20.11

The Measurement of Current and Voltage

Current and voltage can be measured with devices known, respectively, as ammeters and voltmeters. There are two types of such devices: those that use digital electronics and those that do not. The essential feature of nondigital devices is the dc galvanometer. As Figure 20-32a illustrates, a galvanometer consists of a magnet, a coil of wire, a spring, a pointer, and a calibrated scale. The coil is mounted in such a way that it can rotate, which causes the pointer to move in relation to the scale. As Section 21.6 will discuss, the coil rotates in response to the torque applied by the magnet when there is a current in the coil. The coil stops rotating when this torque is balanced by the torque of the spring.

Figure 20-32 (a) A dc galvanometer. The coil of wire and pointer rotate when there is a current in the wire. (b) A galvanometer with a coil resistance of RC is represented in a circuit diagram as shown here.

A galvanometer has two important characteristics that must be considered when it is used as part of a measurement device. First, the amount of dc current that causes a full-scale deflection of the pointer indicates the sensitivity of the galvanometer. For instance, Figure 20-32a shows an instrument that deflects full scale when the current in the coil is 0.10 mA. The second important characteristic is the resistance RC of the wire in the coil. Figure 20-32b shows how a galvanometer with a coil resistance of RC is represented in a circuit diagram.
The physics of an ammeter. Since an ammeter is an instrument that measures current, it must be inserted in the circuit so the current passes directly through it, as Figure 20-33 shows. An ammeter includes a galvanometer and one or more shunt resistors, which are connected in parallel with the galvanometer and provide a bypass for current in excess of the galvanometer’s full-scale limit. The bypass allows the ammeter to be used to measure a current exceeding the full-scale limit. In Figure 20-34, for instance, a current of 60.0 mA enters terminal A of an ammeter, which uses a galvanometer with a full-scale current of 0.100 mA. The shunt resistor R can be selected so that 0.100 mA of current enters the galvanometer, while 59.9 mA bypasses it. In such a case, the measurement scale on the ammeter would be labeled 0 to 60.0 mA. To determine the shunt resistance, it is necessary to know the coil resistance RC (see problem 81).

Figure 20-33 An ammeter must be inserted into a circuit so that the current passes directly through it.

Figure 20-34 If a galvanometer with a full-scale limit of 0.100 mA is to be used to measure a current of 60.0 mA, a shunt resistance R must be used, so the excess current of 59.9 mA can detour around the galvanometer coil.

When an ammeter is inserted into a circuit, the equivalent resistance of the coil and the shunt resistor adds to the circuit resistance. Any increase in circuit resistance causes a reduction in current, and this is a problem, because an ammeter should only measure the current, not change it. Therefore, an ideal ammeter would have zero resistance. In practice, a good ammeter is designed with an equivalent resistance small enough so there is only a negligible reduction of the current in the circuit when the ammeter is inserted.

The physics of a voltmeter.

A voltmeter is an instrument that measures the voltage between two points, A and B, in a circuit. Figure 20-35 shows that the voltmeter must be connected between the points and is not inserted into the circuit as an ammeter is. A voltmeter includes a galvanometer whose scale is calibrated in volts. Suppose, for instance, that the galvanometer in Figure 20-36 has a full-scale current of 0.1 mA and a coil resistance of 50 Ω. Under full-scale conditions, the voltage across the coil would be . Thus, this galvanometer could be used to register voltages in the range 0 − 0.005 V. A voltmeter, then, is a galvanometer used in this fashion, along with some provision for adjusting the range of voltages to be measured. To adjust the range, an additional resistance R is connected in series with the coil resistance RC. The value of R needed to extend the measurement range to a full-scale voltage V can be determined from the full-scale current I by applying Ohm’s law in the form (see problem 80).

Figure 20-35 To measure the voltage between two points A and B in a circuit, a voltmeter is connected between the points.

Figure 20-36 The galvanometer shown has a full-scale deflection of 0.1 mA and a coil resistance of .

Ideally, the voltage registered by a voltmeter should be the same as the voltage that exists when the voltmeter is not connected. However, a voltmeter takes some current from a circuit and, thus, alters the circuit voltage to some extent. An ideal voltmeter would have infinite resistance and draw away only an infinitesimal amount of current. In reality, a good voltmeter is designed with a resistance that is large enough so the unit does not appreciably alter the voltage in the circuit to which it is connected.

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