EMT1150_Lab8_hero

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EMT1150 Lab Manual (08/2020) 1 EMT1150 Lab Experiment Wheatstone Bridge Circuit Objective: Understand the principle of Wheatstone bridge circuit, determine the load voltage of bridge circuit, and use bridge circuit to measure unknown resistor. 8.1 Wheatstone bridge circuit A bridge circuit is a special class of circuits that can be used for measuring resistance, capacitance, and inductance. A resistance bridge is especially useful when a very accurate measurement of a resistance is required. The Wheatstone bridge or four arm bridge, invented by C. Wheatstone in 1843, is the most widely used resistance bridge for measuring resistance values. A Wheatstone bridge as shown in Figure 8.1, is nothing more than two simple series-parallel arrangements of resistances connected between a voltage supply terminal and ground . A typical Wheatstone bridge circuit has two input terminals (A and B) and two output terminals (C and D), consisting of four resistors configured in a diamond-like arrangement as shown. Usually a galvanometer or Multimeter is connected between two output terminals and one resistor, such as R3, is adjustable. When the output voltage is zero, this is called balanced bridge condition. Let’s analyze the bridge circuit. Based on Voltage divider rule, ܸ ஼ = ܸ ௌ ܴ ଶ ܴ ଵ + ܴ ଶ ܸ ஽ = ܸ ௌ ܴ ௫ ܴ ଷ + ܴ ௫ Figure 8.1 Wheatstone bridge circuit

EMT1150 Lab Manual (08/2020) 2 When bridge is balanced , ܸ ஼ = ܸ ஽ , so ܸ ௌ ܴ ௫ ܴ ଷ + ܴ ௫ = ܸ ௌ ܴ ଶ ܴ ଵ + ܴ ଶ ܴ ௫ ܴ ଷ + ܴ ௫ = ܴ ଶ ܴ ଵ + ܴ ଶ ܴ ௫ ( ܴ ଵ + ܴ ଶ ) = ܴ ଶ ( ܴ ଷ + ܴ ௫ ) ܴ ௫ ܴ ଵ + ܴ ௫ ܴ ଶ = ܴ ଶ ܴ ଷ + ܴ ଶ ܴ ௫ ܴ ௫ ܴ ଵ = ܴ ଶ ܴ ଷ ோ య ோ ೣ = ோ భ ோ మ (Resistance ratio at balance) ܴ ௫ = ோ మ ோ య ோ భ (Find unknown resistance) This formula proves that an unknown resistor Rx can be calculated in Wheatstone bridge circuit, if the value of R 1 , R 2 and R 3 are known. Wheatstone bridge circuit has many applications in real world. Most of the industrial sensors like temperature, strain, humidity, displacement, liquid level, etc. produce the change in value of the resistance for a variable change. The sensors can be connected into a Wheatstone bridge circuit, then the resistance change can be measured. After calibration, the corresponding temperature, strain, humidity, displacement, liquid level, etc. can be estimated. Exercise 8.1 Potentiometer 1. Test the connection of potentiometer. There are three legs in potentiometer, measure the resistance between different legs. Turn the knob to three different positions. Table 8.1 R AB R BC R AC Position1 Position2 Position3 C R1 ±²Nȍ Key=A 40 % A B Figure 8.2 Potentiomster 0.03 9.52 9.53 3 44 3 S

EMT1150 Lab Manual (08/2020) 3 Question: Conclude the function of potentiometer. Exercise 8.2 Build bridge circuit 1. Construct the following circuit with the potentiometer at the maximum value. Only close the switch when you are making measurements. 2. Close the switch. Measure voltages around the Loop. Measure and record the voltages around Loop 1(E, V R1 , V R1 ) and Loop 2 (E, V R2 , V R3 ). Pay attention to polarity of the measurements. Record data into Table 8.2. Table 8.2 Loop1 Loop2 E E V R1 V R3 V R2 V R4 Sum of V R1 and V R2 Sum of V R3 and V R4 Question: Use the measurements of Loop1 and Loop2 to prove KVL. Figure 8.3 Wheatstone bridge circuit E 9V R1 ³´µNȍ R2 ¶´·Nȍ R4 ·´¸Nȍ S1 D E F G C B A M ±²Nȍ Key=A 100 % R3 To make it easy to change resistance 9 23 9 23 4.19 5.02 0.020 9.23 5.23 3.78 0.020

