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Measuring pullout torque of synchronous motor for different excitation currents.
Typology: Lab Reports
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The purpose of this experiment is to measure the capacitive reactance and impedance of a series RC circuit. To perform this task, the source frequency was varied and the results were recorded in the observations table (appendices). The theoretical values were matched with the experimental observations. It was observed that as the frequency increases, capacitive impedance decreases exponentially. Results were verified by plotting the observation on Matlab software and it was noted that both the plots follow the same behavior. In the end, it was concluded that at high frequencies (f → ∞), capacitor acts as short circuit and Xc approaches to zero.
The objectives of this lab are: to determine the capacitive reactance of a capacitor and examine its relationship with frequency and capacitance; to determine the total impedance of a series RC circuit and to draw impedance diagram for a capacitive circuit.
The capacitive reactance Xc of a capacitor is the amount of opposition it offers to alternating current. The unit of capacitive reactance is “Ohm”; however, it can’t be measured directly with an Ohm meter. Capacitive reactance must be measured from its effect on current in an AC circuit. The formula for calculation of Xc is as follows: XC =
Where f is the frequency in Hz and C is the capacitance in Farads. From the formula, it can be seen that Xc decreases as the frequency of the applied voltage or the capacitance of the capacitor increases. Since the capacitive reactance depends on the frequency, any value of Xc calculated represents the reactance only for that particular frequency. The basic idea to determine the capacitive reactance of a series RC circuit is shown in Figure 4.1. According to the Kirchhoff’s voltage law, the sum of the voltage drops across the individual components will still be equal to the voltage across the voltage source. However, because the resistor and capacitor and power supply voltages do not reach their maxima at the same time, we cannot
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Function generator Oscilloscope Digital Multi Meter (DMM) 1_._ 5 k Ω Resistor 0_._ 1 μF Capacitor
The procedure given in the lab manual was followed.
Fig 4.2: Series RC Circuit Schematics for the Measurement of Capacitive Reactance and Impedance (two 0.06μF capacitors are placed in parallel to obtain 0.12 μF total capacitance)
Fig 4.3: Plot of Capacitive Reactance Obtained from Theory and Experiment vs Frequency
All voltages including VR, Vc, Vt which were to be observed were noted using the oscilloscope, and all the other parameters including It, Zt and Xc were calculated using the formulas mentioned in the background section. For the calculation of theoretical values of Xc at different frequencies, we used the formula (1 /2 π f C). These results can be verified from appendices (Pre- Lab and Observations). A plot between capacitive reactance, both from theory and experiment against frequency was sketched with the help of Matlab and it was observed that, albeit the exceptional deviation between theoretical and experimental results, both the plots follow the same behavior. This deviation was caused by the difference in values of components and sources between theory and experiment such as; Capacitor of 0.1 μF and Resistor of 1.5 kΩ were used in the calculation of theoretical values; whereas, Capacitor of 0.12 μF and Resistor of 1.476 kΩ were available during experiment which led to these deviations. It was also noted that when the same observation was made using DMM instead of oscilloscope i.e., Vt, their results also deviated from each other.
In this lab, we measured the capacitive reactance and impedance of a series RC circuit. It was observed that capacitive reactance is inversely proportional to the source frequency. On higher frequencies most of the voltage drop is across resistor and at lower frequencies, most of the voltage drop is across the capacitor. This is
Table 4.10.1.1: Theoretical Values of Capacitive Reactance at Different Frequencies
Fig 4.10.1.1: Circuit Schematic for Pre-Lab
f = [500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500]; Xct= [3.18267, 1.59134, 1.06090, 0. 79567 , 0. 63654 , 0. 53045 , 0. 45467 ,
plot(f, Xct);
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Fig 4.10.1.2: Plot of theoretical values on Matlab
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