winnie
Senior Member
- Location
- Springfield, MA, USA
- Occupation
- Electric motor research
I am writing up some background for the single phase or two phase discussion. Please hold off on the comments until I have the whole thing up (at least a week).
-Jon
Instantaneous Voltage
The first thing to understand is that Voltage is a relative measurement. Voltage always is a measurement between two points. In this sense, voltage is analogous to height. You _cannot_ say that a point is at a particular height; you can only say that the point is at a height relative to another point. A _very_ common trick with relative measurements such as height or voltage is to select a reference level, and to use this reference level as one of the two points needed for the measurement. With height, a common reference is 'mean sea level'. When we talk about the height of a mountain, we usually mention the height versus mean sea level...but we could use another reference entirely, as long as we specify it. For buildings, we generally describe how tall they are as the height versus the surrounding terrain, not the height above MSL. Both are entirely correct descriptions of the height of a point at the top of the building, but with different values because different reference points are used.
Voltage is a measurement of the amount of work required to move a charge from one location to another, or equivalently the power associated with a flow of current from one location to another. For example, if the flow of 1 amp from one point to another results in the dissipation of 100W of power, then there is a 100V potential difference between those two points. By definition, the voltage of a single point is undefined. You can only measure the voltage _between_ two points.
When you have a system with N points under consideration, you have a total of N*(N-1) possible pairs of points between which you could measure voltage. Note: this includes both a given pair of points and its inverse; the voltage from A to B is exactly the negative of the voltage from B to A, and N*(N-1) includes both directions. As you can see, with more that a few points, the number of voltage pairs to consider becomes tremendous. For example, in a 3 phase, 4 wire delta with center tap there are actually 12 different possible voltage measurements.
But we do the same simplification trick with voltages that we can do with heights. We pick a single point (or set of points of constant potential) and call this our reference. We then measure the voltage between our points of interest and this reference. This reference point is entirely arbitrary, but as long as we keep the same reference point for all of our calculations, we will get the correct results. Most commonly for electrical work, we use _ground_ as the reference. Physicists like to use 'infinity' as the reference 'point', the idea being that a test charge out very far away cannot interact with your system, but this is just a mathematical trick; 'infinity' as the reference point is just as valid as 'ground', though harder to reach with your test leads.
With a reference point selected, we can define (with suitable measurement) the voltages of all the other points in the system. Each point in the system is identified with a voltage number, but this number is really the voltage from the reference to that point, not the voltage of the single point itself.
Okay. So far in the above we have only defined DC or instantaneous voltage. We've given no consideration to AC voltage, nor to current. But already you can see how the specific voltage numbers that you get will depend upon the voltage reference point that you select. The voltages that you measure between any pair of points in the system will remain the same, no matter which voltage reference you select, but the numbers that are 'voltage between this point and the reference' will change as the reference changes.
-Jon
Instantaneous Voltage
The first thing to understand is that Voltage is a relative measurement. Voltage always is a measurement between two points. In this sense, voltage is analogous to height. You _cannot_ say that a point is at a particular height; you can only say that the point is at a height relative to another point. A _very_ common trick with relative measurements such as height or voltage is to select a reference level, and to use this reference level as one of the two points needed for the measurement. With height, a common reference is 'mean sea level'. When we talk about the height of a mountain, we usually mention the height versus mean sea level...but we could use another reference entirely, as long as we specify it. For buildings, we generally describe how tall they are as the height versus the surrounding terrain, not the height above MSL. Both are entirely correct descriptions of the height of a point at the top of the building, but with different values because different reference points are used.
Voltage is a measurement of the amount of work required to move a charge from one location to another, or equivalently the power associated with a flow of current from one location to another. For example, if the flow of 1 amp from one point to another results in the dissipation of 100W of power, then there is a 100V potential difference between those two points. By definition, the voltage of a single point is undefined. You can only measure the voltage _between_ two points.
When you have a system with N points under consideration, you have a total of N*(N-1) possible pairs of points between which you could measure voltage. Note: this includes both a given pair of points and its inverse; the voltage from A to B is exactly the negative of the voltage from B to A, and N*(N-1) includes both directions. As you can see, with more that a few points, the number of voltage pairs to consider becomes tremendous. For example, in a 3 phase, 4 wire delta with center tap there are actually 12 different possible voltage measurements.
But we do the same simplification trick with voltages that we can do with heights. We pick a single point (or set of points of constant potential) and call this our reference. We then measure the voltage between our points of interest and this reference. This reference point is entirely arbitrary, but as long as we keep the same reference point for all of our calculations, we will get the correct results. Most commonly for electrical work, we use _ground_ as the reference. Physicists like to use 'infinity' as the reference 'point', the idea being that a test charge out very far away cannot interact with your system, but this is just a mathematical trick; 'infinity' as the reference point is just as valid as 'ground', though harder to reach with your test leads.
With a reference point selected, we can define (with suitable measurement) the voltages of all the other points in the system. Each point in the system is identified with a voltage number, but this number is really the voltage from the reference to that point, not the voltage of the single point itself.
Okay. So far in the above we have only defined DC or instantaneous voltage. We've given no consideration to AC voltage, nor to current. But already you can see how the specific voltage numbers that you get will depend upon the voltage reference point that you select. The voltages that you measure between any pair of points in the system will remain the same, no matter which voltage reference you select, but the numbers that are 'voltage between this point and the reference' will change as the reference changes.
