# Why are these capacitor voltages opposite polarity?

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1. Apr 11, 2016

### kostoglotov

1. The problem statement, all variables and given/known data

2. Relevant equations

$$V_L = L\frac{dI_1}{dt}$$

$$V_L + V_1 + V_2 + V_{R1} = 0$$

3. The attempt at a solution

Just using basic KVL, shouldn't $V_L = -V_2 - V_1 - V_{R1}$ and so therefore we should get

$$\frac{dI_1}{dt} = \frac{-V_2 - V_1 - V_{R1}}{L}$$ and not

$$\frac{dI_1}{dt} = \frac{V_2 - V_1 - V_{R1}}{L}$$

which is what the question is asking us to find...it would appear then that the capacitors have opposing polarities...why?

2. Apr 11, 2016

### Staff: Mentor

I think you are right, the terms on the right hand side in (4) should all have negative signs.

3. Apr 11, 2016

### donpacino

It entirely depends on how you define the capacitor voltages. My guess, they (being the book authors) defined the voltages in a different way and didn't actually write it down through an oversight.

4. Apr 11, 2016

### kostoglotov

No, this is not from a textbook, this is from an assignment.

I1 and I3 are going in the same direction around the loop that we use in KVL though, no matter how you set it up.

I've only followed the current directions indicated. I haven't chosen my own directions independent of the problem.

5. Apr 11, 2016

### donpacino

same thing, whoever defined the assignment did a bad job

does not change what I said... saying they have V1 backwards without defining V1 is useless, same goes for V2 and VR1.

My guess, they defined V2 vertically with the positive end on the top and neglected to mention it.

6. Apr 11, 2016

### Staff: Mentor

It isn't up to us to arbitrarily define the voltages. Once you have shown eqn (2) is true, and eqn(3) is true, you have already been manipulated into defining the voltages the way the authors intend. The upshot is that eqn(4) needs that extra - sign.

7. Apr 11, 2016

### Staff: Mentor

kostoglotov, in future could you reduce the size of images. You can probably see how your over-size image in this thread causes the browser to shrink the page (and along with it, the text) so the full image fits onto the screen?

8. Apr 11, 2016

### donpacino

good point... only [(2) and (3)] or [(4)] can be correct

then assuming op presumed 2 and 3 are correct, then yea 4 is missing a (-) sign.

9. Apr 11, 2016

### kostoglotov

No worries. I don't notice what you're seeing, perhaps because I'm using a large monitor?...I'll keep it in mind.

10. Apr 11, 2016

### kostoglotov

Exactly, eqn 4 needs to have that missing - sign if we are to accept the previous equations. So, I need to take this back to the tutor or professor.