Basic Circuit Analysis
Name
Institutional analysis

Abstract
This report is about an experiment that is done to verify Thevenin’s theorem and Norton’s theorem. The verification is done by first determining the resistance of a circuit of resistances by determining the nodal voltages and nodal currents using Partsim Software. The measured currents and voltages are the used to determine the equivalent resistance of the circuit that is the used to determine the Thevenin voltage, Thevenin resistance and also the Norton circuit.
Introduction
Thevenin theorem states that it is possible to represent any linear power supply by using an ideal voltage source and single resistance that is connect in series to the power source. The series resistance is described as the Thevenin resistance and the power supply is known the Thevenin voltage. The Thevenin theorem is very vital to most designers since it helps in simplification of the conceptual design and operation of the circuit. This report analyses the process of determining the Thevenin circuit from the given circuit. To create a Thevenin circuit all voltages sources are taken as short circuit while all current sources are replaced by open circuit (Leach, 1976).

According to the Norton’s Theorem, a circuit can be simplified so that its complexity is reduced to a simple equivalent that contains a single current source and parallel resistance and is also parallel to a load resistance.

To implement the Norton’s theorem that the Norton current and Norton resistance have to be calculated. Once the two parameters have been established they will arranged as shown in the figure above. To determine the values for the two equivalent circuits, the nodal voltages and the nodal currents have to be determined using the Partsim software. The software works in a manner that once the circuit is designed then using current and voltage probes it is possible to measure the current and voltage at specific point on the circuit.
Objective
The objective of this experiment was to establish the nodal voltage and the nodal currents in the given circuit using the Partsim software. From the measured nodal voltages and current, the Thevenin equivalent circuit and the Norton’s equivalent circuit were to be determined.
Procedure
The circue.it shown below was designed in Partsim which is an online software. Once the circuit was draw, the value of the R5 was determined by the student number. The supply voltage was taken to be 12V.

The basic circuits from the software was the used to determine the nodal currents and nodal voltages. An additional resistor was added to the design so as to ease the process of measuring the nodal and voltage and nodal currents. Once the parameters were measured and noted, they were used to calculate the overall equivalent resistance for resistors that are connected as bridge. The calculated resistance was then used to calculate the equivalent Thevenin circuit and equivalent Norton circuits (Leach, 1976).

Results
The source voltage was found to be 12V. A 1kΩ resistors was added to the design so that the nodal voltage and nodal current would be easily determined. The voltage at node R1 was found to be 10V. The results were summarised by the figure shown below.

Discussion
The voltage at resistor R1 node was found to be 10V. The addition of the 1kΩ led drop in voltage from the supply. This shows that the voltage drop across resistor is 2V and the remaining 10 voltage is fed to the resistor network that is comprises of R1, R2, R3, R4, and R5 (Leach, 1976).
The voltage drop across resistor R5 is given by
VR5 = 12V – 10V = 2V
From the voltage drop, the current flow through the resistor is then determined. IR5=12 – 10 volts1 k=2mA
Since current across resistors in series is equal, the equivalent resistance that arises from of R1, R2, R3, R4, and R6 is the calculated as.
Current through the equivalent resistor = 2mA
Voltage across the equivalent resistor = 10V

The equivalent resistance =VI =10V2mA =5kΩ
From the value of the resistance calculated the resistance of the system is determined by subtracting assumed resistance of 1k ohms from the total equivalent resistance (Leach, 1976).
Circuit Resistance for our circuit = 5k – 1k = 4k (series resistors)
Equivalent Thevenin circuit
The Thevenin equivalent circuit is determined by calculating the Thevenin equivalent resistance and the Thevenin voltage.
Rth = Total resistance of the circuit
Rth = 4k
From the Thevenin Theorem, the Vth is the source voltage. Thus, the equivalent Thevenin circuit is found to be as shown below.

Equivalent Norton circuit
Equivalent Norton circuit requires the Norton current and the Norton resistance.
Norton resistance = Rth = 4k
Norton current = Rnt/ Vth = 12V/4k = 3mA
Norton circuit

Conclusion
The objectives of the experiment were met as the nodal voltages and the nodal currents were established using the Partsim software. The Thevenin voltage was found to be 12V and Thevenin resistance was found to be 4kΩ. The Norton current was found to be 3mA and the Norton resistance was found to be 4kΩ.

Reference Leach, D. (1976). Basic electric circuits (2d ed.). New York: Wiley.