Null Measurements Quiz

PDF page 1016: Standard measurements of voltage and current alter the circuit being measured, introducing uncertainties in the measurements. Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages so that there is no current flowing through the measuring device and, therefore, no alteration of the circuit being measured. Null measurements are generally more accurate but are also more complex than the use of standard voltmeters and ammeters, and they still have limits to their precision. In this module, we shall consider a few specific types of null measurements, because they are common and interesting, and they further illuminate principles of electric circuits.

PDF page 1016: Standard measurements of voltage and current alter the circuit being measured, introducing uncertainties in the measurements. Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages so that there is no current flowing through the measuring device and, therefore, no alteration of the circuit being measured. Null measurements are generally more accurate but are also more complex than the use of standard voltmeters and ammeters, and they still have limits to their precision. In this module, we shall consider a few specific types of null measurements, because they are common and interesting, and they further illuminate principles of electric circuits.

PDF page 1016: Standard measurements of voltage and current alter the circuit being measured, introducing uncertainties in the measurements. Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages so that there is no current flowing through the measuring device and, therefore, no alteration of the circuit being measured. Null measurements are generally more accurate but are also more complex than the use of standard voltmeters and ammeters, and they still have limits to their precision. In this module, we shall consider a few specific types of null measurements, because they are common and interesting, and they further illuminate principles of electric circuits.

PDF page 1016: Standard measurements of voltage and current alter the circuit being measured, introducing uncertainties in the measurements. Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages so that there is no current flowing through the measuring device and, therefore, no alteration of the circuit being measured. Null measurements are generally more accurate but are also more complex than the use of standard voltmeters and ammeters, and they still have limits to their precision. In this module, we shall consider a few specific types of null measurements, because they are common and interesting, and they further illuminate principles of electric circuits.

PDF page 1016: Suppose you wish to measure the emf of a battery. Consider what happens if you connect the battery directly to a standard voltmeter as shown in Figure 21.33. (Once we note the problems with this measurement, we will examine a null measurement that improves accuracy.) As discussed before, the actual quantity measured is the terminal voltage , which is related to the emf of the battery by , where is the current that flows and is the internal resistance of the battery. The emf could be accurately calculated if were very accurately known, but it is usually not. If the current could

PDF page 1016: Suppose you wish to measure the emf of a battery. Consider what happens if you connect the battery directly to a standard voltmeter as shown in Figure 21.33. (Once we note the problems with this measurement, we will examine a null measurement that improves accuracy.) As discussed before, the actual quantity measured is the terminal voltage , which is related to the emf of the battery by , where is the current that flows and is the internal resistance of the battery. The emf could be accurately calculated if were very accurately known, but it is usually not. If the current could

PDF page 1017: be made zero, then , and so emf could be directly measured. However, standard voltmeters need a current to operate; thus, another technique is needed.

PDF page 1017: be made zero, then , and so emf could be directly measured. However, standard voltmeters need a current to operate; thus, another technique is needed.

PDF page 1017: (represented by script in the figure) connected in series with a galvanometer. Note that opposes the other voltage source. The location of the contact point (see the arrow on the drawing) is adjusted until the galvanometer reads zero. When the galvanometer reads zero, , where is the resistance of the section of wire up to the contact point. Since no current flows through the galvanometer, none flows through the unknown emf, and so is directly sensed. Now, a very precisely known standard is substituted for , and the contact point is adjusted until the galvanometer again reads zero, so that . In both cases, no current passes through the galvanometer, and so the current through the long wire is the same. Upon taking the ratio , cancels, giving

PDF page 1018: connection since no current flows through the galvanometer. The unknown emf is thus proportional to the resistance of the wire segment. Because a long uniform wire is used for , the ratio of resistances is the same as the ratio of the lengths of wire that zero the galvanometer for each emf. The three quantities on the right-hand side of the equation are now known or measured, and can be calculated. The uncertainty in this calculation can be considerably smaller than when using a voltmeter directly, but it is not zero. There is always some uncertainty in the ratio of resistances and in the standard . Furthermore, it is not possible to tell when the galvanometer reads exactly zero, which introduces error into both and , and may also affect the current .

PDF page 1018: connection since no current flows through the galvanometer. The unknown emf is thus proportional to the resistance of the wire segment. Because a long uniform wire is used for , the ratio of resistances is the same as the ratio of the lengths of wire that zero the galvanometer for each emf. The three quantities on the right-hand side of the equation are now known or measured, and can be calculated. The uncertainty in this calculation can be considerably smaller than when using a voltmeter directly, but it is not zero. There is always some uncertainty in the ratio of resistances and in the standard . Furthermore, it is not possible to tell when the galvanometer reads exactly zero, which introduces error into both and , and may also affect the current .

PDF page 1018: There is a variety of so-called ohmmeters that purport to measure resistance. What the most common ohmmeters actually do is to apply a voltage to a resistance, measure the current, and calculate the resistance using Ohm’s law. Their readout is this calculated resistance. Two configurations for ohmmeters using standard voltmeters and ammeters are shown in Figure 21.35. Such configurations are limited in accuracy, because the meters alter both the voltage applied to the resistor and the current that flows through it.

PDF page 1018: measures current, and resistance is calculated as . (b) Since the terminal voltage varies with current, it is better to measure it. is most accurately known when is small, but itself is most accurately known when it is large. The Wheatstone bridge is a null measurement device for calculating resistance by balancing potential drops in a circuit. (See Figure 21.36.) The device is called a bridge because the galvanometer forms a bridge between two branches. A variety of bridge devices are used to make null measurements in circuits. Resistors and are precisely known, while the arrow through indicates that it is a variable resistance. The value of can be precisely read. With the unknown resistance in the circuit, is adjusted until the galvanometer reads zero. The potential difference between points b and d is then zero, meaning that b and d are at the same potential. With no current running through the galvanometer, it has no effect on the rest of the circuit. So the branches abc and adc are in parallel, and each branch has the full voltage of the source. That is, the drops along abc and adc are the same. Since b and d are at the same potential, the drop along ad must equal the drop along ab. Thus, 21.73 Again, since b and d are at the same potential, the drop along dc must equal the drop along bc. Thus, 21.74 Taking the ratio of these last two expressions gives