Wheatstone Bridge Circuit Analysis: Current and Voltage Relationships, Papers of Electrical Circuit Analysis

Download Wheatstone Bridge Circuit Analysis: Current and Voltage Relationships and more Papers Electrical Circuit Analysis in PDF only on Docsity! GRAND VALLEY STATE UNIVERSITY PADNOS SCHOOL OF ENGINEERING The Wheatstone Bridge EXPERIMENT #4 A TECHNICAL PAPER by Matthew J. Nibbelink for EGR 214 CIRCUIT ANALYSIS 20 February 2000 1 Introduction The circuit used in this experiment and shown in Figure One is a simple Wheatstone bridge circuit. The Wheatstone Bridge circuit is named after its inventor, Charles Wheatstone, who also contributed to the invention of the telegraph. The circuit is considered ‘balanced’ when there is no current flow between nodes a and b. According to the lab handout, when this occurs, we also know that the products of the cross-arm resistances are equal. R 1 R 4  R 2 R 3  (eq.1) Because of this fact, the theory behind a Wheatstone Bridge can be used to find values of different electrical components without the use of direct measurement. The purpose of this report is to show how the current through the bridge and the node voltages of a Wheatstone Bridge circuit relates to the resistor values used in the circuit. Section Two will cover the theory and mathematical relationships behind the 1 3 Experiment The following items were used to conduct the experiment: Qty Item 1 CADET Trainer (CDT) (GVSU #12196) 1 Digital Multimeter Fluke Model 8050 (DMM) (GVSU#31083) 6 ¼ watt resistors of assorted value miscellaneous leads and connectors masking tape The Wheatstone Bridge circuit shown in Figure One was constructed multiple times, using different resistor values in each implementation. These values have been recorded in Table One in the columns labeled: R1, R2, R3, and R4. We were careful not to go over the power rating of each resistor (¼ watt) by keeping all resistor values over 100 ohms. p 1 4 watt V2 R 1 4 watt R 100  The +5V voltage source on the CADET Trainer was used. The actual voltage produced was 5.112 volts. The node voltage and the current across the bridge were both measured using the digital multimeter and recorded in Table One as well under the columns labeled I and va. Each of these experimental values was calculated using the formulas derived in Part Two of this report and entered into Table Two. Table 1: Experimental Values R1 (ohms) R2 (ohms) R3 (ohms) R4 (ohms) Va (volts) I (mA) 219.9 1001.3 441.3 665.2 3.050 2.519 335.6 1001.3 242.0 219.9 1.6021 3.823 4 1001.3 335.6 665.2 441.3 2.642 1.4602 441.3 335.6 219.9 1001.3 2.459 5.351 665.2 219.9 335.6 1001.3 3.059 6.150 Table 2: Theoretical Values R1 (ohms) R2 (ohms) R3 (ohms) R4 (ohms) Va (volts) I (mA) 219.9 1001.3 441.3 665.2 3.044 2.509 335.6 1001.3 242.0 219.9 1.607 3.811 1001.3 335.6 665.2 441.3 2.625 1.463 441.3 335.6 219.9 1001.3 2.485 5.346 665.2 219.9 335.6 1001.3 3.084 6.142 4 Comparison and Discussion All of the data found in the experimental procedure match very closely to that of the data calculated by using the formulas derived in Section Two. The percent errors in each of the measurements have been calculated and placed in Table Three using the formula: Measured Actual Actual 100 %Error Table 3: Error Experiment Va I 1 0.60% 1.00% 2 0.49% 1.20% 3 1.70% 0.28% 4 2.60% 0.50% 5 2.50% 0.80% This error can be mostly attributed to the digital Multimeter. The multimeter is accurate to +/- 0.1% of the reading plus two digits plus .02 ohms. This gives a typical 500 ohm resistor an error in the reading of about 1%. This accuracy is also rated for one year of purchase. The DMM used was much older than one year. By comparing Tables 5 1 and 2, the experimental data supports that of the theoretical, verifying the formulas and calculations from Section Two. 5 Conclusions The current and node voltages of the Wheatstone Bridge are definitely dependent on the size of the resistors and the size of the voltage source used in the circuit. This dependence is shown in equations 5 and 6, and was verified and supported by the experiment outlined in Section Three. This experiment also helped in the understanding of the Wheatstone Bridge circuit. Any of the components of the Wheatstone Bridge should be able to be calculated using the equations in Section Three. The Wheatstone Bridge did behave as expected during the experiment. It is also evident that the Wheatstone Bridge circuit is a very useful circuit in calculating unknown values when only some parts of the circuit are known. 6