Introduction: The Purpose Of This Experiment Was To Gain Exp

Introductionthe Purpose Of This Experiment Was To Gain Experience Find

The purpose of this experiment was to gain practical experience in analyzing AC circuits, specifically focusing on finding the impedances, phasor voltages, and currents within a series RLC circuit. The experiment involved measuring these values and plotting them to verify the accuracy of preliminary calculations. Additionally, the experiment demonstrated how varying the frequency and capacitor values affect impedance, phasor voltages, and currents, providing valuable insights into the behavior of AC circuits.

Paper For Above instruction

Understanding the impedance characteristics of RLC circuits is fundamental in AC circuit analysis and design. The objective of this experiment was to equip students with hands-on experience in calculating, measuring, and interpreting the impedance, voltage, and current in series RLC circuits. Through a combination of theoretical calculations and experimental measurements, students learned to analyze the effects of changing circuit parameters such as frequency and capacitance on circuit behavior.

The preliminary calculations involved determining the impedances of individual components (Z1 and Z2) and the entire circuit (Zs). These calculations accounted for both resistance and reactance components, incorporating the frequency-dependent nature of inductive and capacitive reactances. For example, at 1 kHz with a capacitor of 0.1 μF, the calculations showed that the impedance of the inductor-resistor series (Z1) was approximately 1084.3 + j427.3 ohms, and the capacitor-resistor series (Z2) was 680 - j1591.5 ohms. These values shifted at different frequencies and capacitance values, illustrating how circuit impedance varies with frequency.

The experimental phase involved constructing the circuit as shown in the schematic figure. Using a function generator set to produce a 1 V peak sinusoid at 1 kHz, the voltages across various components were measured using an oscilloscope. Notably, V1 was 1.12 V with a phase angle of 43.2°, V2 was 1.40 V with 37.4°, and the source voltage Vs was 1.88 V at 0°. The current through the circuit was inferred from the voltage across the 680 Ω resistor, yielding a phasor of approximately 1 mA with an angle of 17.4°, which aligns with theoretical expectations.

Phasor diagrams were constructed to visually represent the relationships between the voltages and currents, confirming the additive property V_s = V₁ + V₂. These diagrams helped to verify the phase shifts and magnitudes obtained, illustrating the complex impedance relationships effectively. Measurements and calculations were repeated at different frequencies and capacitances, demonstrating consistent trends with the theoretical predictions.

One key insight from the experiment was the necessity of converting between polar and rectangular forms when performing phasor arithmetic. Addition and subtraction require rectangular coordinates to ensure accuracy, while multiplication and division are best performed in polar form. The experimental data closely matched the calculated impedance values when internal resistance in the inductor was accounted for, emphasizing the importance of including parasitic resistances in real-world circuit analysis.

The experiment's observations reinforced the conceptual understanding that impedance increases with frequency in inductors and decreases in capacitors, affecting the overall circuit response. The graphical plots verified that the total impedance (Z_s) equals the sum of Z₁ and Z₂ in the complex plane, demonstrating the principle of impedance addition in series circuits. Slight deviations from theoretical values were attributed to component tolerances and measurement uncertainties.

In conclusion, this laboratory exercise provided comprehensive hands-on experience in AC circuit analysis, emphasizing the importance of impedance calculations, phasor diagrams, and the effects of varying circuit parameters. Such skills are foundational for advanced studies in electronics and electrical engineering. The ability to experimentally verify theoretical predictions enhances critical thinking and understanding, essential attributes for future engineers and scientists.

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