Electronics > Beginners
Calculating value of resistors in parallel
soldar:
This is a purely mathematical & Kirchoffian problem.
I have the heating element of a hot plate and it has four terminals. I am assuming internally it has four resistors (heating elements) connected as the sides of a square or diamond. I suppose it could have two more elements connected in diagonal but I think this is very unlikely. I have access only to the four corner terminals and not to the individual elements.
If I had the values of the four resistors I could easily calculate the value of the different combinations but here I have the opposite problem: measuring only from the four corners determine the value of the individual resistors. I start writing equations and they soon get so complex it is hopeless.
Measuring between terminals 2 and 3 the meter reads 327 ohm
Measuring between terminals 1 and 4 the meter reads 181 ohm
Measuring between terminals 2 and 4 the meter reads 90.4 ohm
Measuring between terminals 1 and 3 the meter reads 62.5 ohm
We have four unknowns and we would need four equations so the above should be enough to resolve the problem.
From the above it seems that R1 would be the lowest value, then R3, then R4 and R2 the highest.
If I connect terminals 1 & 2 together and measure resistance to 4 I get 60.3 Ohm. etc
If I connect 1&2 and measure to 3&4 then I get 30.8 ohms.
Can anyone help me calculate the resistance of the four individual elements?
If using equations directly is too complicated I wonder if it could be solved using recursive iterations with a spreadsheet.
Zero999:
https://en.wikipedia.org/wiki/Wheatstone_bridge
mbest:
I'm still learning, when I see a textbook problem like this, I immediately start thinking algebraic substitution or linear equation solving.
First step I would take it to collect the measurements in a more useable form, and/or create circuit diagrams for all the measurements.
Measurement 1 of 327 ohm is from a circuit where R2 is in parallel with R1,R3,R4 in series, etc...
327 = R2 // R1+R3+R4
90.4 = R3 // R1+R2+R4
181 = R4 // R1+R2+R3
62.5 = R1 // R2+R3+R4
60.3 = R3 // R4
61.7 = R1 // R2
46.9 = R1 // R4
89.6 = R2 // R3
30.8 = R1+R2 // R3+R4
Write the calculation for each circuit and then solve for R1, by substitution, until only a single variable remains?
Does this seem like the correct approach? I tried to solve it this way, but came up a bit short on the algebra, probably need more coffee.
soldar:
--- Quote from: Zero999 on January 02, 2019, 04:29:22 pm ---https://en.wikipedia.org/wiki/Wheatstone_bridge
--- End quote ---
I cannot see how that helps at all. Maybe I am missing something. Maybe you could add an explanation rather than a bare link.
soldar:
mbest, that is what I tried to do but got bogged down in the algebra. It seems it is not easy.
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