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In my first course on Electrical Engineering, we have an experiment in the Electrical lab that asks us to verify the Thevenin theorem and the Superposition theorem and cross-check our results with our calculations on paper.

Here are the circuit diagrams, straight from my lab manual.

Thevenin's theorem:

Thevenin's theorem

Superposition theorem:

Superposition theorem

Question:

I was asked, during my post-lab viva, to explain why the errors for the Superposition theorem were greater than those of Thevenin's. I answered saying that both theorems were dependent on the linearity of the circuits for their functioning, and the increased current in superposition theorem was heating up the rheostats and promoting non-linear behavior. However, she was dissatisfied. She said there was something more important that I was missing. I couldn't figure it out. This was months ago, and I still wonder about it but haven't been able to come up with an alternative explanation.

TL;DR Why is Thevenin's theorem more accurate than the superposition theorem, experimentally?

Note: Please forgive the incorrect labeling of the DPDTs in the first schematic. I am redrawing them.

William R. Ebenezer
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    Could you clarify the schematics a bit? From first glance, the best guess I would have is that all those current meters in the superposition measurement cause error. – Joren Vaes May 23 '20 at 13:06
  • @JorenVaes Would you like me to redraw them? Or should I include an explanation/procedure? Sorry about the diagrams though. I know it looks like a rat's nest. – William R. Ebenezer May 23 '20 at 13:08
  • What is the resistance of your ammeters? – Andy aka May 23 '20 at 13:13
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    @Andyaka I don't know that, unfortunately. I do remember that they were portable MC ammeters with 2 ranges. And it's nice to see you again :) – William R. Ebenezer May 23 '20 at 13:18
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    LOL @WilliamR.Ebenezer if you check the ammeter's resistance it might be 1 ohm and this will cause a significant error because the proof of the superposition theorem uses 3 ammeters as opposed to 1 in the Thevenin proof. More meters also means more likely that accumulated errors creep in. – Andy aka May 23 '20 at 13:21
  • @Andyaka Yes, it makes sense. – William R. Ebenezer May 23 '20 at 13:22
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    Others have mentioned errors caused by ammeter resistance. Here's a different source of error: Superposition requires **adding** or **subtracting** two readings, each having reading error. If those two measurements are similar in value, relative error climbs significantly. Thevenin doesn't have this problem. – glen_geek May 23 '20 at 14:46

1 Answers1

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Why is Thevenin's theorem more accurate than the superposition theorem, experimentally?

The last word in this question is the most important one.

To verify the superposition theorem you measure your circuit voltages and currents several times. Each measurement implies a measurement error. The error is generally a number of fixed digits and a percentage.

Other errors are also introduced: your measurement equipment is not necessarily linear - the devices introduce possibly non linear impedances.

Every measurement will also include thermal noise. You will add this up in superposition, but measure it only once for a global measurement.

So once you add up all these errors in superposition, your total error will be bigger than when you make a single measurement.

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