Essay, Research Paper
Construction of Direct Current Voltmeters and AmmetersTheory:Whenever working with electrical systems, the measurement of both current and voltage can be very important. Without accurate measurements of current and voltage, calculations of resistance and other pertinent values could not be completed. This need for measuring electric values in circuit lead to the construction of ammeters and voltmeters. The ammeter measures the electric current flowing into its terminals, and the voltmeter measures the potential difference applied to its terminals (Ohanian 715). Current, the flow of an electric charge, is measured in amperes (A), with 1 Amp being equal to 1 Coulomb of charge moving past a point in 1 second. The current is therefore related to voltage where current is flowing through a conductor or some other component of a system across which is a difference in electric potential. Therefore, electric potential is measured in volts (V). A galvanometer is a device used in the construction of both ammeters and voltmeters (Serway and Faughn 623).The galvanometer is defined as an instrument used to determine the presence, direction, and strength of an electric current in a conductor. When an electric current is passing through the conductor, the magnetic needle tends to turn at right angles to the conductor so that its direction is parallel to the lines of induction around the conductor and its north pole points in the direction in which these lines of induction flow. In general, the extent to which the needle turns is dependent upon the strength of the current. In the first galvanometers, a freely turning magnetic needle was hung in a coil of wire; in later versions the magnet was fixed and the coil made movable. Modern galvanometers are of this movable-coil type and are called d’Arsonval galvanometers (after Ars ne d’Arsonval, a French physicist). If a pointer is attached to the moving coil so that it passes over a suitably calibrated scale, the galvanometer can be used to measure quantitatively the current passing through it. Such calibrated galvanometers are used in many electrical measuring devices. The DC ammeter, an instrument for measuring direct current, often consists of a calibrated galvanometer through which the current to be measured is made to pass. Since heavy currents would damage the galvanometer, a bypass, or shunt, is provided so that only a certain known percentage of the current passes through the galvanometer. By measuring the known percentage of the current, one arrives at the total current. The DC voltmeter, which can measure direct voltage, consists of a calibrated galvanometer connected in series with a high resistance. To measure the voltage between two points, one connects the voltmeter between them. The current through the galvanometer is then proportional to the voltage as is indicated through the pointer reading. Ohm s Law is the principle that ties these two concepts together. Ohm s Law states that although current is directly proportional to the voltage, the flow through the system also experiences some resistance from the materials carrying the electricity. Just as internal friction (viscosity) affects fluid flow, the internal resistance of materials affects the flow of electrons (Wilson 523). The phenomenon occurring here leaves the current in a position of inverse proportionality to the resistance of the materials. This is the simplified form of Ohm s Law. This law can be demonstrated in equation form as I= V/R or V= IR. An ammeter uses a slightly derived version of the Ohm s Law equation. Since the series is in parallel, the galvanometer and the shunt resistor are exposed to a constant value for voltage. The equation form of this is RgIg = RsIs. The term Rg is the known resistance in the galvanometer and Ig is the current required to produce full deflection of the current. The terms Rs and Is are the resistance and current in the shunt, respectively. Since the current in the shunt is unknown, the current in the galvanometer must be subtracted from the current in the system. This is represented, in terms of Rs, by the equation: Rs= Rg (Ig/ I- Is). For voltmeters, the interpretation of Ohm s Law is a little different from the equations derived for ammeters. In this case, a multiplier resistance is placed in series with the galvanometer. This requires that the galvanometer resistance (Rg) be added to the resistance of the multiplier (Rm). This sum is then multiplied to the current in the galvanometer that produces a full deflection. In terms of voltage (V), the equation is stated as: V= Ig (Rm + Rg). With these simple equations, the ammeter and voltmeter can be used to effectively monitor current and potential difference in a circuit.Procedure: The instrument to be used is the Sargent Welch S- 30305 Galvanometer. It contains a galvanometer meter movement and keys to select either of two resistors in series with the galvanometer movement. The resistance of the coil, Rg, is 35d with 10% error. As a galvanometer, a current of 500mA will result in a full-scale deflection (Ig). These are the two values that need to be known in order to construct any ammeter or voltmeter you desire. Galvanometer: To use this meter as a galvanometer, connect it in series with the current source to be measured. A 500 mA current will result in a full-scale deflection. Figure 1 is a representation of the component key arrangement in the meter. The conducting strip and the two resistors are bypassed. Therefore, for a galvanometer, depress the left key. As a first exercise, you will check to see if Ig is 500 mA. Wire the galvanometer in series with a multimeter and the large resistance provided, Figure 2. Set the multimeter to the 3mA DC range (500 mA= 0.5mA). Connect the circuit as shown below to the DC power supply with the rheostat turned down. Slowly turn up the rheostat until the galvanometer (left key depressed) reads full scale. Read Ig from the multimeter. Figure 1 component and key arrangement. Figure 2.Voltmeter: To make the galvanometer into a voltmeter, a resistance needs to be put in series with the meter. The size of the necessary resistance, Rm, should be calculated from manipulation of the derived equation used for voltmeters. Remember that Rg= 35d and that Ig= 500 mA.First, we want to make a 100mV voltmeter. Put this value in for V and calculate the resistance of the multiplier. You should have gotten an answer of 165d. When the right key is depressed, a 162d resistor is put into series with the meter. This then makes a 100mV voltmeter from the galvanometer. Second, using the voltmeter equation, calculate the necessary resistance of the multiplier, to make a 5V voltmeter. When no keys are depressed, the 10Kd resistor is automatically in series with the galvanometer. The answer you should have gotten from the equation is 10,000d. It is thus a 5V voltmeter with no keys depressed. The 35d, galvanometer resistance, can be ignored because of its relatively small value.
