# Two voltmeters in parallel measure these different voltages

## Homework Statement

I'm currently studying induction law and circuits with inductors. I came however with the following circuit:

[1]: https://i.stack.imgur.com/ghaiE.png

## Homework Equations

3. The Attempt at a Solution [/B]

Now my text says the following:

"Unlike what your intuition might tell you, oscilloscopes 1 and 2 will measure different voltages. For a N-turn coil you will get

$$u' = N\frac{d\phi}{dt}$$
$$u'' = (N-1)\frac{d\phi}{dt}$$
"

How is that possible? I'm having trouble on understanding why this results are obtained. I understand (I think) that the oscilloscopes will measure different values because the induction E field is non conservative. But I don't understand their computation. How does the left side sees one coil less than the right side?

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RPinPA
Homework Helper
I might be wrong, but if the wires are physically laid out as the circuit diagram shows, then the wires connecting up to ##u''## form a loop in the opposite direction around the coil, thus inducing an EMF in those wires which is in the opposite direction to one turn of the coil.

berkeman
Mentor
Unlike what your intuition might tell you, oscilloscopes 1 and 2 will measure different voltages. For a N-turn coil
I have two words for you... "Z-Lead Probes"

(Oh, and that should be "For an N-turn coil"...

http://i.stack.imgur.com/cbLXI.png

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gneill
Homework Helper
Gold Member
I have two words for you... "Z-Lead Probes"

(Oh, and that should be "For an N-turn coil"...

http://i.stack.imgur.com/cbLXI.png

View attachment 233070
@berkeman With the OP's sketch, the problem is not the leads.(It is because EMF's are being generated depending on how the wires are routed). This is a very good example of Professor Walter Lewin's paradox. Please see the video in post 52 of the "link" that I posted. Professor Walter Lewin explains it completely in his video.

Last edited:
berkeman