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Straight from my textbook:

If the direction of the path from initial location to final location is the same as the direction of the electric field, the potential difference is negative.

Yet a voltmeter will provide a positive reading if you put the positive lead at the location with higher potential and the negative lead at the location with lower potential. Why is this?

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2 Answers 2

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Why is this?

By convention. If you put the negative (black) lead at GND (or, e.g., battery minus) and you put the positive (red) lead at VDD (or, e.g., battery plus) the reading on the meter is positive. It's telling you how much higher in voltage the red lead is than the black lead. It's a convention.

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Yet a voltmeter will provide a positive reading if you put the positive lead at the location with higher potential

But this is precisely what one should expect given the quote in your question.

Consider a conductor with resistance $R$, oriented vertically, and with a constant downward electric (conventional) current through. In this case, there is a downward directed electric field within the conductor.

Consider placing the voltmeter leads at the same point on the conductor - the voltmeter will read zero (assuming no time varying fields).

Now, leave the black lead at that point and move the red lead to a point on the conductor below the black lead so that the red lead is moved in the direction of the electric field.

The voltmeter reads a negative value since the black lead is at a higher potential than the red lead. This is consistent with the quote in your question.

Conversely, moving the red lead to a point on the conductor above the black lead moves the red lead against the direction of the electric field and the voltmeter reads a positive value; the red lead is at a higher potential than the black lead.

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  • $\begingroup$ So in a voltmeter the conventional current flows from the black lead to the red lead? $\endgroup$
    – m0meni
    Apr 10, 2015 at 11:29
  • $\begingroup$ @AR7, for an ideal voltmeter, there is no current through. For a physical voltmeter, there is a very small current through and the direction is from the higher potential lead to the lower potential lead just as in the case of a resistor. If the red lead is connected to the higher potential, the conventional current is into the red lead and out of the black lead. $\endgroup$ Apr 10, 2015 at 11:55

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