A device that measures the potential difference across a circuit element is called a voltmeter. Because potential difference is measured across a circuit element, from one side to the other, a voltmeter is placed in parallel with the circuit element whose potential difference is to be measured.

FIGURE 28.27a shows a simple circuit in which a $17\text{Ω}$ resistor is connected across a 9 V battery with an unknown internal resistance. By connecting a voltmeter across the resistor, as shown in FIGURE 28.27b, we can measure the potential difference across the resistor. Unlike an ammeter, using a voltmeter does not require us to break the connections.

FIGURE 28.27 A voltmeter measures the potential difference across an element.

Because the voltmeter is now in parallel with the resistor, the total resistance seen by the battery is $R_{\text{eq}}=(1\text{/}17\text{Ω}+1\text{/}{R}_{\text{voltmeter}}{)}^{-1}$. In order that the voltmeter measure the voltage without changing the voltage, the voltmeter’s resistance must, in this case, be $\gg \text{17}\text{Ω}$. Indeed, an ideal voltmeter has $R_{\text{voltmeter}}=\infty \text{Ω}$, and thus has no effect on the voltage. Real voltmeters come very close to this ideal, and we will always assume them to be so.

The voltmeter in Figure 28.27b reads 8.5 V. This is less than $\epsilon$ because of the battery’s internal resistance. Equation 28.18 found an expression for the resistor’s potential difference $\text{Δ}{V}_{\text{R}}$. That equation is easily solved for the internal resistance $r$:

Here a voltmeter reading was the one piece of experimental data we needed in order to determine the battery’s internal resistance.