As mentioned previously, whenever a voltmeter (or multimeter) is used to measure a voltage, it is really measuring a voltage difference between the two points in the circuit to which the leads to the voltmeter are attached. Thus, any reading from the voltmeter is really a reading of DV. Also, recall that this voltage difference is the difference between the voltage in the circuit at the point connected to the red lead minus the voltage at the point connected to the black lead:
DVvoltmeter = Vred – Vblack .
It is possible to define a point in a circuit to be zero volts—this point is then called electrical ground (or just “ground”).
Let’s consider two points in a circuit that we label A and B. If we connect the red lead of a voltmeter to point B and the black lead to point A, then the voltmeter reading would be telling us DVAB = Vred – Vblack = VB – VA. Remember that a voltage difference between two points is really just telling us about how much energy it would take for us to move a charge from the initial point (A) to the final point (B) while combatting the electrical forces in the region of the two points.
Sometimes, however, just a voltage at a point is given: for example, VD = 12 V. What this means is simply that the voltage difference between point D and ground (remember that Vground = 0 V) is 12 V:
VD = DVground,D = VD – Vground = 12 V – 0 V = 12 V.
To measure the voltage at a point, we thus only have to put the red lead of the voltmeter at the point of interest, and the black lead at the ground point in the circuit. Be sure to keep in mind, however, that such a voltage at a point is really a voltage difference, as always.
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