EE 442. Lab Experiment No. 2 1/17/2007. Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading

Transcription

1 EE 442 Lab Experiment No. 2 1/17/27 Introduction to the Measurement of Voltage, Current, Resistance; and Voltmeter Loading 1

2 I. INTRODUCTION The purpose of this experiment is to become familiar with a multimeter and to use it to make voltage, current, and resistance measurements. A final aspect of this lab is to understand how a piece of test equipment affects the circuit it is connected to. II. PRELIMINARY BACKGROUND READING A. INSTRUMENT DESCRIPTION General Remarks All voltmeters, ammeters, and ohmmeters make measurements by means of a two terminal connection to a circuit or circuit element under test. All voltmeters, ammeters, and ohmmeters have at least two jacks into which only two test probes are inserted. If there are more than two jacks on the face of a particular meter, there is usually an indication of some sort, next to each jack, to inform the user which jacks to use to measure a particular quantity. Many times a voltmeter, an ammeter, and an ohmmeter are combined into one package called a multimeter. Multimeters come in two flavors: analog and digital. Analog meters have a display that consists of a needle which points to a number scale. These meters have function and range controls which allow the user to select what kind of meter (voltmeter, ammeter, or ohmmeter) the multimeter will be and what range of values the meter will read. Digital multimeters typically have a LCD or LED display and in many cases are auto-ranging. That is, the meter will automatically select the most appropriate range for making the measurement. In this lab either an analog or a digital meter can be used with little difference in operation. Voltmeter A voltmeter measures electrical potential between its terminals. Voltmeters are always placed in parallel with the circuit or circuit element where the voltage measurement is desired. Since the voltage across two or more parallel elements is the same, the voltage measured by the meter will be the same as the element to which the meter is connected. When using a non-auto-ranging meter, select the highest possible range and reduce the range as necessary until the desired level of accuracy is reached. Always start with a range higher than the expected value to prevent damage to the meter. Ammeter An ammeter measures the current that flows between its terminals. An ammeter is always placed in series with the circuit or circuit element where the current flow is of interest. Since the current in each element 2

3 of a series circuit is the same, the current flow through the meter will be the same as the current flow to the element of interest. Never connect an ammeter in parallel unless you intend to measure the short circuit current of a circuit or circuit element and you have made sure that destructive current levels won t be reached. When using a non-auto-ranging meter, select the highest possible range and reduce the range as necessary until the desired level of accuracy is reached. Always start with a range higher than the expected value to prevent damage to the meter. Ohmmeter An ohmmeter measures the electrical resistance between its terminals. An ohmmeter is connected to the circuit or circuit element of interest after the element of interest has been isolated from the rest of the circuit. The element of interest has to be isolated from the rest of the circuit so that its resistance value isn t obscured by the resistance values of the other circuit components connected to the element of interest. Never connect an ohmmeter to an energized circuit or the meter could be destroyed. There is an additional caveat for an analog ohmmeter; it has to be zeroed every time the resistance range is changed. To zero the analog ohmmeter, touch its probes together (the needle will deflect to approximately full scale, use the zeroing knob to adjust the needle to read zero. The analog meter can now be used in this particular range. Zeroing Needle-Indicating Meters Before meters with mechanical needle displays can used the displays need to be zeroed. This procedure is performed with the piece of equipment turned off and the equipment placed in the position where it will be used. Use a screw driver to turn the adjusting screw near the base of the needle until the needle is on the zero mark. Precautions 1. Never leave a multimeter on any ohms scale. If the meter must left on, set it to its highest DC voltage range. 2. Never make a resistance measurement on a circuit element while the circuit is energized. 3. Always turn test equipment off (if possible) when it is not in use. 4. Never connect any meter to any circuit before adjusting the function and range controls appropriately. 3