Using the DC part of the power supply, a comparison can be made between this meter and a standard voltmeter. Wire up the circuit, Figure 3, using the multimeter set on 250mV and check different voltages against the constructed 100mV voltmeter. Similarly, set the multimeter on 5V and check this with the constructed 5V voltmeter. Figure 3.Ammeter: To construct an ammeter, a shunt resistance will have to be put in parallel with the galvanometer, Figure 4. Its value can be calculated using the equation derived for it in the theory section. For our meter, once the Shunt resistance is in place, the right- hand key should be depressed to make the ammeter work.The right-hand key puts the 162d resistance in series with the galvanometer coil. Thus, galvanometer resistance in the equation is 200d rather than 35d. The current in the galvanometer is still 500 mA. The larger value of galvanometer resistance is used here to allow a larger value of the resistance shunt. Sensitivity is lost by doing this and in most ammeters only the internal resistance of the meter movement is used as the shunt resistance.Calculate the shunt resistance necessary for the ammeter to be both 0.5A and 1.0A. Substitute these values of I into the equation and calculate the shunt resistance. Using the ohmmeter provided, compare the resistance of the 0.5A and the 1.0A shunt with what you calculated. These are small so the ohmmeter might not be very accurate.Notice that in the 0.5A ammeter, still only 500 mA flows through the actual meter movement. The reason we could call full-scale 0.5A is that we designed the shunt so 0.4995A will flow through it. The same is true of the 1.0A ammeter except the shunt was designed t carry 0.9995A at full scale.Using the DC power supply, we can compare the standard ammeter of the multimeter with the ammeters constructed. Wire the standard ammeter, the 10d resistance and the constructed ammeter in series. Turn up the power and compare your meter with the multimeter. Be sure to depress the right key.Compare the constructed 0.5A ammeter and the 1.0A ammeter with the readings on the multimeter. Figure 4.Data:Set-up# Constructed Voltmeter Term Values GalvanometerResistanceRg (Ohms) GalvanometerCurrentIg (amps) Voltage In The SystemV (volts) Calculated MultiplierResistanceRm (Ohms)1 Rg= 35d Ig= 500mA V= 100mV Rm= 165d2 Rg= 35d Ig= 500mA V= 5V Rm= 9,965dSet-up# Constructed Ammeter Term Values GalvanometerResistanceRg (Ohms) GalvanometerCurrentIg (amps) Current In The SystemI (amps) Shunt ResistanceRs (Ohms)1 200d Ig= 500mA I= 0.5A Rs= 0.2d2 200d Ig= 500mA I= 1.0A Rs= 0.1dCalculations: These are the equations and calculations for the constructed voltmeter. These are the equations and calculations for the constructed ammeter.Results: In the voltmeter construction section, the value of the galvanometer resistance was 35 Ohms for both situations. The value of the galvanometer current for both situations was 500 micro amps. The value of the voltage in the system for the first situation was set at 100 millivolts. The system voltage value for the second situation was set at 5 volts. The value for the resistance of the multiplier was found to be 165 Ohms when the voltage was 100 millivolts. The value for the resistance of the multiplier, when the voltage was changed to 5 volts, was found to be 9,965 Ohms. In the ammeter construction part of the laboratory, the value of the galvanometer resistance for both situations was set at 200 Ohms. The value of the current in the galvanometer was set at 500 micro amps for both situations. The current in the system for the first situation was set at 0.5 amps. The current for the second situation was changed to 1.0 amps. The shunt resistance for the first situation was found to be 0.2 Ohms. The shunt resistance for the second situation was found to be 0.1 Ohms. Percent Error Analysis: This laboratory dealt with set values for the terms used in the experiments. Due to this fact, the experimental values calculated were found to be the exact same value of the accepted values. This left no potential for error. The equipment was of good enough quality to match the theoretical values with extreme precision. Therefore there is no calculable percent error. The percent error is then said to be 0%.Conclusion:A. As stated in the percent error analysis section, there is no significant error in this laboratory. All of the values set in the procedure were easily duplicated with the laboratory equipment. B. This laboratory was based on the construction of ammeters and voltmeters from galvanometers. By setting up the circuits in the described ways, the galvanometer was easily converted into either an ammeter or a voltmeter. The values set in the procedure were incorporated into the systems and resulted in the exact values that the procedure predicted. The placing of a shunt resistor in parallel with the galvanometer, as explained in the theory section, worked in creating the ammeter and producing accurate values. The placement of a multiplier resistance in series with the galvanometer, as described, also completed the construction of the voltmeter. The values attained through this were also accurate. At anytime that the values of the set values were altered, the end results were found to be of the correct proportions to the system and the basic principles found in Ohm s Law. The galvanometer proved to be as useful as it was invented to be.
1. Ohanian, Hans C. Physics. 2nd ed. W. W. Norton & Company, New York, 1989.2. Serway, Raymond A and Faughn, Jerry S. College Physics. 5th ed. Saunders College Publishing, Orlando, 1999.3. Wilson, Jerry D. College Physics. 2nd ed. Prentice Hall, New Jersey, 1994.