# 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:

: 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 #### Attachments

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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.

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• berkeman