30 DC Voltmeters and Ammeters

Analog Meters: Galvanometers

Many electrical measuring instruments originally displayed their readings using a moving pointer rather than a digital display. These instruments are known as analog meters. Although digital meters are now more common because they are easier to read and generally more accurate, analog meters are still useful for understanding how electrical measurements are made and are occasionally used in laboratories and industrial equipment.

The heart of most analog meters is a device called a galvanometer, represented by the symbol G. A galvanometer contains a small coil of wire suspended in a magnetic field. When current flows through the coil, magnetic forces cause it to rotate, moving a needle across a calibrated scale. The greater the current, the greater the needle deflection, making the instrument capable of measuring electrical current.

Two characteristics determine how a galvanometer behaves:

• Internal resistance (r), which is the electrical resistance of the galvanometer itself.
• Current sensitivity, which is the current required to produce a full-scale deflection of the needle.

For example, suppose a galvanometer has a current sensitivity of 50 μA. A current of 50 μA moves the needle to the end of the scale, while 25 μA produces a half-scale reading.

If this galvanometer has an internal resistance of 25 Ω, the voltage required for full-scale deflection is determined using Ohm's law:

This tiny operating voltage illustrates why galvanometers are extremely sensitive devices. By adding carefully chosen external resistors, the same galvanometer can be converted into either a voltmeter or an ammeter capable of measuring much larger voltages or currents.

Using a Galvanometer as a Voltmeter

A galvanometer can be converted into a voltmeter by placing a large resistor R in series with it, as shown in Figure 30.4. The added resistor limits the current through the galvanometer, allowing the instrument to measure much larger voltages without damaging its sensitive moving coil.

Suppose we wish to build a voltmeter that gives a full-scale reading at 10.0 V using the same galvanometer described above (25 Ω internal resistance and a full-scale current of 50 μA). The total resistance required is

[latex]R_{\text{tot}}=R+r=\frac{V}{I}=\frac{10.0\ \text{V}}{50\ \mu\text{A}}=200\ \text{k}\Omega[/latex]

Therefore, the required series resistor is

[latex]R=R_{\text{tot}}-r=200\ \text{k}\Omega-25\ \Omega\approx200\ \text{k}\Omega[/latex]

Because the series resistor is so much larger than the galvanometer resistance, the 25 Ω internal resistance has a negligible effect on the total resistance.

If only 5.0 V is applied, half the current flows through the galvanometer, producing a half-scale deflection. This proportional relationship allows the instrument to measure voltage accurately over its designed range.

Voltmeters designed for multiple voltage ranges simply switch different series resistors into the circuit. Larger voltage ranges require larger series resistances to keep the galvanometer current below its safe operating limit.

Using a Galvanometer as an Ammeter

The same galvanometer can also be converted into an ammeter by placing a very small resistor in parallel with it. This resistor, called the shunt resistor, provides an alternate path for current. Since the shunt has a very low resistance, nearly all of the current flows through it, while only a small, safe current passes through the galvanometer.

Suppose we wish to construct an ammeter that gives a full-scale reading at 1.00 A using the same galvanometer (25 Ω internal resistance and 50 μA full-scale current).

Because the galvanometer and shunt resistor are connected in parallel, the voltage across each is the same. Setting these voltage drops equal leads to the required shunt resistance:

[latex]R=r\frac{I_G}{I}=(25\ \Omega)\frac{50\ \mu\text{A}}{0.999950\ \text{A}}=1.25\times10^{-3}\ \Omega[/latex]

This extremely small resistance allows almost all of the current to bypass the galvanometer, protecting its delicate moving coil while enabling the instrument to measure currents many thousands of times larger than it could alone.

Like voltmeters, many ammeters include multiple measurement ranges. These are obtained by switching different shunt resistors into the circuit. Smaller shunt resistances allow the meter to measure larger currents.

Clinical Application

Modern medical equipment often measures currents that are only a few microamperes or less. Instruments used in electrophysiology, pacemaker testing, and neural recording rely on electronic circuits that perform the same function as the shunt resistor: they safely redirect current while allowing highly sensitive components to measure only a tiny fraction of the total current.

Taking Measurements Alters the Circuit

Every electrical measuring instrument becomes part of the circuit when it is connected. As a result, no measurement is perfectly noninvasive. A voltmeter or ammeter always changes the circuit slightly because it introduces its own resistance. Good instrument design minimizes this effect, but it can never be eliminated completely.

Understanding how measuring instruments affect a circuit is especially important in healthcare and biomedical engineering. For example, electrocardiographs (ECGs), electroencephalographs (EEGs), and other physiological monitoring devices are designed with extremely high input resistance so that they measure tiny electrical signals without significantly changing the voltages produced by the body.

Consider first a voltmeter, which is always connected in parallel with the component whose voltage is being measured. If the voltmeter has a resistance that is much larger than the resistance of the component, only a tiny amount of current flows through the meter. The equivalent resistance of the parallel combination is then almost identical to the resistance of the component itself, so the circuit behaves essentially the same as if the voltmeter were not connected (Figure 30.6a).

If, however, the voltmeter's resistance is comparable to that of the component being measured, a significant amount of current is diverted through the meter. The equivalent resistance of the parallel combination decreases, changing the current distribution throughout the circuit. As a result, the voltage across the component is no longer the same as it was before the measurement, producing an inaccurate reading (Figure 30.6b).

An ammeter is connected in series with the component whose current is being measured. Since components in series carry the same current, the ammeter measures the current flowing through the branch. Ideally, the ammeter should have an extremely small internal resistance so that adding it to the circuit produces almost no change in the total resistance (Figure 30.7a).

If the ammeter's resistance is not negligible, however, adding it in series increases the total resistance of the branch. The increased resistance reduces the current, meaning that the meter changes the very quantity it is trying to measure (Figure 30.7b).

An even more serious problem occurs if an ammeter is connected incorrectly. Because its resistance is intentionally very small, connecting an ammeter directly in parallel across a voltage source or a component effectively creates a short circuit. This can cause a very large current to flow through the meter, potentially blowing an internal fuse, damaging the instrument, or even damaging the circuit.

One way to reduce measurement errors is to use more sensitive galvanometers or, in modern instruments, highly sensitive electronic amplifiers. Greater sensitivity allows engineers to build voltmeters with extremely large input resistance and ammeters with extremely small internal resistance, minimizing their effect on the circuit.

Although practical limits exist, modern digital instruments can achieve extremely high accuracy. The remaining measurement error often comes not from poor instrument construction, but from the unavoidable fact that every measurement requires the instrument to interact with the system being measured.