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EMT1150 Lab Manual (08/2020) 4 3. Close the switch. Measure voltages to a Common Reference Point (GROUND), G. Measure the voltage between the following points to Ground point. Table 8.3 V A V B V C V D V E V F V M Question: Compare these voltages with measurement in part2, and explain the similarities and differences. Hint: use the concepts of double-subscript notation and single-subscript notation. 4. Measure and record the current supplied by the battery (I total ) and the current through each branch. The branch #1 consists of R1 and R2, the branch #2 consists of R3 and R4. Table 8.4 I total I 1 I 2 Question: Compare the current supplied by the battery to the sum of the currents through each branch. 9.230 9.230 9.230 3.780 OV OV 5.020 These voltages are relatively the same the source is the same VD is like Upitry and Vm is like VRzs.rs 1.4mA 0.4mA 1mA They are equivalent

EMT1150 Lab Manual (08/2020) 5 5. Resistance Measurements, record data in Table 8.5 a. Open the switch in circuit. (Isolate the components being measured). b. Measure and record the resistance in Branch # 1. c. Measure and record the resistance in Branch # 2. d. Measure and record the Total resistance in the circuit. Table 8.5 R total R branch1 R branch2 Question: Show your calculations. 6. Balance the bridge. a. Close the switch and measure the voltages between the Point D and Point M. V DM = b. How could you obtain this voltage from the measurements made in steps 2 and 3? c. 3ODFH D /RDG UHVLVWRU ±². ³ EHWZHHQ 3RLQW 0 DQG 3RLQW '´ 0HDVXUH WKH /RDG voltage (V Load ) V Load = d. To balance the bridge, adjust the potentiometer (R3) so that there is no voltage across the Load resistor. Remove potentiometer from the circuit and measure the resistance, check whether it follows the ratio formula derived before. R3 (Pot) = Check ratio: 6.361452 10.29141 16.69141 IR.tR.IN R tRulRt 6.36km 4.714 5.614 10.319 1014 16.814 1.230 159mV 5.55191

EMT1150 Lab Manual (08/2020) 6 ோ య ோ ర = ோ భ ோ మ = Exercise 8.3 Measure an unknown resistor 1. Pick up any resistor from your lab kit which is LQ WKH UDQJH EHWZHHQ ²N WR ²µN ´ Measure the resistance of this resistor, fill in Table 8.6. Treat this resistor as an unknown resistor, use Wheatstone bridge circuit to measure the resistance. 2. Build a bridge circuit, use this unknown resistor to replace R4 in Figure 8.3. 3. Adjust the potentiometer to balance the bridge again. Remove potentiometer from the circuit and measure the resistance, calculate the resistance of unknown resistor. Table 8.6 Nominal value of R Unknown Measurement of R Unknown Measurement of R3 (pot) Calculation of R Unknown Question: Show your calculations. Questions: 1) Calculate each voltage in exercise 8.2.2 and compare it to the measured value. 2) Calculate each current in exercise 8.2.4 and compare it to the measured value 3) Calculate the resistances in exercise 8.2.5 and the total resistance and compare it to the corresponding measured values. 4) Of what advantage is it to measure voltage to a common point (or ground)? 58 4 0.82 4 1 0.841 3.3192 3.24142 2.71km 3.741952 3 14km 3.314 5 73.314 165 3.314 165 3.47142 73.314 165 3.141952

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EMT1150 Lab Manual (08/2020) 7 5) Research Resistance thermometer on internet, discuss how to use bridge circuit to measure the temperature change. ----------- L AB E XPERIMENTS E NDS H ERE , P ROCEED W ITH L AB R EPORT ----------------- 1 4.714 5.614 10.314 R 1019 6.819 16.8K By V12 Vt 91 9 0.62 9 5.980 4 Rt 6.36192 V34 Vt Y z V34 9 5.58 3.420 V4 2