scheme (and in this way KCL is observed). Note that the act of growing or shrinking the rectangle for \(\text{R}_1\) also affects the voltage (width), which is correct in the electricity world; the ratio for resistance is maintained this way. Likewise, if you vertically edge-wise join two rectangles representing resistors, it’s a similar accounting; but the horizontal dimension is preserved this time, which corresponds to voltage (and in this way KVL is observed).
Or read this on Hacker News