Assignment

As engineers, it is essential to attain a theoretical and an experimental understanding of electric circuits, including the basic laws of voltages and currents. This report presents analyzing electric circuits, and the study and analysis of resistors, voltages, and currents for each electric circuit. Measurements are going to be taken and calculated for each of the resistors, voltages, and currents. The experimental values and theoretical values obtained using Elvis board and MULTSIM, are going to be used to calculate the percentage errors and to formulate a way to calculate the uncertainty of voltage drop across all resistors. Engineering circuit analysis is a process through which engineers are able to set up electrical models and are able to express physical situations in terms of mathematical relations. It is also used in predicting the behavior of the electric circuit, and plays a key role in the design process.

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Contents Abstract i Introduction 1 Procedure 1 Results and discussion 2 Conclusion 3 Appendix 4 List of Tables 4 Table 1: Circuit 1 Experimental Measurement 4 Table 2: Circuit 1 MULTISIM Measurement 4 Table 3: Circuit 1 Percentage Error 4 Table 4: Circuit 2 Experimental Measurement 4 Table 5: Circuit 2 MULTISIM Measurement 4 Table 6: Circuit 2 Percentage Error 4 Table 7: Circuit 3 Experimental Measurement 5 Table 8: Circuit 3 MULTISIM Measurement 5 Table 9: Circuit 3 Percentage Error 5 Table 10: Circuit 3 Nominal and Tolerance Values 5 Table 11: Uncertainty 6 List of Figures 7 Figure 1: Circuit 1 Diagram 7 Figure 2: Circuit 1 Elvis board 7 Figure 3: Circuit 1 MULTSIM 8 Figure 4: Circuit 1 Currents 8 Figure 5: Circuit 1 Voltages 8 Figure 6: Circuit 2 Diagram 9 Figure 7: Circuit 2 Elvis Board 9 Figure 8: Circuit 2 MULTISIM 10 Figure 9: Circuit 2 Currents 10 Figure 10: Circuit 2 Voltages 11 Figure 11: Circuit 3 Diagram 11 Figure 12: Circuit 3 Elvis Board 12 Figure 13: Circuit 3 MULTISIM 12 Figure 14: Circuit 3 Currents 13 Figure 15: Circuit 3 Voltages 13 Figure 16: Excel Nominal and Tolerance Values 14 List of Equations 15 1- 15 Reference 16

An electric circuit is a connection of circuit elements such as resistors, inductors, capacitors, and voltage/current sources. With these elements there is some power that is being supplied and dissipated. This means that if a resistor is connected to a battery using conductive wires, then an electrical circuit is created. There is a technique to find the voltages across and the current through, every component in the circuit, which is called circuit analysis. Circuit analysis is used to mathematically analyze a circuit [2].In order to analyze an electric circuit, we need to know the behavior of each circuit element in terms of its voltage current. The lab report includes the practical and theoretical perspective of electric circuits along basic flaws of voltages and currents.

This experiment consists of the 3 Electrical Circuits. Circuit 1 is given in a diagram (Figure 1), so that the circuit can be constructed using the Elvis board. Using the same values of resistors in the diagram circuit one is built by connecting the 3 resistors to a 5V voltage source (Figure 2). After that the NI-Elvis instrument program is launched so the measurements of the built circuit is calculated. Measurements of voltage and current across each resistor is taken (Table 1). After using the Elvis board to get the experimental values, the MULTISIM simulator program is used to calculate the theoretical values of voltage and current for Circuit 1. Circuit 1 is constructed using the software (Figure 3). The measurements are taken and the value of the voltage and current across each resistor is taken (Table 2). The values are compared and the Percentage Error is taken between them (Table 3). Using the diagram for Circuit 2 (Figure 6), Circuit 2 is constructed connection 4 resistors to a 5V voltage source (Figure 7). The experimental values for voltage and current across are taken (Table 4). After getting the experimental values, the MULTISIM software is used to obtain the theoretical values. Using the software the circuit is built (Figure 8), and the measurements are taken (Table 5). The experimental and the theoretical values are compared and the percentage error is calculated (Table 6).The same steps used in Circuit 1 and 2 are used for Circuit 3, it is constructed in reference with the diagram (Figure 11). Building a circuit with 7 resistors and a 5V voltage source to obtain experimental values (Figure 12). The values for voltage and current across the resistors are measured (Table 7). After that the MULTISIM is used to build a circuit and measure the voltage and the current across each resistor (Figure 13). The theoretical values are obtained through the MULTISIM (Table 8). Comparing the theoretical and experimental values is needed to calculate the percentage error between the values for Circuit 3 (Table 9). Lastly, a way has to be formulated to calculate the uncertainty of each voltage drop across all resistors using the nominal and tolerance values for each resistor (Table 10).

