# Experimental Validation of Kirchhoff's Rules: Circuit Analysis and Precision Considerations

Categories: Physics

This experiment aims to vividly illustrate Kirchhoff's Rules for electrical circuits by excluding the use of a specific resistor, the 10-ohm one. Through various observations, the values of resistance, voltage, and currents in both series and parallel circuits are determined. The experiment emphasizes Kirchhoff's principle, asserting that the sum of currents flowing into a junction must precisely match the sum of currents flowing out of the same junction, aligning with the conditions set by Kirchhoff's Rules.

In 1845, the German physicist Gustav Kirchhoff formulated a fundamental pair of rules governing the conservation of current and energy in electrical circuits.

Kirchhoff's Current Law (KCL) addresses current flow, emphasizing that the total current or charge entering a junction is exactly equal to the charge leaving the node. This equality arises from the fact that no charge is lost within the node, providing no alternative path for the current.

On the other hand, Kirchhoff's Voltage Law (KVL) deals with voltage distribution in closed loop networks.

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It stipulates that the total voltage around any closed loop is equal to the algebraic sum of all the voltage drops within that loop, ultimately balancing to zero. This experiment will explore and validate these principles by manipulating resistors and observing the resultant electrical parameters in both series and parallel circuit configurations.

The primary objective of this experimentation is to systematically explore the variables influencing the functionality of an electrical circuit and, in the process, validate the principles encapsulated in Kirchhoff's Rules.

Kirchhoff's loop rules represent a manifestation of energy conservation applied to potential changes within a circuit.

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A crucial aspect of these rules is the assertion that electric potential must possess a unique value at any given point in a circuit. This uniqueness is irrespective of the specific path taken to reach that point. Consequently, when traversing a closed path in a circuit—commencing and concluding at the same point—the algebraic sum of potential changes within that path must equate to zero.

The first law encapsulates the fundamental concept that the sum of currents entering a node must precisely match the sum of currents exiting the node. This law finds its roots in the uniqueness of potential at every point on a circuit. Analogous to elevation changes, if one follows various paths in a circuit, ultimately returning to the starting point, the sum of potential changes along each path must add up to zero.

The second law is a concise expression of current conservation, reminiscent of the principles discussed in Ohm's law lectures. Specifically, for a node on the right, the equation i1 = i2 + i3 holds true. If all currents are defined as entering the node, the sum of these currents is necessarily zero. This experiment will provide empirical evidence supporting these principles, shedding light on the intricate dynamics of electrical circuits.

Experimental Methodology

1. The experimental setup involved connecting the circuit according to the configuration illustrated in Figure 2.1. Notably, all resistors were utilized, excluding the 10Ω resistor.
2. Initial recordings included noting the resistance values, with particular attention to the total circuit resistance when no current was flowing.
3. Voltage measurements across each resistor were meticulously taken as the circuit was connected to the battery, and current flowed. These values were diligently recorded.
4. For further analysis, the individual currents passing through each resistor were measured. To achieve this, the circuit was interrupted, and a Digital Multimeter (DMM) was strategically placed in series.
5. The currents for each resistor were recorded individually, and special focus was given to the current flowing into or out of the main circuit, denoted as IT.
6. To expand the scope of the investigation, the circuit was reconfigured as depicted in Figure 2.2. The procedures outlined in steps 1 and 5 were meticulously repeated under these new conditions.

RESULT AND DISCUSSION

 Resistance,Ω Voltage,volts Current,mA R1 330.5 V1 1.979 I1 00.10 R2 322.4 V2 1.927 I2 00.10 R3 325.6 V3 1.963 I3 00.10 R4 319.3 V4 1.924 I4 00.10 R5 99.5 V5 3.000 I5 -00.01 RT 0.510k VT 3.890 IT 00.24

TABLE 2.1

 Resistance,Ω Voltage,volts Current,mA R1 330.5 V1 1.010 I1 0.060 R2 322.4 V2 0.984 I2 0.070 R3 325.6 V3 0.483 I3 -0.010 R4 319.3 V4 1.446 I4 0.110 R5 99.5 V5 0.446 I5 0.110 RT 0.510k VT 3.433 IT 0.110

DISCUSSION

The sum of all currents entering a branch point of a circuit (where three or more

wires merge) must be equal to the sum of the currents leaving the branch point

SAMPLE OF CALCULATION

∑Iin − ∑Iout = 0

RESULT 2.1
(I1+I3) – (I2+I4) = 0
(0.1+0.1) – (0.1+0.1) = 0
RESULT 2.2
(I1+I2) – I5 0
(0.06+0.07) – 0.11 =-0.02

The experimental findings lead to a significant conclusion indicating that the entering current and the leaving current in the circuit are equal, and their summation results in a net value of zero. This observation substantiates the validity of Kirchhoff's rules, specifically the expression ∑Ienter - ∑Ileaving = 0. The experiment provides empirical support for the fundamental principle that the sum of currents entering a junction in a circuit equals the sum of currents leaving that junction, confirming the conservation of electric charge in accordance with Kirchhoff's laws.

Recommendations

1. It is imperative to exercise caution in selecting the appropriate resistor for each experimental set to ensure accurate and meaningful results.
2. When employing the Digital Multimeter (DMM), meticulous attention should be paid to recording readings with precision, promoting data accuracy and reliability.
3. For enhanced accuracy in measurements, consider utilizing both wound and film resistors during the experimentation process. This approach can contribute to obtaining more precise readings.
4. Carefully observe the unit displayed on the DMM and consistently use the same unit for all calculations. This practice helps maintain uniformity and consistency in data interpretation.
5. Adhere strictly to the instructions outlined in the laboratory manual regarding the configuration of resistors in the circuit. Ensure that resistors are not in physical contact with each other, as this can introduce undesired variables and affect the integrity of the experimental results.
Updated: Feb 20, 2024