4 B. METER LOADING Discussion Ideally, a meter would have no effect on the circuit that it is measuring. In reality, however, it is not possible to make a measurement without having some effect on what is being measured. These effects can usually be ignored, but a good engineer will make sure that assuming the meter to be ideal is a valid assumption. Since a voltmeter is connected in parallel to a circuit or circuit element being measured, it should ideally have an infinitely high resistance. This condition is necessary so the parallel combination of the meter and the circuit element do not result in a different total impedance than what the circuit element originally had. Since an ammeter is connected in series with a circuit or circuit element were the current is of interest, it should have no resistance and resemble a short. As a short, the ammeter would have no effect on the total impedance of the circuit or circuit element being measured. It should be obvious now why an ammeter shouldn t be connected in parallel to the circuit or circuit element of interest. The ammeter is a short circuit which could draw excessive currents. In reality, neither voltmeters nor ammeters have ideal resistances. A typical voltmeter will have a resistance on the order of a million to several million ohms. A typical ammeter will have a resistance on the order of tenths to hundredths of an ohm. When performing circuit analysis, the meter should be replaced with its approximate resistance. In this manner, the non-idealities can be accounted for. If a voltmeter is placed in parallel with a circuit or circuit element and the difference between the resistance of the circuit or circuit element and the resistance of that circuit or circuit element parallel combined with the resistance of the meter are insignificant, then the effects of the meter can be neglected. A similar statement can be made for the ohmmeter. Example As an example of voltmeter loading, consider the following circuit (Figure 1) where voltage measurement across the 3 kω resistor is desired. 4

5 R1 1k R2 2k 12Vdc V1 A + B R3 3k VAB - Figure 1 Series circuit Preliminary calculations suggest that the voltage from points A to B will be 6V. Assume a voltmeter with an internal resistance of 6 kω is connected across terminals A and B (Figure 2). R1 1k R2 2k 12Vdc V1 A + R3 3k VAB RM 6k Voltmeter B - Figure 2 Series circuit being loaded by a voltmeter 5

6 It can easily be determined, as shown below, that the new resistance between terminals A and B has decreased to 2 kω. R Eq = RM R3 R + R M 3 = 6kΩ 3kΩ 6kΩ+ 3kΩ = 2kΩ The difference between the resistance of the branch without the meter and the resistance of the branch with the meter is 1 kω which is certainly significant. Using the voltage divider formula, we can see that the meter reads a significantly different voltage than what was expected through preliminary calculations. k v = 2 Ω AB 12 = 48 1kΩ+ 2kΩ+ 2kΩ Note the V AB would change if any finite resistance were connected across terminals A and B. Voltmeter loading always occurs and is simply a matter of degree. C. RESISTOR COLOR CODES The values of most of the resistors in you lab kit are indicated by color bands. These color bands are painted on the body of each resistor and are decoded in the following manner: Look at the resistor. There will be a group of color bands clumped together at one end and a lone band at the other. Orient the resistor so the lone band points to the right and the clumped bands point to the left. The resistor can be read left to right using the guidelines listed below. 1. The first color band indicates the first digit in the numerical value of the resistance. 2. The second color band gives the second digit in the numerical value of the resistance. Any subsequent bands before the last band in the clump give subsequent digits in the numerical resistance value. 3. The last color band in the clump gives the number of zeros that follow the first digits. 4. The lone color band on the right end gives the tolerance. Note: Tolerance is the amount by which the actual resistance can be different from the color-coded value and it is given in percent. For 6

7 example, a 1 Ω resistor with a +-1% tolerance can have an actual resistance value between 9 Ω and 11 Ω. The color codes for digits and tolerance are given in Figure 3. Your instructor might suggest a convenient mnemonic which may help you to remember the code. (Image courtesy Figure 3 Resistor color codes III. PRELAB EXERCISES A. Current Calculations In part D of the lab exercise section (V) of this experiment, current measurements will be made on a series connected circuit. To provide a basis for comparison, those currents will be calculated as a preliminary problem. Calculate the current i for different values of resistance R (Figure 4) and record below. 7

