1Grand Valley State UniversityPadnos College of Engineering & ComputingEGR 214 – Circuit Analysis IProf. B. AdamczykSection 01February 22, 2005Lab Report #1ByDan Schwarz2AbstractThis 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 IntroductionKirchhoff’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 acrosseach 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 Lawwas verified by comparing the nominal resistance values to the values calculated using Ohm’s Law.3This paper explains the fundamental circuit laws and outlines the procedure used to provethose laws. Sections 2.0-2.3 discuss the significance of KCL, KVL and Ohm’s Law and offer formal definitions for each. Sections 3.0-3.2 demonstrate how the resistive circuit was used to prove the fundamental circuit laws. Lastly, Sections 4.0-4.2 offer a detailed description of the experimental procedure conducted on the circuit.2.0 Fundamental Circuit LawsTo obtain a full appreciation of the significance of Kirchhoff’s Voltage Law, Kirchhoff’s Current Law, and Ohm’s Law, one must understand their applications to circuit analysis. KVL can be used to evaluate a loop of interconnected elements within a circuit. A loop is a subdivision of a circuit, which may be defined as a closed path that can be traced back to its origin without crossing the same node twice. A node is a point within the circuit where two or more current paths intersect. With this in mind, KCL can be used to evaluate the currents flowing in and out of a node. When current and voltage is known through a resistive element, Ohm’s Law can be used to determine the amount of resistance created by the element.2.1 Kirchhoff’s Current LawAccording to KCL, the sum of the currents entering a node must be equal to the sum of the currents leaving that node. This means that all of the current entering a node must pass through it without any current building up at that node. Figure 2.0 shows a node that satisfies KCL since two amperes enter the node and two amperes leave the node.41 Ampere2 Ampere 1 AmpereFigure 2.0 Sum of the current entering the node is the same as the sum of the current leaving.2.2 Kirchhoff’s Voltage LawKVL states that the sum of the voltages in a loop must equal zero at every moment. In other words, voltage increases within the loop at any particular point must be counteracted by voltage decreases at other points in the loop. Figure 2.1 shows a loop that satisfies KVL since the sum of the voltages from each element are equal to zero.-1V-1V1V1VFigure 2.1 The sum of the voltages in this simple loop are equal to zero.2.3 Ohm’s LawOhm’s Law states that the voltage across an element is equal to the product of current andresistance. This law allows one to calculate either the voltage across an element, resistance through an element or current through an element as long as any two of the other values are known.53.0 Analysis and Verification of a Resistive CircuitTo 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 I2I3 I4V1R3 V3R1V2R2R4 V4A B CDFigure 3.0 This schematic describes the experimental resistance circuit.Before the experimental procedure took place, four resistors with values between one andten 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 ValuesResistor NominalValue (KΩ)MeasuredValue (KΩ)R1 6.8 6.67R2 8.2 8.14R3 8.2 8.12R4 10 9.843.1 Analysis and Design6To 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. 321III (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. Thedefinition of KVL states that the sum of the voltages in a loop must equal zero. Hence, KVL results in Equation (3.2) since2V, 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).nnnIVR (3.3)3.2 Simulation and Design VerificationAfter 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)7Next, the voltage values derived