Electrical Engineering Report

Abstract

The objective of this experiment is to research and to comprehend the manner by which the quality of tolerance that is manifested by the resistors has the capacity of influencing the voltage. The tolerance that is demonstrated by the resistor also influence the flow of current in a circuit. The operation of the Elvis board was investigated in this laboratory report. In addition, the operation of the Multisim program was studied. The circuits that are examined in the laboratory are contained on the Elvis board. The voltage that is possessed by each of the resistors that compose the circuit are documented by means of the DNM application that is contained in the Elvis board. Subsequent to the documentation of the amperage and the voltage in the circuits, the Multisim program was applied in order to create a simulation of the circuits in the absence of the tolerance demonstrated by the resistors. The amperage and the voltage are discovered by comparing the readings from the Multisim board to the readings on the Elvis board. The outcome demonstrated a small differential between the hypothetical and actual values that were derived with the assumed tolerances. In the final circuit, the level of error in the measurement of the power manifested by the 330Ω R6 resistor by means of applying the mathematical error propagation model.

Introduction

In all of the experiments that require evaluation, there is an index of error that is designated as uncertainty. The level of uncertainty is a deterrent in acquiring the complete accuracy of the readings. The precision of an assessment implement is decreased as the measurement departs from the range of the implement. When an object is weighed by means of a scale, the precise measurements are restricted by the variances that are manifest on the scale. Considering the digital scales, when the reading exceeds the range of the variances of the implement, the readings will fluctuate to a particular degree until the device can select the most appropriate reading. In the experiment that had been conducted, the amperage and the power assessments are derived from a circuit. The tolerance manifested by the resistors, in addition to the inherent resistance that is demonstrated by the Elvis board cause the measurement to contain a certain level of uncertainty.
In the laboratory experiment, the Elvis board readings were compared to the readings that were demonstrated in the Multisim program. This comparison was performed between the Multisim and the Elvis board in order to ascertain the manner by which the tolerances of the resistors and the tolerances in the measuring tools influence the precision of the measurements. Furthermore, the importance of the uncertainty readings.

Experimental Procedure

The initial circuit that is demonstrated in Fig. 1 was attached to the Elvis board. The initial circuit was ensued by starting the software on the Elvis board and choosing the tab marked “DNM”. The spring loaded clip that hade the quality of serrated jaws were attached to the appropriate position that was demonstrated on the DNM tab of the Elvis board. The amperage measurements were conducted by taking one of the ends of the resistor wire and attaching a spring loaded seated clip to the wire, with the other end of the wire being fastened to the resistor. The identical steps were performed for the second circuit that is demonstrated in Fig. 2. Subsequent to the circuits being reviewed with the Elvis board, the circuits were simulated on the Multisim program. In the application of the DNM option on the software, the amperage and the voltage were assessed in a similar manner on the Elvis Board. Subsequent to all of the currents being recorded, the third circuit that is demonstrated in Fig. 3 was reviewed in order to measure the wattage of the R6 resistor by means of the wattmeter option on the Multisim.
The wattmeter was applied by attaching the left side that was connected in parallel to the R6 resistor and the side aspect which was connected in series with the R6 resistor. Each of the resistors was placed into a format while measured one at a time from the most elevated tolerance to the lowest tolerance while the wattage was documented with each of the transpositions. In each of the circumstances the resistor was transposed with the most elevated tolerance value for the R6 resistor which demonstrated the lower value of wattage. This was performed in order to provide the lowest wattage value that passed through the R6 resistor.

