How is the plus and minus voltage sign for resistance voltage drops for battery voltages and currents be determined?

Answer 1

The plus and minus voltage sign for resistance voltage, drops for battery voltages, and drops for currents is determined by convention. You can use whatever method you want - so long as your use is consistent, your analytical results will be correct for you.

The commonly accepted convention, however, is best. This way, other people reviewing your results will not be confused unless, of course, they use an atypical convention.

Electric current flow is electron flow. The battery terminal marked "negative", or the cathode, is the source of electrons, and those electrons are drawn to, and flow towards, the "positive" terminal, or anode.

Consider a simple circuit, consisting of a battery in series with a resistor. Draw the battery on the left, with the anode up. Draw the resistor on the right. Connect the anode to the top of the resistor, and the cathode to the bottom of the circuit. (Actually, this is also a parallel circuit, with the battery in parallel with the resistor. It depends on how you see it, because this is a simple circuit.)

Current flows out of the bottom (cathode, negative) battery terminal, into the bottom of the resistor, up through the resistor to its top, over to the left, and into the top (anode, positive) battery terminal, and down through the battery, completing the circuit at the cathode. This is counter-clockwise, if you have drawn the circuit as stated.

If you place a voltmeter across the battery, you will see that the anode (top) is more positive than the cathode. If you place a voltmeter across the resistor, you will see that the top is more positive than the bottom. It does not matter if you measure across the battery or the resistor, the voltage will be the same. If you place the voltmeter across the wire on the bottom, or across the wire on the top, you will see that the voltage is zero.

With the preliminaries out of the way, now to the convention.

Current flow is counter-clockwise, from cathode to anode. If you were to draw a current arrow, you could draw it counter-clockwise, down through the battery and up through the resistor. You would label the first point that the current encounters (the bottom of the resistor) as negative, or minus. As the current goes through the resistor, it becomes more positive, so you would label the top of the resistor positive, or plus. Go over to the anode. That is also plus. The current is made more negative due to the battary being a source, rather than a load, so the cathode is minus.

These pluses and minuses are relative to each other, and they are also relative to some common reference point, said point by convention being the cathode. In this simple circuit, there is only one point that has any voltage different than the cathode, and that is the anode, so this distinction might be vague.

Consider then, the case where the resistor is actually two resistors in series. Again, the bottom resistor starts minus on its connection to the cathode, it becomes more positive as the current goes up, making the top of the bottom resistor plus. The bottom of the top resistor is minus, because current is flowing into it, and it becomes more positive as the current goes up, with the top of the top resistor plus.

When you measure voltage across an element, you see the voltage for that element. If, instead, you measure the voltage relative to the common reference point, and there is more than one element between the voltmeter's leads, you add up the voltage rises or drops to figure out what to expect. In fact, this is the basis for Kirchoff's voltage law - that the signed sum of the voltage drops around a series circuit always adds up to zero.

So, this preliminary convention is that current flow leaves the minus terminal of a voltage or current source, and enters the minus terminal of a voltage or current load. It then enters the plus terminal of a voltage or current source, and leaves the plus terminal of a voltage or current load.

Now, to confuse you, another convention states that current flows from plus to minus, not from minus to plus. This means that current leaves the plus terminal of a source, and enters the plus terminal of a load, and it enters the minus terminal of a source and leaves the minus terminal of a load.

It does not really matter which convention you use. The positions of the plus and minus signs will be the same - its just that the current arrow will point in the opposite direction - in this example, clockwise instead of counter-clockwise. What is important is to be consistent in your use of the plus or minus sign as the current enters and leaves a source or a load.

The convention of current flow is arbitrary. So long as you are consistent in your application, you will get the correct results.

It is generally accepted that current flow is electron flow, which means that current flows from the negative side of a voltage or current source towards the positive side.

Often, however, current is considered to flow from positive to negative. While this makes perception in circuit analysis more straightforward, it does not change the analytical results.