Voltage and Work

Current is generated by an electro-motive force (EMF). Recall that a force that is applied for a specified distance generates work. So when we have an electro-motive force move charges over a specified distance (i.e. through a wire or device), then work is being done. This work is called voltage. In particular, a volt (abbreviated as $v$ or $V$) is defined as the work done in applying a force of one newton on 1 coulomb of charge over a distance of one meter. Since one joule equals one newton-meter, this means that one volt equals one joule/coulomb.

Given a circuit element as shown in figure 18, we label one terminal ($a$) with a positive sign $(+)$ and the other terminal ($b$) with a negative sign $(-)$. We label the device with the number of volts between these two terminals. That label can be either a variable or a signed number. In figure 18, terminal $a$ is said to be $v$ volts positive with respect to terminal $b$.

Figure 18: Labelling voltage across a circuit element

Note that the label can also be a number. That number is signed (just as it was for current). For example, the two labels in figure 19 represent the same voltage across the device's terminals. In the first case, we see that terminal $a$ is 5 volts positive with respect to terminal $b$. In the second case, we see that terminal $b$ is $-5$ volts positive with respect to terminal $a$. These two cases describe the same voltage difference between the two terminals.

Figure 19: Two different labelings of the same voltage