This Lab Report shows the practical and theoretical study of the core areas of circuit analysis. In this report there are calculations of voltage and current in the three electric circuits, estimation of the error propagation using resistor nominal values and associated tolerances, and the verification of the accuracy of the predicted voltage and current values using instruments. In the first part of the experiment values of voltage and current across the resistors were acquired using the Elvis board (Table 1) and the theoretical values using MULTISIM Software (Table 2). The resistor values used in the Elvis board and the MULTISIM were the same. There was no change in the theoretical values, but the experimental values were a little different (Table 1), they still fall within the tolerance of 5%. Using the MULTISIM a circuit is built, and the values of voltage and current across the resistors are measured (Figure 3 and 4). A slight difference between the theoretical and experimental values happen, and after calculating the error percentage (Table 3), it is concluded that the percentage errors are really slight and fall within the tolerance. For the second part of the experiment, the theoretical and experimental values are obtained the same way. Experimental are obtained using the Elvis Board (Table 4), and theoretical values using MULTISIM (Table 5). It is noticed that the experimental resistors are also different, but they fall within the 5% tolerance range. The theoretical values acquired from the MULTISIM (Figure 9 and 10), and the experimental values experience a difference. The error percentage of voltage and current across resistor 2 and 4 are somewhat bigger than those for 1 and 3 (Table 6). Part 3 is a bit more complicated. The experimental values for Circuit 3 (Table 7) are compared to the theoretical values obtained from the MULTISIM (Table 8). A slight difference in the experimental resistors is noticed, and it also falls within the 5% tolerance range of the resistors. The MULTISIM theoretical values are acquired from (Figure 14 and 15). Comparing the experimental and theoretical values and calculating the percentage error, it’s noticed that all the errors voltage and current are below 4% except for resistor 6 it is 55%. The values of current and voltage, along with the nominal and tolerance values for each resistor are used to calculate the voltage drop (Table 10). Using excel to build table 10, the values are used to derive an expression to estimate the uncertainty of the voltage (Figure 16). From what can be seen, the error propagation was derived along with the final values, uncertainty, and tolerances for each resistor (Table 11). Not all the values fall within the uncertainty range (Equation 1). The difference in the experimental and theoretical values in all three circuits can be due to many errors, such as Human Error, DMM being out of calibration. Beyond component tolerance there are other factors involved. Every component exhibits some parasitic properties, unlike idealistic components that exist only in simulators like MULTISIM.

This laboratory focuses on circuit analysis and design although, as a result of this, many fundamental aspects of electrical engineering and circuit theory are brought to light. Without the knowledge of circuit theory and fundamentals of circuit analysis and design this lab can’t be completed. The knowledge and understanding of these principles in circuit theory are a necessity in order to develop higher order knowledge and skills within an occupational and furthering academic environment [1]. The difference in manual calculations and software calculations is visible. But it could be due to human error, precision handling and other internal and external factors due to which the error percentage is calculated.

Table 5: Circuit 2 MULTISIM Measurement

Table 8: Circuit 3 MULTISIM Measurement

Table 10: Circuit 3 Nominal and Tolerance Values

Figure 9: Circuit 2 Currents

Figure 11: Circuit 3 Diagram

List of Equations

[1] Basic Engineering Circuit Analysis by J. David Irwin  R. Mark Nelms

[2] Introductory Circuit Analysis (12th Edition) by Robert L. Boylestad