Potential Difference and the Notion of a Reference Node
One of the fundamental concepts that we consider in circuit analysis is potential difference. We commonly refer to potential difference as voltage difference or just voltage. The potential difference between two points in a circuit is the energy it takes to move one Coulomb of charge between the two points. The units of potential difference therefore are Joules per Coulomb (i.e. energy per unit charge), or simply Volts. The Volt is abbreviated a ‘V.’
A critically important point to be made is that potential difference is measured between two points in a circuit. Consider for example, the circuit in Figure 1 in which a digital multimeter (DMM) is set up to measure the potential difference across resistor R2 – that is, the voltage difference between nodes B and C in the circuit. If we want to measure the voltage drop across R3, that is the potential difference between points C and D in the circuit, we would move the probes accordingly. Clicking on Figure 1 will toggle the image between a measurement of VBC (voltage from node B to node C) and VCD (voltage from node C to node D).
Figure 1: A demonstration of the measurement of the potential difference between nodes B and C. The value shown on the meter assumes the following component values: VS = 9V, R1 = 1Ω, R2 = 2Ω, and R3 =3Ω.
Remember, when we quote a value of voltage or potential, it is really the potential difference between two points in a circuit. In the next tab, we will consider the notion of a reference to facilitate quoting values of potential difference in describing an entire circuit.
Consider the circuit of Figure 2. We could describe the voltage levels in the circuit by listing the voltage differences between each adjacent node as suggested in the figure. This becomes quite cumbersome with larger circuits and we seek a simple way to describe each node with some value of potential. Remembering that we are truly speaking about potential differences – what we really need is a common point of reference. Shown in Figure 3 are three common symbols one will find to denote such a reference.
Figure 2: An electric circuit consisting of generic circuit elements. The voltage difference across each element is shown.
Figure 3: Three common symbols used to denote the reference point (node) in an electric circuit. In a laboratory setting, these symbols may mean much more than a simple reference.
In the circuits we solve this semester, we will take the three symbols to mean the same thing, namely, the reference. Arbitrarily, we set the voltage at the reference to 0V. We can now quote the voltage at each node in the circuit with respect to this common point! To see how this works, consider Figure 4 which once again shows the circuit of Figure 2, along with the same circuit but in which voltage levels are given with the help of a reference. Typically, the location of the reference will be given to us, but occasionally it won’t be. In such cases one may place the reference in a location to facilitate calculations. Clicking on Figure 4 will toggle between the various locations one could place the reference. Make an effort in each case to verify that the voltage values at the nodes make sense regardless of the location of the reference.
Figure 4: LEFT: The circuit of Figure 2 and RIGHT: The generic electric circuit of Figure 2 in which a reference has been chosen. We may now express the voltage at each node with respect to this reference. Clicking on the figure will move the location of the reference. See if you can relate the voltage values at each node to the potential differences displayed in Figure 2 regardless of the location of the reference.
It should be noted that in the lab, ground is more than a simple reference to aid in calculations. The ground connection of an instrument typically goes to “earth ground” through the third prong of the cable connecting the instrument to power outlet. We will talk about this more in lab. For now, simply treat the node at which one of the symbols of Figure 3 is placed as the reference node and take the voltage at this node to be 0V.
To see if you understand how the reference node works, consider the generic electric circuit of Figure 5 and answer the questions that follow.
