During the lab portion of your circuits and electronics courses, you will routinely use a digital multimeter to measure voltage and current. Voltage and current measurements are quite distinct and require the meter to behave very differently in the two cases. In this reading application we will review the proper way to connect the digital multimeter for voltage and for current measurements. We will also review the ideal model for the meter while performing a voltage measurement and its ideal model while performing a current measurement.

Recall that voltage refers to the potential difference between two points in a circuit. A voltmeter has two connection terminals, one typically denoted with a “V” and the second denoted “COM” for the common terminal. These two terminals allow one to measure a difference in potential. A voltage measurement requires us to connect the meter between the two points of interest without disturbing the behavior of the circuit. That is, when we make a voltage measurement, the meter should not change how the circuit operates.

Let’s consider the circuit of Figure 1 consisting of an ideal independent voltage source and three resistors in series.

Let’s say that we wish to know the voltage difference between nodes B and C, that is the voltage across resistor R_{2}. Before describing the voltage measurement, we should be clear that each of the four elements shares the same current. The value of I in the circuit is 150 mA in this case (V_{S}/R_{total} =9V/60Ω = 0.15A). By Ohm’s law we know that the voltage across a given resistor is the product of the current associated with the resistor and its resistance. It is critically important therefore, that the current in the circuit is not changed when we place the voltmeter in the circuit to measure a potential difference. * Voltage measurements are made in parallel* with the element or elements across which we want to know the potential difference. Clicking on Figure 1 will show a voltmeter properly connected to measure the voltage drop across resistor R

With Figure 1 showing the voltmeter, notice the current labeled I_{meter}. For the meter to not alter the current in the circuit, I_{meter} must equal zero. This observation gives us insight into the model for an ideal voltmeter -- * the ideal voltmeter must behave like there is an open circuit between its two terminals*. While an open circuit can sustain a voltage difference, it will carry no current. Clicking on Figure 1 again will show the meter replaced with its ideal model. Since we know that the current in the circuit is 150 mA, Ohm’s law reveals that the voltage drop across R

Figure 2 again shows the voltmeter connected to measure the voltage drop across resistor R_{2}, this time the measured voltage is displayed. The voltmeter has two terminals -- does it matter which terminal we connect to node B and which to C? Remember that potential difference has a magnitude and a polarity and voltmeters allow us to determine this polarity. Click on Figure 2 to switch the meter connections in measuring the voltage between nodes B and C. In doing so, we see that the meter now reads - 3V. A positive reading on a voltmeter indicates that its common terminal (typically labeled COM) is connected to the lower potential node whereas a reading of a negative voltage indicates that the meter’s common terminal is connected to the higher potential node. In the next tab we consider how a DMM set to measure current behaves.

An ammeter has two connection jacks, one typically denoted with an “A” and the second denoted “COM” for the common terminal. Recall that current is a measure of charge flow -- we want an ammeter to observe this charge flow without interfering with it. A properly functioning ammeter could not act like an open circuit for an open circuit allows no charge flow and thus no current. What element ideally allows charge flow without impeding it? A simple wire -- a short circuit! * Therefore, an ideal ammeter may be modeled with a short circuit between its two terminals.* Let’s say that we wish to measure the current in the series circuit we have been considering. Clearly, we don’t want to introduce a new path in which charge could flow and so we must place the meter in the path of the charge flow we wish to probe.

There is only one current in the circuit of Figure 3 and so we could break the circuit anywhere and insert the meter. In the case of Figure 3, the meter has been placed between resistors R_{2} and R_{3}. Clicking on Figure 3 will show the ammeter replaced with its ideal model -- a short circuit between its terminal terminals. Clearly, an * ideal* ammeter will not perturb the circuit.

Figure 4 shows the circuit with the meter displaying the current, a positive 150 mA. This current is simply the source voltage divided by the equivalent resistance seen by the ideal voltage source. The ammeter has two terminals – does it matter which terminal we connect to the leg of R_{2} and which to the leg of R_{3}? Recall that current has a magnitude and a direction and ammeters allow us to determine the direction. Click on Figure 4 to switch the meter connections in measuring the current in the circuit. In doing so, we see that the meter now reads - 150 mA. A positive reading on an ammeter indicates that current leaves the meter’s common terminal (typically labeled COM), whereas a reading of a negative current indicates that the current is directed into the meter’s common terminal.

We have looked at the models of ideal voltmeters and ammeters. All meters have some impact on circuit performance but unless we are measuring very small voltages and currents, the impact of the meter should be minimal. In the final tab you will have a chance to solve a couple of circuits to determine the values shown on the meters. **Remember that the first step in solving such circuits is to redraw them, replacing the meters with their ideal models.**

Consider the circuit of Figure 5 in which a voltmeter is wired in series with a circuit consisting of a voltage source and three resistors. ** We should immediately see that this is the incorrect way to wire a voltmeter as the meter changes the functioning of the circuit.** Nevertheless, let’s see if we can figure out what voltage will be displayed by the meter. The first step is to redraw the circuit, replacing the voltmeter with its ideal model. The values for the elements are given in the figure’s caption. Determine the voltage that will be displayed and submit your response using the provided box.

What is the value of voltage displayed on the meter?