# UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE. Department of Electrical and Computer Engineering

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1 UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE Department of Electrical and Computer Engineering Experiment No. 6 Precision Resistance Measurements Introduction: It is sometimes necessary to make resistance measurements particularly of very small resistances with precision greater than that which can be obtained with a hand held multimeter. This is frequently encountered with sensors. For example, the resistance of a strain gauge must be measured very accurately in order to determine deflection of solid materials under mechanical load. This experiment introduces four different methods for making precision resistance measurements: Benchtop multimeter 2-wire Benchtop multimeter 4-wire (Kelvin) Wheatstone bridge LCR meter Students should review the following materials: Agilent 34401A Digital Multimeter User s Guide o Chapter 1: Front panel connections o Chapter 7: Measurement tutorials for 2- and 4-wire resistance WINSCO GS-470 Wheatstone Bridge Instructions SM-1102A Galvanometer Specification Sheet B&K 889B LCR/ESR meter Multimeters function as Ohmmeters when operated in resistance measurement mode. Inexpensive multimeters measure resistance by applying known voltage to the unknown resistance, measuring the resulting current, and then applying Ohm s law. More accurate meters apply a known current and measure the resulting voltage. In either case, meter test leads can introduce substantial error into low resistance measurements. Because the wire leads have small, but finite resistance, voltage division occurs between the resistance being measured, and the resistance of the leads. Fig. 1 shows a simplified schematic diagram of a meter connected to an unknown resistance R unknown by two wire leads of resistance.

2 Applying Ohm s law to the meter circuit: V ( R 2R ) R I = + = unknown lead measured When <<R unknown, the measurement error is small. For ideal, zero resistance leads, R measured =R unknown. As R unknown, accurate resistance measurement becomes impossible. For extremely small resistance values, contact resistance of the probe connections is also a factor. I ammeter A + Current source voltmeter V V R unknown - Ohmmeter Fig Wire Resistance Measurement The 2-wire resistance measurement is inherently inaccurate for low resistances because undesired voltage appears across the lead resistances due to current flowing through them. This source of error can be eliminated by supplying current to the unknown resistance by means of a separate circuit. This is known as the 4-wire, or Kelvin method. In the diagram of Fig. 2, a separate pair of test leads is used to connect the unknown resistance directly to the Ohmmeter s internal voltage sensing circuit. As before, current flowing through the leads connected to the current source produces a voltage drop across the wires. This unwanted voltage is not included in the resistance calculation, however, because voltage is measured directly across the unknown resistance. The voltage sensing circuit draws negligible current due to high internal resistance, so voltage dropped across the voltmeter leads is essentially zero, and the voltage measured is identical to the voltage across R unknown. 2

3 I ammeter A Current source voltmeter V + V R unknown - Ohmmeter Fig Wire Resistance Measurement The Wheatstone bridge circuit of Fig. 3 is used to obtain accurate resistance measurements for a large range of resistance values. A battery provides the source of current flow, while a galvanometer measures very small currents. The basic principle of operation is that when the bridge is balanced, R 1 /R 2 = R 3 /R unknown. In this condition, the voltages at nodes A and B are equal, and the galvanometer current is zero. The general procedure is, therefore, to select appropriate values for R 1 and R 2, and then adjust variable resistor R 3 to obtain an indication of zero on the galvanometer. Unknown resistance can then be calculated from the equation: R R RR = R = R R R unknown 2 unknown 1 3

4 A R 1 R 2 gal R 3 R unknown B battery Fig. 3. Wheatstone Bridge Circuit 4

5 Pre-Lab: 1. A meter being used for a 2-wire resistance measurement has an internal current source of 1 ma. If the meter s test leads have equal resistances of 0.06 Ω, what is the measured resistance for: a. A resistor of actual value 0.5Ω? b. A resistor of actual value 1KΩ? R R %error = 100% Calculate %error for 1a. and 1b. above. R 2. actual measured actual 3. Refer to the Wheatstone Bridge diagram of Fig. 3. If the galvanometer indicates zero when R 1 =110Ω, R 2 =10Ω, and R 3 is set at 2.97KΩ, what is the value of R unknown? 4. Refer to the Wheatstone Bridge diagram of Fig. 3. If R 1 =1Ω, R 2 =111Ω, R unknown = 1Ω, R 3 is set at 1KΩ, and the battery is 9V: a. What is the current flowing through the galvanometer? Use 60Ω for the internal galvanometer resistance in calculations. b. The measurement range of the galvanometer is +/- 500µA. What is the ratio of galvanometer current to its maximum range of 500µA? c. Is there danger of damage to the galvanometer with these resistance values? When using the Wheatstone bridge, always begin with R 1 and R 2 set to high values to minimize current drain on the battery, and to protect the sensitive galvanometer from damaging over-current. Before the lab session for this experiment, study the manuals (available on the ECE Laboratory Website) for: Agilent 34401A Digital Multimeter WINSCO GS-470 Wheatstone Bridge SM-1102A Galvanometer Specification Sheet B&K 889B LCR/ESR Meter Instruction Manual Know how to set up and connect the multimeter for 2- and 4-wire resistance measurements. Be familiar with the Wheatstone bridge circuit and measurement technique. 5

