Experimental Proof of Kirchhoff's Laws and Ohm's Law in a Resistive Circuit, Lab Reports of Electrical Circuit Analysis

Download Experimental Proof of Kirchhoff's Laws and Ohm's Law in a Resistive Circuit and more Lab Reports Electrical Circuit Analysis in PDF only on Docsity! 1 Grand Valley State University Padnos College of Engineering & Computing EGR 214 – Circuit Analysis I Prof. B. Adamczyk Section 01 February 22, 2005 Lab Report #1 By Dan Schwarz 2 Abstract This paper describes an experimental procedure that was used to demonstrate the validity of Kirchhoff’s Current Law, Kirchhoff’s Voltage Law and Ohm’s Law. The procedure implemented a simple circuit constructed of resistors. Current and voltage measurements were taken from the circuit and compared to Kirchhoff’s current and voltage laws in order to prove them. After confirming Kirchhoff’s Current Law and Kirchhoff’s Voltage Law, the voltage and current measurements taken during the procedure were used to confirm Ohm’s Law. 1.0 Introduction Kirchhoff’s voltage and current laws in combination with Ohm’s Law are the fundamental tools of circuit analysis and as such must be investigated. Kirchhoff’s Current Law states that the sum of the currents entering a node must be equivalent to the sum of the currents leaving that node. To verify this law, measurements were taken of the current at every path that was connected to a node. Kirchhoff’s voltage law states that the sum of the voltages in any given loop of interconnected elements must be equal to zero. To verify KVL, measurements were taken across each resistive element in one loop to determine whether the loop would adhere to KVL. Ohm’s Law states that the voltage across any element is equal to the product of current and resistance. Since the current through each element and the voltage across each element was measured, Ohm’s Law could be implemented to calculate each element’s resistance. Ohm’s Law was verified by comparing the nominal resistance values to the values calculated using Ohm’s Law. 5 3.0 Analysis and Verification of a Resistive Circuit To verify the three aforementioned fundamental circuit laws, a resistive circuit was constructed for experimental analysis. A schematic representation of the circuit is provided in Figure 3.0. I1 I2 I3 I4 V1 R3 V3 R1 V2 R2 R4 V4 A B C D Figure 3.0 This schematic describes the experimental resistance circuit. Before the experimental procedure took place, four resistors with values between one and ten kΩ were selected. The values of the resistors selected for the experimental resistance circuit are listed in Table 3.0 and correspond to the circuit described in Figure 3.0. Table 3.0 The resistors selected for the circuit must have values between 1kΩ and 10 kΩ. Resistor Values Resistor Nominal Value (KΩ) Measured Value (KΩ) R1 6.8 6.67 R2 8.2 8.14 R3 8.2 8.12 R4 10 9.84 3.1 Analysis and Design 6 To verify KCL experimentally, node B was analyzed in the experimental circuit. The definition of KCL states that currents entering a node must equal currents leaving the node. Thus, KCL results in Equation (3.1) since 1I enters node B and 2I and 3I leave node B. 321 III  (3.1) The “approximately equals” symbol was used in the KCL equation to signify that the experimental findings are seldom perfect and may not be exactly equal. To confirm KVL experimentally, loop B-C-D-B was analyzed in the resistive circuit. The definition of KVL states that the sum of the voltages in a loop must equal zero. Hence, KVL results in Equation (3.2) since 2V , 4V and 3V are the voltages around loop B-C-D-B.      3420 VVVV  (3.2) To validate Ohm’s Law, nominal resistance values of each element had to be compared with the resistance values calculated using Ohm’s Law. To calculate the resistance values with Ohm’s Law, the equation had to be manipulated so that it solved for resistance instead of voltage. Manipulating Ohm’s Law to solve for resistance resulted in the generic Equation (3.3). n n n I V R  (3.3) 3.2 Simulation and Design Verification After the circuit was built and tested, the current values taken from node B were substituted into equation Equation (3.1) to prove KCL. The resultant Equation (3.4) validated KCL without any error. mAmAmA 55.025.080.0  (3.4) 7 Next, the voltage values derived from the experimental procedure were substituted into Equation (3.2) to prove KVL. As shown in Equation (3.5), the experiment validated KVL with little error. VVVVV 570.4505.2073.2008.00  (3.5) Finally, the voltage and current values from each element were substituted into the Equation (3.3) which resulted in Equations (3.6), (3.7), (3.8), and (3.9).  k mA V R 8125.6 80.0 450.5 1 (3.6)  k mA V R 292.8 55.0 073.2 2 (3.7)  k mA V R 309.8 25.0 570.4 3 (3.8)  k mA V R 635.9 26.0 505.2 4 (3.9) When the calculated resistance values are compared with the nominal resistance values and the resistance values measured using the digital multimeter, it is apparent that this circuit adhered to Ohm’s Law. The deviation between measured and calculated resistances was no more than 2.27% as shown in Table 3.2. Table 3.2 The comparison of nominal, measured and calculated resistance values verify Ohm’s Law. Resistor Values Resistor Nominal Value (KΩ) Measured Value (KΩ) Calculated Value (KΩ) %Error (Meas. vs. Calc,) R1 6.8 6.67 6.8125 2.09% R2 8.2 8.14 8.292 1.83% R3 8.2 8.12 8.309 2.27% R4 10 9.84 9.635 2.13% 4.0 Experimental Procedure