8 R1 1k i 1Vdc V1 R Figure 4 Circuit for current calculations R = Ω, R = 5 kω, R = 1 kω, i =. i =. i =. B. Voltmeter Loading Calculations In part E of the lab exercise section, the following circuit (Figure 5) will be used to investigate voltmeter loading. Calculate V AB and record below. R1 1k A 4Vdc V2 R2 1k + VAB B - Figure 5 Voltmeter loading circuit V AB =. The meters will be represented as resistances with the digital multimeter having a resistance, in its DC mode, of 1 MΩ. The resistance of the analog multimeter will be 5 kω when it is used on its 2.5 Volt range. The resistance of the digital multimeter is found 8

9 from its specifications sheet while the resistance of the analog multimeter is calculated by multiplying its sensitivity (found on its specifications sheet) by the range it is being used in. ( 2kΩ / V 2. 5V = 5kΩ ) Calculate the voltages these two meters would read if each were separately connected to terminals A and B. Record your results below. V ABDMM =. V ABAMM =. Finally, calculate V AB read by each voltmeter if the two 1 kω resistors were replaced by two 1 kω. V ABDMM =. V ABAMM =. IV. LABORATORY EXPERIMENTS In the first three parts of the performance section of this experiment an analog and a digital multimeter will be used. Compare the readings of both meters and report any major discrepancies to you lab instructor. A. DC Voltage Measurement Set the DC supply to a voltage of your choosing using the meter on the face of the supply. Write down this voltage value. Use both an analog and a digital meter to measure the DC voltage of the supply. Remember to start in the highest range and work your way down when using an analog meter. (The most accurate measurement is made when the needle is in the middle of the scale). V DCSUPPLY =. V DMM =. V AMM =. B. AC Voltage Measurement Set the signal generator to output a sinusoid 1 V p, 1 khz. Measure this voltage with the scope, analog multimeter, and digital multimeter. Note, the multimeters read volts RMS. RMS stands for root-mean-square which is defined as follows 9

10 v RMS = T 1 T 2 vt () dt. A more formal presentation about RMS will be given later. For vp now, you just need to know that for a sine wavev =. Your 2 multimeters should both read about 7.7 V rms. C. Resistance Measurement Choose a 1% (or a 5% tolerance if you don t have a 1%) tolerance resistor from your kit. Use the color bands on the resistor body to determine the nominal resistance for the device. Use both an analog and a digital multimeter to measure the actual resistance of the device. Is the measured value within the allotted tolerance? R NOMINAL =. R DMM =. R AMM =. RMS D. Current Measurement Build the following circuit (Figure 6). R1 1k RM Ammeter i 1Vdc V1 R Figure 6 Circuit for current measurement Measure the current with both analog and digital meters. Use the following resistor values for R: Ω, 5 kω, 1 kω. (Hint: both meters can be placed in series with each other and the current 1

11 through each will be the same.) Remember to start in the highest current range and work you way down. R = Ω, R = 5 kω, R = 1 kω, i AMM =. i DMM =. i AMM =. i DMM =. i AMM =. i DMM =. E. Voltmeter Loading Consider the circuit below (Figure 7). R1 1k A 4Vdc V2 R2 1k + VAB B - Figure 7 Voltmeter loading circuit Measure the V AB with a digital multimeter and record below. Compare this result with the preliminary result. V ABDMM =. Remove the digital multimeter and replace with an analog meter set on its 2.5 Volt range. Record V AB below and compare this result with the preliminary result. V ABAMM =. Reconnect the digital multimeter across terminals A and B with the analog multimeter still connected. Record the reading of the digital multimeter below. Did the reading of the analog multimeter change from its previous value? Why? Now disconnect the analog multimeter and note the reading of the digital multimeter. Why did this reading change? V ABDMM =. 11

12 Swap the 1 kω resistors for 1 kω resistors and measure V AB with both meters again, compare these results with you preliminary values. V ABDMM =. V ABAMM =. Explain why these voltage readings were the same as, or different from, the readings taken from the circuit composed of 1 kω resistors. V. CONCLUSION You should now be an expert at the using the digital multimeter. You should also be familiar with the effects of a meter on the circuit it is measuring. Finally you should be able to use the color bands on a resistor to determine its value. 12