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Voltmeters and Ammeters
Voltmeters and ammeters are used to measure voltage and current, respectively. Voltmeters and ammeters measure the voltage and current, respectively, of a circuit. Some meters in automobile dashboards, digital cameras, cell phones, and tuner- amplifiers are voltmeters or ammeters. Voltmeters A voltmeter is an instrument that measures the difference in electrical potential between two points in an electric circuit. An analog voltmeter moves a pointer across a scale in proportion to the circuit’s voltage; a digital voltmeter provides a numerical display. Any measurement that can be converted to voltage can be displayed on a meter that is properly calibrated; such measurements include pressure, temperature, and flow. In order for a voltmeter to measure a device’s voltage, it must be connected in parallel to that device. This is necessary because objects in parallel experience the same potential difference.
Ammeters An ammeter measures the electric current in a circuit. The name is derived from the name for the SI unit for electric current, amperes (A). In order for an ammeter to measure a device’s current, it must be connected in series to that device. This is necessary because objects in series experience the same current. They must not be connected to a voltage source — ammeters are designed to work under a minimal burden, (which refers to the voltage drop across the ammeter, typically a small fraction of a volt).
galvanometer’s needle — in other words, the maximum current that the instrument can measure. For example, a galvanometer with a current sensitivity of 50 μA has a maximum deflection of its needle when 50 μA flows through it, is at the scale’s halfway point when 25 μA flows through it, and so on. If such a galvanometer has a 25-Ω resistance, then a voltage of only V = IR = (50 μA) (25 Ω) = 1.25 mV produces a full-scale reading. By connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter to measure a broad range of voltages or currents. Galvanometers as Voltmeters A galvanometer can function as a voltmeter when it is connected in series with a large resistance R. The value of R is determined by the maximum voltage that will be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a 25-Ω galvanometer with a 50-μA sensitivity. Then 10 V applied to the meter must produce a current of 50 μA. The total resistance must be:
Rtot=R+r=VI=10V50μA=200kΩ,Rtot=R+r=VI=10V50μA=200kΩ, or:
R=Rtot−r=200kΩ−25Ω≈200kΩ.R=Rtot−r=200kΩ−25Ω≈200kΩ.
(R is so large that the galvanometer resistance, r, is nearly negligible. ) Note that 5 V applied to this voltmeter produces a half-scale deflection by sending a 25-μA current through the meter, and so the voltmeter’s reading is proportional to voltage, as desired. This voltmeter would not be useful for voltages less than about half a volt, because the meter deflection would be too small to read accurately. For other voltage ranges, other resistances are placed in series with the galvanometer. Many meters allow a choice of scales, which involves switching an appropriate resistance into series with the galvanometer. Galvanometers as Ammeters The same galvanometer can also function as an ammeter when it is placed in parallel with a small resistance R , often called the shunt resistance. Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those that would produce a full-scale deflection of the galvanometer. Suppose, for example, we need an ammeter that gives a full-scale deflection for 1.0 A and that contains the same 25-Ω galvanometer with 50-μA sensitivity. Since R and r are in parallel, the voltage across them is the same. These IR drops are: IR = IGr
so that: IR=IGI=Rr.IR=IGI=Rr.
Solving for R, and noting that IG is 50 μA and I is 0.999950 A, we have:
R=rIGI=(25Ω) 50 μA0.999950A=1.25×10−3Ω.R=rIGI=(25Ω)50μA0.999950A=1.25×
Null Measurements Null measurements balance voltages so there is no current flowing through the measuring devices that would interfere with the measurement.l measurements. Null Measurements Standard measurements of voltage and current alter circuits, introducing numerical uncertainties. Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages, so there is no current flowing through the measuring device and the circuit is unaltered. Null measurements are generally more accurate but more complex than standard voltmeters and ammeters. Their precision is still limited. The Potentiometer When measuring the EMF of a battery and connecting the battery directly to a standard voltmeter, as shown in, the actual quantity measured is the terminal voltage V. Voltage is related to the EMF of the battery by V = emf − Ir , where I is the current that flows and r is the internal resistance of the battery.
using a voltmeter directly, but it is not zero. There is always some uncertainty in the ratio of resistances Rx/Rs and in the standard EMFs. Furthermore, it is not possible to tell when the galvanometer reads exactly zero, which introduces error into both Rx and Rs , and may also affect the current I. Resistance Measurements Many so-called ohmmeters measure resistance. Most common ohmmeters apply a voltage to a resistance, measure the current, and calculate the resistance using Ohm ‘s law. Their readout is this calculated resistance. Simple configurations using standard voltmeters and ammeters have limited accuracy, because the meters alter both the voltage applied to the resistor and the current flowing through it. The Wheatstone bridge is a null measurement device for calculating resistance by balancing potential drops in a circuit. The device is called a bridge because the galvanometer forms a bridge between two branches. A variety of bridge devicesare used to make null measurements in circuits. Resistors R 1 and R 2 are precisely known, while the arrow through R 3 indicates that it is a variable resistance. The value of R 3 can be precisely read. With the unknown resistance Rx in the circuit, R 3 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. Since b and d are at the same potential, the IR drop along ad must equal the IR drop along ab. Again, since b and d are at the same potential, the IR drop along dc must equal the IR drop along bc. This equation is used to calculate the unknown resistance when current through the galvanometer is zero. This method can be very accurate, but it is limited by two factors. First, it is not possible for the current through the galvanometer to be exactly zero. Second, there are always uncertainties in R 1 , R 2 , and R 3 , which contribute to the uncertainty in Rx.
