Lab 5 v5 - Wheatstone Bridge(1)

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Apr 3, 2024

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Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab EECE 2105-2 Electric Circuits Laboratory LAB 5: Wheatstone Bridge Circuit Student Name: Gerardo(jerry) Gamez-moreno Cessar Lechuga 1

Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab LAB 5: Wheatstone Bridge Circuit A. OBJECTIVES  Become familiar with the construction and terminal characteristics of the Wheatstone Bridge circuit  Use the Wheatstone bridge circuit to measure an unknown resistance  Learn the different connections of the potentiometer B. EQUIPMENT  HP-3631A DC Power Supply  Digital Multimeter (DMM)  Prototype Board  Device Test Leads and Cables C. PARTS  ¼ Watt Resistors: 110 Ω, 220 Ω, 330 Ω  One 1 kΩ Potentiometer  One unknown resistor of your choice, in the range from 200 Ω to 600 Ω  Hook-up Wires (#20 or #22 gauge solid conductor) D. BEFORE THE LAB 1) The Potentiometer The potentiometer is a special type of resistive electronic component. It is basically a three- terminal resistor that can have its resistance value vary over a specified range. It usually has a knob or screw that can be adjusted to change the amount of resistance across its terminals. As shown in Figure 1, by turning the wiper of the potentiometer, the amount of resistance on either side of the wiper changes. This wiper is connected to the center pin of the potentiometer. This therefore changes how close the wiper pin is to either other pin. As suggested in the diagram, when the wiper rotates clockwise, the resistance between pin 1 and pin 2 is decreased, while the resistance between pin 3 and pin 2 is increased. 2

Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab Figure 1: Potentiometer Function Diagram and Symbol For this lab, we will connect only two pins of the potentiometer: the middle one (pin 2), and either one of the side pins (pin 1 or 3). The third pin will remain unconnected. This setup effectively makes the potentiometer act as a 2-terminal variable resistor. 2) The Wheatstone Bridge The Wheatstone bridge is an instrument used to make precision measurements of unknown resistance levels. The basic configuration appears in Figure 2. The unknown resistance is R x , and the precision resistors of known values are depicted as R 1 , R 2 , and R 3 . Figure 2: Wheatstone Bridge Circuit 3

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Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab Here, the galvanometer (G) is a type of very sensitive ammeter: an instrument for detecting very small amounts of electric current. Galvanometer sensitivities are usually at 10 -10 A or better. This instrument is used in the Bridge to be able to tell whether it is balanced or not. The network is balanced when the galvanometer reads zero amperes. We know from circuit theory that if I G = 0 A, then the voltage V bd is zero volts, and therefore: V ab = V ad and V bc = V dc In terms of currents and resistances, the expressions become: I 1 R 1 = I 3 R 3 ( 1 ) I 2 R 2 = I x R x ( 2 ) Solving equation (1) for I 1 yields: I 1 = I 3 R 3 R 1 Recalling that I G = 0 A, this means that I 1 = I 2 and I 3 = I x . Therefore, we can replace I 2 by I 1 and I x by I 3 in equation (2): I 1 R 2 = I 3 R x yields → I 3 R 3 R 1 R 2 = I 3 R x Finally, we can cancel I 3 and solve for the unknown resistance R x : R x = R 2 R 1 R 3 ( 3 ) The resistive ratio form is then: R 2 R 1 = R x R 3 ( 4 ) In the Wheatstone Bridges commercially available, R 1 and R 2 are variable in decade steps so that the ratio R 2 /R 1 is a decimal or integral multiplier. R 3 is a continuous variable resistor, such as a slide-wire potentiometer. Before the unknown resistor R x is connected to the terminals of the commercial Wheatstone Bridge, the R 2 /R 1 ratio is adjusted for that particular unknown resistor. After the resistor is connected, R 3 is adjusted until there is no detectable current indicated by the galvanometer. The unknown resistance value is then calculated using the ratio factor times R 3 . E. IN THE LAB 1) Wheatstone Bridge Network 4

Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab (a) Build the Wheatstone Bridge shown in Figure 3. Notice that R x represents the potentiometer. Make sure you also connect the voltmeter as shown. Figure 3: Wheatstone Bridge Circuit (b) Measure each one of the resistors’ resistances used in the circuit. R 1 =218.1 Ohms color code: Red Red Brown R 2 = 326.26 Ohms color code: Orange Orange Brown R 3 = 108.9 Ohms color code: Brown Brown Brown (c) Instead of a galvanometer, we will be using the connected voltmeter in order to balance the Bridge. Starting with the voltmeter on the highest range value, vary the potentiometer until the voltage V ab is as close to zero as possible. Then set the voltmeter to the lowest range possible to accurately set V ab even closer to zero. When done, the Wheatstone Bridge is now considered to be balanced. (d) Now measure the voltages V da , V db , V ac , and V bc . V da =4.004V V db = 4.04V V ac = 5.99V V bc = 5.95V (e) Next, calculate the currents I 1 and I 2 using Ohm’s Law. CALCULATIONS: I 1 =18.35mA I 2 = 18.35mA Are the above currents equal to each other, as defined in part 2 of the Before the Lab section? 5

Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab Yes, both currents are equal to each other. ** Show your results to your instructor to obtain a signature. Instructor’s Signature: Jaime Ramos (f) Now disconnect the potentiometer and measure its resistance, but be careful not modify its value by readjusting the knob/wiper! Do not move the potentiometer. Move out the rest of the circuit . Leave the potentiometer on the breadboard as it is. Disconnect from node b resistor R 3 . From node c disconnect R 2 and power source 10 V . Add extra wires to the potentiometer to measure its resistance R pot = R x = 159.77Ohms (g) Calculate the currents I 3 and I x using the voltage measurements from part E1.d and Ohm’s law. CALCULATIONS: I 3 = 37.098mA I x = 37.24mA Are the above currents equal to each other, as defined in part 3 of the Before the Lab section? Yes, both I3 and Ix are equal to each other. (h) Verify if the ratio from equation (4) in part 2 of the Before the Lab section is satisfied. Does it hold? Yes equation 4 does hold, the values we got for the ratios were approximately 1.46. 2) Wheatstone Bridge with unknown resistor (a) Replace the 110 Ω resistor (R 3 ) by the unknown resistor you choice, between 200 and 600 Ohms. What is new R 3 nominal value 270 Ohms ? What is the color code Red purple brown Repeat step (c) in order to balance the Wheatstone Bridge once again. Afterwards, isolate the potentiometer to measure its resistance with the ohmmeter. R pot = R x = 393.97Ohms (b) Next, calculate the unknown resistance using equation (4). CALCULATIONS: R 3 (calculated) = 264.41Ohms 6

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Lab 5-v5: Wheatstone Bridge Circuit Electric Circuits I Lab (c) Measure the unknown resistance with the ohmmeter and compare the result with the one from part (j) by calculating the percent difference between R 3 Calculated and R 3 Measured . R 3 (measured) =266.73Ohms %Difference = 0.87% ** Show your results to your instructor to obtain a signature. Instructor’s Signature: Jaime Ramos **When done with the laboratory, please return every component to its respective storage. Thank you! F. AFTER THE LAB 1) Simulate the last bridge circuit on PsPICE. Use the measured resistors values of Sections E.2(a) and E.2(c). Verify that the bridge is balanced, that is obtain node voltages V a = and V b = Did you obtain equal values? YES / NO 2) Referring to the Wheatstone Bridge in Figure 2, if R 1 and R 2 are 1.5 Ω and 3.3 Ω, respectively, can the bridge be balanced by using resistors of 1.5 MΩ and 3.3 MΩ for R 3 and R x , respectively? Explain your answer below. R2R3=3.3*1.5*10^6= 4.95x10^6 R1Rx=1.5*3.3x10^6 4.95x10^6 From (1) & (2) as they are equal, the bridge is balanced. 3) Considering the Wheatstone Bridge from Figure 3, what is the maximum value of R 3 that this network is able to measure? Hint: Consider the maximum range that the potentiometer can be set to, and use equation (4) to calculate. 7