University DC Circuits Laboratory EE 104 EA Workbook Lab 4KI

14universitydc Circuits Laboratory Eet 104eaworkbook Lab 4kirchhoffs

Verify and apply Kirchhoff’s Current Law (KCL) in single-node-pair circuits, and analyze the circuit behavior through measurements and calculations to demonstrate the law’s validity.

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Kirchhoff’s Current Law (KCL) is fundamental in electrical circuit theory, stating that the total current entering a junction must equal the total current leaving the junction. This principle embodies the conservation of charge and is critical in analyzing complex electrical networks. The laboratory exercise outlined aims to verify KCL through practical experimentation involving measurements of currents and voltages in a constructed circuit, as well as applying theoretical laws such as Ohm's law to interpret the data.

The experiment begins with the measurement and recording of resistor values at specified points—specifically, resistors with nominal values of 2.2kΩ, 3.6kΩ, 4.3kΩ, and 10kΩ. These resistances are measured precisely using a digital multimeter, which enables accurate calculations of conductances (the inverse of resistance, expressed in siemens). Conductance calculations facilitate easier analysis of parallel circuits, as their combined conductance equals the sum of individual conductances. This principle is particularly useful when determining the total conductance of multiple resistors connected in parallel and analyzing how they influence circuit behavior in terms of current distribution.

The constructed circuit employs a 10 V power source alongside a 10kΩ resistor approximating an ideal current source. The visual setup involves a breadboard, with various connections to facilitate measurements, including the voltage across each branch. Using the multimeter, voltages are recorded, and currents are calculated via Ohm’s law (I = V/R). The basic premise is that, if KCL holds true, the sum of the currents at the junction—the algebraic sum of the individual branch currents—should be zero or negligibly close to zero, accounting for measurement errors.

The results from the measurements reaffirm the validity of KCL. The measured resistor values do not significantly deviate from their nominal values, with minor discrepancies attributable to manufacturing tolerances, wiring resistances, and instrument precision. For example, the resistors 2.2kΩ, 3.6kΩ, and 4.3kΩ measured approximately 2.1737kΩ, 3.5641kΩ, and 4.2578kΩ, respectively. Using the measured voltages, the calculated branch currents (I1, I2, I3, I4) range from approximately 0.221 mA to 0.919 mA. Summing these currents yields a value close to zero (around 0.002 mA), confirming that KCL is upheld within experimental accuracy.

The experiment extends to analyzing a single-loop circuit, where Ohm’s law and KCL are used to verify that the total conductance, determined through parallel or series combinations, matches theoretical expectations. For example, the total conductance calculated during the experiment closely matched the measured value (sum of conductances approximately 1.025 kS versus the experimental 1.0768 kS). These correspondences support the assertion that circuit analysis using KCL and Ohm’s law reliably predicts circuit behavior.

Further, the experiment includes designing a microammeter (milliammeter) with a specified full-scale current (e.g., 1mA). Calculations for the shunt resistor, Rm, are performed using Ohm’s law, ensuring that the microammeter can correctly measure the intended current. Testing involves verifying the actual current flow through the meter at different supply levels, which underscores the importance of scale calibration and the effect of internal resistance on measurement accuracy.

The concluding remarks emphasize that the verification of KCL through this laboratory exercise confirms its critical role in circuit analysis. The small measurement errors observed are within acceptable limits, reinforcing the law's validity. The experiment also underscores the importance of precise measurements, understanding of resistive properties, and the application of fundamental laws like Ohm's law in practical electrical engineering tasks. Furthermore, the design and testing of a milliammeter illustrate the practical considerations for ensuring measurement devices operate accurately within their specified ranges. Overall, this exercise validates Kirchhoff’s Law as an essential tool in electrical circuit analysis and measurement.

References

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