LABORATORY 2 MEASUREMENTS IN RESISTIVE NETWORKS AND CIRCUIT LAWS


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1 LABORATORY 2 MEASUREMENTS IN RESISTIVE NETWORKS AND CIRCUIT LAWS The objective of this experiment is to provide working knowledge of the ammeter, voltmeter, and ohmmeter as well as their limitations in making measurements in resistive networks. In addition to the above, verification of Ohm's Law, Kirchhoff's Voltage and Current Laws, as well an introduction the potentiometer and current and voltage division will be presented. A voltmeter is used for measuring voltages. For the measurement of a voltage across a circuit component, a voltmeter must be connected in parallel with the component so that the voltage across the voltmeter is the same as that across the component. An oscilloscope is a special type of voltmeter. (The operation of an oscilloscope is presented in Laboratory 6.) An ammeter is used for measuring currents. For the measurement of a current flowing through a circuit component, an ammeter is connected in series with the component so that the current flowing through the ammeter is the same as that flowing through the component. In other words, the branch must be disconnected, the ammeter inserted, and the branch reconnected. An ohmmeter is used for measuring resistances of resistors. If a resistor is in a circuit, one end of the resistor must be disconnected from the circuit before a resistance measurement is made. Then, the ohmmeter leads are connected to the resistor terminals. Never connect an ohmmeter to an energized circuit because the reading will be incorrect. In measuring a voltage or a current, always start at a high range setting and work down to a suitable range. This safety precaution will prevent the meter from being destroyed by an unexpected high voltage or current. Also, when connecting a meter to a circuit, always consider the effect of the meter on the circuit. Clearly, a meter should not significantly affect the circuit operation. Otherwise, the presence of the meter will change the electrical quantity being measured, and thus have an erroneous reading. Ideally, a voltmeter or an oscilloscope should have an infinite input resistance, and an ammeter should have a zero internal resistance. Since such meters do not exist, the effect of inserting a meter should always be accounted for by considering the meter resistance as a part of the circuit. Consider the circuit shown in Fig. 2.1 in which a voltmeter with input resistance R v is connected to measure the voltage across resistor R 2. Ideally, the reading of the voltmeter should be, by voltage division,
2 R2 Vs (R1 + R2 ) The actual reading, however, will be (R R ) 2 V Vs (R 1 + R 2 R V ) in which R 2 R v designates the resistance of the parallel combination of R 2 and R v. Since RR v 2 R 2 R v = (R v + R 2 ) As the resistance R v approaches infinity, the voltmeter reading approaches the correct value. Thus, it is desirable for the voltmeter input resistance to be much greater than the resistance of the resistor that the voltmeter is connected across. Then, the voltmeter will not load the circuit. Figure 2.1 Now consider the circuit shown in Fig. 2.2 in which an ammeter with internal resistance R A is connected to measure the current flowing in resistor R L. The current, I, measured by the ammeter will be: V S I = ( R A + R L ) instead of the correct value of I = V S R L
3 Clearly, though, the ammeter reading will approach the correct value as R A approaches zero. Thus, the internal resistance of an ammeter should be negligible in comparison with the resistances of the resistors that it is in series with. Fig. 2.2 As mentioned, an analysis should be made of the new circuit consisting of the circuit under test plus the resistance of the meter. Often, this analysis will show that the meter has a negligible effect on the circuit operation. Then, the meter resistance can be ignored. This is the desired condition, but one which should be assumed only after careful consideration. Procedure: Ohm s Law 1. Construct the circuit of Fig. 2.3, using for R a resistor of unknown resistance obtained from the laboratory TA. Connect an ammeter to measure the current through R and a voltmeter to measure the voltage across R. Remember to connect the ammeter in series and the voltmeter in parallel. Also, be sure to use the DC scales on the meters. V s is a variable source of voltage. Fig. 2.3
4 2. Vary V s from 10 V to +10 V in steps of 5 V and measure the current through R and the voltage across R. Please be aware that the ELVIS station has two different variable DC outputs, one with a range of 012V the other with a range of 120V. BE SURE THAT YOU SELECT THE CORRECT OUTPUT AND CHECK YOUR CONNECTIONS BEFORE APPLYING POWER. 3. Plot these results using the horizontal axis for the current, I, and the vertical axis for the voltage, V. From the plot determine the unknown resistance. Does the plot go through the origin? Should it? 4. Check the resistance using the digital ohmmeter. 5. Insert a DC voltage source of 2V in series with R, as shown in Fig Fig. 2.4 Now place the voltmeter across both R and the 2V source. Repeat steps 2 and 3 (i.e. do steps 2 and 3 but this time you will measure the current through R and the 2V source and the voltage across R AND the 2V source). Comment on the meaning of the term resistance by comparing the two graphs.
5 Prelab: Consider the circuit of Figure 2.5. Let V s = 12V. 1. Find the equivalent resistance seen by the source. 2. How much current is provided by the source? 3. Find the current in the 3.3 kω resistor. Procedure: 1. Build the circuit shown in Fig Kirchhoff s Voltage and Current Laws Fig Adjust the source voltage such that V s = 12V. Then, measure the voltage across each resistor and the current in each branch. 3. Using the data collected in step 2, verify Kirchhoff s voltage law (KVL) and Kirchhoff s current law (KCL).
6 4. Using the pertinent results from step 2, experimentally determine the total resistance by measuring V s and I, or with the help of Ohm s law. Compare this with the calculated resistance. Potentiometer A potentiometer (or pot ) is a circuit component with three terminals as shown in Fig Terminal 3 is connected to a movable contact or arm. The resistance between terminals 1 and 2 is fixed and is equal to the rated value for the potentiometer. The resistance between terminals 3 and 1 or between 3 and 2 can be varied by moving the arm up or down. If terminals 1 and 2 are connected across a voltage source, then the voltage between terminals 3 and 1 and between 3 and 2 can be varied by moving the arm. Procedure: Fig Measure the resistance between terminals 1 and 2 of the potentiometer at the lab station. Then, construct the circuit shown in Fig. 2.7 for V s = 7 V. Fig Adjust the potentiometer arm to yield output voltages of V o = 3 V and V o = 5 V. Measure the resistance between points 13 and 2 3 for each case. Compile the data and place in a table.
7 3. Show how the results agree with voltage division.
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