6 Lab-Session: In this experiment, resistance measurements will be made using a hand held multimeter, a bench top multimeter (2-wire and 4-wire), the Wheatstone bridge, and an LCR meter. Obtain three resistors that will be used as unknowns : ~1Ω, ~10Ω, and ~1KΩ. Call them R X1, R x2, and R x3, respectively. The resistors are labeled with nominal values. But all resistors have tolerances, and will have values different from nominal when measured with precision. 1. Record the labeled values for R X1, R x2, and R x3 in Table Use the hand held multimeter from your lab kit to measure resistances R X1, R x2, and R x3, and record the values in Table Referring to the user s manual, configure the Agilent 34401A digital multimeter for 2-wire resistance measurement. Measure resistances R X1, R x2, and R x3, and record the values in Table Referring to the user s manual, configure the Agilent 34401A digital multimeter for 4-wire resistance measurement. Measure resistances R X1, R x2, and R x3, and record the values in Table 1. Locate a WINSCO GS-470 Wheatstone bridge apparatus, an SM-1102A Galvanometer, a decade resistance box and a 9 volt battery. These items are shown in Fig. 4. Fig. 4. Wheatstone Bridge Components 6

7 Note that the galvanometer has three terminals. The black terminal is common. G0 is the low impedance input (60Ω G0 105Ω). G1 is the high impedance input (1.5KΩ G1 2.0KΩ). Always begin by making connections to the G1 and - terminals to prevent burning out the galvanometer. Connection to the G0 input may be made after the bridge has been brought closer to balance in order to increase galvanometer current, if desired. 5. Connect the Wheatstone bridge circuit as shown in diagram A of the WINSCO GS-470 Instructions. (A DC power supply set at ~10V may be substituted for the 9V Battery.) 6. Zero the galvanometer by turning the adjustment screw at the bottom of the meter window before making measurements. 7. Given the range of the decade resistance box and the approximate values of unknown resistances, calculate values for R 1, R 2 and R 3 (using values obtainable with the GS-470 for R 1 and R 2 ) that will approximately balance the bridge for unknowns R X1, R x2, and R x3. 8. Measure resistances R X1, R x2, and R x3, and record the values in Table 1. Remember to multiply the decade box resistance by the scaling factor R 2 /R 1 to obtain R unknown. a. Set R 1 R 2 and R 3 to their calculated values. This is accomplished by closing rocker switches on the Wheatstone bridge unit to short appropriate resistors. i. Press and hold the BATT button to energize the circuit. Always close the battery switch first. ii. Press and hold the GALV switch and observe the galvanometer s deflection. iii. Immediately release both momentary switches. If switches are held closed for too long, the resistors will heat and change values. iv. Adjust the decade box resistance. The direction of galvanometer deflection indicates whether the decade box resistance must increase or decrease. v. Repeat steps i iv until a null is obtained. Locate the B&K 889B LCR/ESR meter. Note that the test leads for this instrument are equipped with Kelvin clips (Fig. 5.) These provide an easy way of making connections for a 4-wire measurement. One side of each Kelvin clip is attached to a current source wire. The other half of each clip is for sensing voltage. 7

8 Fig. 5. Kelvin Clips 9. Use the B&K 889B LCR meter to measure resistances R X1, R x2, and R x3, and record the values in Table 1. a. Press the L/C/Z/DCR key until DCR (DC Resistance) is displayed. b. Connect the LCR meter to the resistor using the Kelvin clips, and read DC resistance from the meter display. The LCR meter can also be used to accurately measure inductance, capacitance, and impedance. 8

9 Lab Session Precision Resistance Measurements (Data Sheet) Nominal Value Hand Held Multimeter 2-Wire Bench Top Multimeter 4-Wire Bench Top Multimeter Wheatstone Bridge LCR Meter R X1 R X2 R X3 Table 1. Measured Resistances INSTRUCTOR'S INITIALS DATE: 9

10 Post-Lab: 1. Using the 4-wire Agilent 34401A digital multimeter measurements as the actual resistance values, produce a bar graph showing per-cent error vs. nominal value and the three other measurement methods for R X1, R X2 and R X3. See the example of Fig. 6. R R R actual measured %error = 100% actual 2. Discuss the effect on %error of higher vs. lower unknown resistances. 3. What are some sources of error with the Wheatstone bridge set-up? 4. How can accuracy of the Wheatstone bridge be improved by appropriately adjusting the ratio R 2 /R 1? 10 % Error vs. Resistance Measurement Method % Error RX1 % error RX2 % error RX3 % error 0 Nominal Hand-Held 2-Wire Wheatstone Bridge LCR Meter Fig. 6. Example Per-Cent Error Comparison Chart 10

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