Results

The outcomes from the measurement of the first circuit in Table 1 demonstrate that there was a slight differential that was shown between the theoretical and the actual voltage values. These differentials were measured to be 14.73%, 10.86% and 15.31%. The amperage that was derived from the measurement of the circuit manifested a smaller degree of uncertainty with the exception of the 330 Ω resistor value that demonstrated a degree of error that was equivalent to 15. 33%. In the consideration of the second circuit that is demonstrated in Table 2, the percentage of error that was manifested for the voltage measurement becomes comparatively less than the values of 1.04%, 1.66%, in addition to 0.79% and 1.29% that were demonstrated next to the 220 Ω resistor. The percentage error that was demonstrated with the 220 Ω approximated the value that was shown at the percentage of error of the first circuit.
The amperages of the second circuit demonstrated a more elevated percentage of error in comparison to the values of the first circuit which were 0.55%, 38.45%, 0.93% and 0.77%. The percentage error in the measurement of the current of the 220Ω resistor was maintained at a value of 0.55%, which was comparatively near to the percentage of errors that were derived for the amperage measurements of the second circuit. In the consideration of the third circuit in Table 3, the voltage values were comparatively near to the percentage errors that were derived from the first circuit and the second circuits with the exception of the resistor that had an impedance of 47Ω. The 47Ω resistor demonstrated a percentage error in the measurement of the amperage that was equivalent to 0.599%.
The amperage in the third circuit (47Ω) demonstrated a more elevated quality of error and was rated with the highest percentage of error in the measurement of the amperage at 21.79%. The substantial assessment of the percentage of error that was manifested in the 47Ω resistor may be attributed by the internal characteristic of resistance that was manifest by the Elvis board. Considering that the theoretically assessed measurement of the wattage and the amperage were minimal, a slight modification in the input would have the outcome of a substantial enhancement in production. When the spring loaded serrated jawed clips were not attached to any of the circuits, the Elvis software continued to provide a reading.
Reviewing the percentage error of the measurement of the voltage and amperage values of each of the circuits, the tendency appears that the more numerous the resistors, the more elevated the quality of percentage error. In Table 4, the resulting wattage of the R6 330Ω demonstrates the resulting power of the R6 330Ω resistors subsequent to modifying the tolerance values of each of the resistors by ± 5%. The resistor that has the higher level of power is extracted and placed into the Multisim. The maximum wattage that was documented was assessed at 6.061 mW. The wattage is re-evaluated with the resistors at a lower power setting which has the outcome of a reading of 4.583 mW.
In order to create the theoretical tolerance value for the wattage that was measured through the R6 resistors, the maximum wattage is subtracted from the nominal wattage value. The amount of uncertainty was determined to be ±0.788 mW. Considering the experimental values of tolerance, in order to determine the tolerance value, the mathematical equation that is applied for the calculation of the error prorogation (dPi/ dR1) with regards to each of the resistors is determined by graphically showing the nominal, minimum and maximum value of each of the resistors compared to the values of ± 5% and zero tolerance for each of the values demonstrated by the resistors.

Discussion

Propagation of error is delineated as the influences on a function with regards to the uncertainty of a variable. The propagation of uncertainty is derived from statistical calculations in order to mix the uncertainty values of distinct variables, which are applied in order to make a precise assessment of uncertainty. Each of the assessments possesses a level of uncertainty and not all of the levels of the uncertainties are equivalent. Consequently the capacity of correctly combining the levels of uncertainty that are derived from distinct measurements is important. The uncertainty in assessment is achieved in a variety of manners. These manners may include the variance on the measurement instruments, the distinct observers, the distinctions in the samples and the conditions of the experiments. Normally, the error is manifested as the standard deviation that is a quality of the experiment (Balke, 2000).
In the case that a calculation has the requisite of more than one variable in order to reach a resolution, the application of the propagation of error equation is a requisite in order to ascertain the level of uncertainty. The error propagation goes by the assumption that the comparative uncertainty in each of the amounts is relatively small. The level of uncertainty never has the quality of decreasing with tabulations, the measurement can only become more precise (Balke, 2000).

Conclusion

The percentage error values of the measurements of the voltage and amperage of each of the three circuits were comparatively low with the exception of the measurements of the voltage and amperage in the circuit with the 47 Ω in the third circuit. The causal attribute of the error may have been due to the internal impedance of the measurement tool. The measurement tool that was applied that manifested the internal impedance was the Elvis board. In the review of the percentage of error that was manifested by each of the circuits, the tendency appears to be that the more numerous the resistors, the more elevated the quality of the percentage error. The laboratory experiment demonstrated a defect. The defect was that the lab was carried out over a period of five days. The defect in the laboratory experiment had the outcome of distinct resistors being used on the Elvis board. The distinct resistors would have varying tolerance values and would influence the values derived in the experimental data if the documentation were interrupted as a result of time limitations. The goal of assessing the value of amperage or wattage is to perform the assessment with as much precision as possible. As a result of the distinct considerations of human error, uncertainty and tolerance that influence the precision of the measurements, the uncertainty is applied into assessments in order to compensate for any factors that cause the measuring tool not to make a precise evaluation

Tables of Voltage and Current

Measuring Current:
Measuring Voltage:
Figure 2: Circuit 2

Measuring Current

Measuring Voltage:
Figure 3: Circuit 3
Measuring Current

References

Balke, S.T. (2000). Quantitative column liquid chromatography: A survey of chemometric methods. Amsterdam, Netherlands: Elsevier Science Publishers B.V.