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I'm coaching a Science Olympiad Circuit Lab team (both Division B (middle school) and Division C (high school)). As part of this, I'm coming up with little challenges comparable to what they might see at a tournament related to what I am teaching them at the time. I'll post some of them here in case folks are interested in trying them. I'm also open to thoughts and suggestions.
We've just gotten started, so they are learning about voltage sources and resistors and Ohm's Law, KCL, and KVL. As part of this, I'm also introducing them to the difference between ideal and real world measurements and instruments. This is the challenge I came up with to drive that home:
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The following circuit is provided to you:
You are also provided with a voltmeter that has an input resistance, RM, of 1 MΩ.
Using this meter, you are to determine the values of R1 and R2. You may not modify the circuit. You may only make voltage measurements, using the provided meter, across the labeled nodes (i.e., you can measure Vab, Vbc, and/or Vac).
The two resistors are 5% tolerance resistors whose values are in the E12 set of preferred values.
What are the colors of the bands on each resistor, left to right, with the tolerance band on the right?
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Here are the three measurement so that everyone has the same data to work with:
Vab = 3.12 V
Vbc = 317 mV
Vac = 6.70 V
Please limit yourselves to the same conditions that the teams would face, namely that they have a basic scientific calculator and pencil/paper. They can also bring a binder with whatever reference material they want, but it is unlikely that they would have anything in it that would directly help them with this problem.
Out of curiosity, I fed this problem to three LLMs (only asked them to find R1 and R2, not determine what the nominal resistance was) and half of them got it wrong.
ChatGPT: 484 kΩ, 22.5 kΩ (it gave a very detailed derivation of how it arrived at these values, which sounded very reasonable and addressed the key issues)
Gemini: 500 kΩ, 47 kΩ (it claimed that these were the nearest standard values, even though I didn't ask for that).
Perplexity: 48.7 kΩ, 1.05 MΩ
Copilot got the correct values, but it did so through an iterative approach.
Grok and DeepSeek got the correct values, but didn't indicate how it got them.
Claude: Didn't respond.
We've just gotten started, so they are learning about voltage sources and resistors and Ohm's Law, KCL, and KVL. As part of this, I'm also introducing them to the difference between ideal and real world measurements and instruments. This is the challenge I came up with to drive that home:
--------------------------------------------------------
The following circuit is provided to you:
You are also provided with a voltmeter that has an input resistance, RM, of 1 MΩ.
Using this meter, you are to determine the values of R1 and R2. You may not modify the circuit. You may only make voltage measurements, using the provided meter, across the labeled nodes (i.e., you can measure Vab, Vbc, and/or Vac).
The two resistors are 5% tolerance resistors whose values are in the E12 set of preferred values.
What are the colors of the bands on each resistor, left to right, with the tolerance band on the right?
--------------------------------------------------------
Here are the three measurement so that everyone has the same data to work with:
Vab = 3.12 V
Vbc = 317 mV
Vac = 6.70 V
Please limit yourselves to the same conditions that the teams would face, namely that they have a basic scientific calculator and pencil/paper. They can also bring a binder with whatever reference material they want, but it is unlikely that they would have anything in it that would directly help them with this problem.
Out of curiosity, I fed this problem to three LLMs (only asked them to find R1 and R2, not determine what the nominal resistance was) and half of them got it wrong.
ChatGPT: 484 kΩ, 22.5 kΩ (it gave a very detailed derivation of how it arrived at these values, which sounded very reasonable and addressed the key issues)
Gemini: 500 kΩ, 47 kΩ (it claimed that these were the nearest standard values, even though I didn't ask for that).
Perplexity: 48.7 kΩ, 1.05 MΩ
Copilot got the correct values, but it did so through an iterative approach.
Grok and DeepSeek got the correct values, but didn't indicate how it got them.
Claude: Didn't respond.
