Electronics > Beginners
Calculating value of resistors in parallel
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kulky64:

--- Quote from: ArthurDent on January 02, 2019, 11:25:50 pm ---I first assumed no real hotplate would have a diamond shaped resistor configuration because it would probably make the switching too complex. Next I rounded the values so they were more common and easier to visualize. I then noticed that 60+90+180=330 so I guessed there might be just 3 resistors, not 4. Then I tried different series combinations to see if I could get a combination that fit the data given and found one. On the first go around I copied the last equation wrong and that slowed me down until I realized that it was 2*4-1*2 which would put the 3 resistors in parallel to give 30 ohms where I originally got 90 because I had 2*4-1 so I was missing one jumper.

It actually took a while to see what to do and there were a few dead ends before I got it right. No higher math was used, only the parallel resistor equation. It is simple once you see how it's done.

--- End quote ---

Except you didn't come up with anything new. All numbers what you posted are already in OPs first post.
ArthurDent:
kulky64 - "Except you didn't come up with anything new. All numbers what you posted is already in OPs first post."

You may have missed it but the question was what was the values of the four individual resistance elements, not the measured terminal resistance. I showed that the original assumption of the diamond shape was wrong and showed the correct wiring of the resistors. I also determined that the values of the "four" individual resistance elements were 60, 90, 180, and no fourth resistor, in case you missed that point. These values were not initially known because it was assumed that there was some configuration that put resistor elements in parallel and the values of individual elements were unknown. I didn't see your solution.
kulky64:
I thik OPs assumption on the configuration of the resistors is correct, because he provided redundant (more than necessary) measurements that are supporting each other.
soldar:
ArthurDent, that was very ingenious of you and I thank you!  I sheepishly admit that I should have thought of that because I have seen similar heaters but instead of the elements being enclosed they are open, of the spiral wire that gets red hot type, and they have the configuration you discovered. I don't know why I didn't think of it. Sometimes intuition and ingeniousness beats raw math and algebra.

Doing it by algebra brute force should have yielded an extremely high or infinite value for the assumed fourth element.

The problem with the values as they are is that the different combinations of switching sometimes results in repeated values of resistance and power so of 16 possible combinations of the four switches, 6 result in zero power, six result in unique values and three result in repeated values.

Two things that come to my mind now is that it would be interesting to use a thermal camera to see the distribution of heat on the hot plate as the different elements are used and also that for combinations that result in the same power it may be preferable to use the one that uses more resistors so that the heat is more distributed and it would prolong the life of the heater.

All very interesting. Thank you!

E.T.A. I did a quick calculation of the resistance and power for each combination of switches but chances are there might be some mistake because my head hurts. I will review it again tomorrow.

By the way, this was/is a hotplate that was controlled by a rotary switch that failed and I could not find a replacement so I fitted four switches as shown and I have a card with a table showing the switch combinations and corresponding power. The most common combinations I know by heart now. :)
The Electrician:
soldar, as you said in the first post, it's a problem with 4 equations in 4 unknowns:

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