The purpose of this laboratory test was to make comparisons between theoretical and practical results and to develop a greater understanding of factors affecting the operation of complex AC networks.
The results from the Series Parallel RC network have minimal errors, however the small differences are mainly due to slight machine and human error. The DSO should be turned on at least a day earlier to achieve steady values, therefore this not being done, could have caused some of the errors. When measuring the change in time, it is difficult to determine the exact point at which the curve crosses the line. Because there is two points to determine, the error is then doubled.
These factors also affect the results of the RLC circuit, however the inductor causes the main errors in this circuit. At low frequencies, the inductor interferes with the signal generator, not only causing the values to be slightly wrong but also projects a graph that doesn’t completely represent a sinusoidal function. This causes the change in time to be incorrect and therefore the phase angle. The inductor is also the equivalence of a 24″ resistor, which will consequently alter the results.
Whilst measuring voltage, it is important that the component is connected to ground. The ground point is considered to have a voltage of zero and is therefore the reference point. If this was not the case and the component was not connected to the ground, there would not be a reference point of zero, rather the voltage of the terminal it is connected to. To measure the magnitude and phase without shifting the ground, a value could be directly read off the graph. The phase would be the same, as it is just compared to the current.
Kirchhoff’s voltage law (KVL) can be proven if the voltage of the source is completely consumed through the circuit. Calculations, found in the appendix, prove that the series parallel RC network follows KVL, as the voltage consumed by the resistors and capacitors approximately equals the voltage supplied by the source. There is only an error of 2. 4% and a phase difference of half a degree, therefore it can be concluded that KVL holds for the measured values for this circuit.
Calculations, found in the appendix, prove that the RLC Circuit follows KVL, as the voltage consumed by the resistor, inductor and capacitor approximately equals the voltage supplied by the source. There is only an error of 1. 02% and a phase difference of 0. 86°, suggesting that the circuit is an accurate representation of KVL. Kirchhoff’s current law (KCL) can be proven if the current leaving a node is equal to the current entering it.
Calculations, found in the appendix, prove that the series parallel RC network follows KCL, as the current through IR2 added to the current through IC2 is approximately equal to the total current. There is only a 0. 647% error and a phase difference of 0. 903°, suggesting the KCL holds true for the measured values for this circuit. Calculations, found in the appendix, prove that the RLC circuit follows KCL. The current supplied by the source and the current through the resistor, inductor and capacitor are all approximately equal. The errors are 0%, 2. 3% and 7. 99% and the phase differences are 0°, 3. 15° and 14°. This does suggest the KCL holds true but there are slight errors in our measurements.
The large errors are either due human error, machine error of inductive interference. This laboratory demonstrates that results can be measured very accurately with simply resistors and capacitors but that inductors largely affect the circuit’s performance. Our results prove the DSO performs accurate measurements, but allowances need to be made for the inductors’ resistances and signal interference.
University/College: University of California
Type of paper: Thesis/Dissertation Chapter
Date: 16 December 2016
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