Lab report on the Thevenin experiment

**Abstract **

There were a number of main objectives which to be accomplished at the end this experiment. The main objectives included learning about the Thevenin equivalent circuit; knowing it is obtained and how all the parameters associated with it are gotten. Among the parameters that were to be established include the Thevenin voltage and resistance. The values were to be found experimentally and also through calculations. The other aim of the experiment was to investigate the idea of having maximum power transfer and knowing how to establish the load resistor values that have the maximum power from any given Thevenin circuit. At the end of the experiment, it was to be established that at the maximum power factor, the Thevenin resistance is equal to the value of the load resistance. During the test the Thevenin equivalent circuit was set and results were recorded from the open circuit voltage and the other results taken from the short circuit were also noted. Again the values of current in short circuit the voltage in an open circuit were calculated using the values parameters in ideal condition. The values obtained in the experiment were used in comparison with calculated values to find the percentage in the experiment. Then the Thevenin equivalent circuit was constructed and its values of the voltages and the resistances were recorded. The acquired results were noted down and were used to plot the graph of power dissipated thorough the heat in the load resistor against the resistance of the load. The groups were used in drawing the conclusions of the Thevenin circuits by comparing the results from the constructed circuited against the

**Introduction **

An experiment was carried out in the laboratory to determine Thevenin circuit values and compare the parameters to those that are given in theory. The various measured values used to determine and construct a Thevenin circuit are the Thevenin resistance, Thevenin current, and the currents. There are values for the open circuit voltages and the short-circuit currents. Resistive loads are also added to the circuit and to establish if there is any difference. This lab experiment aims at establishing that all the resistive load circuits take the form of Thevenin circuit which is composed of the Thevenin voltage and Thevenin resistance. It also looks at the error that is found between the calculated theoretical values from the experimental values through the graphical analysis.

**Theoretical calculations**

Figure 1 shows the Thevenin equivalent circuit. From the circuit shown of the Thevenin circuit, it can be shown through experiment that all resistive circuits i.e. all circuits that only have sources and resistors are equivalent to the simplified circuit of the Thevenin circuit. The circuit contains the Thevenin resistance which is labeled R_{th} in the circuit and the Thevenin voltage labeled as the V_{th}. Thus, in any given circuit, these values of the resistance and voltages are to be calculated and found. The circuit can be connected to other external resistance between the endpoints of the circuit labeled A and B and can receive maximum power if they have values that are equal R_{th}.

There are various ways of calculating the resultant value of the resistance R_{th}. One method of finding this resistance value is through calculating the short circuit current I_{sc} in the initial circuit. This is that current that passes through the endpoints A and B. From this the Thevenin resistance can be calculated since the circuit is supposed to offer the same amount of the short circuit current. Thus Thevenin resistance can be found through the formula:

Equation 1: finding the Thevenin resistance

The second method of calculating the Thevenin resistance is through connecting the terminals to an infinite resistance and taking the readings of the voltage drop in comparison to that of an open circuit. This is the method used in the finding of the source resistance whereby the formula below is applied.

Equation 2 Finding Thevenin resistance with terminals connected to infinite resistance

The third method used in finding the Thevenin resistance that is only functional without dependent sources is done by replacing wires in place of the voltages sources and then the current sources are removed. The resistance between the nodes A and B are then calculated or measured from the experiment.

**Results analysis**

The experiment was performed in accordance to the theory and experimental set up and the obtained outcome helped attain the objectives set for the test. The experiment was carried out by setting up the Thevenin circuits and the values obtained used to calculate the resistance values of the Thevenin resistance. The experimental results were obtained from both the Thevenin equivalent circuit and the circuit with additional resistance shown in the circuit below.

Figure 1The circuit with more resistive loads

The values obtained from the experiment were used to plot a graph of power dissipated by the load resistor against the value load resistance used in the initial circuit. The plot was to establish the characteristics of the resistive circuits which show that all resistive circuit .take on a simple circuit structure of the Thevenin equivalent circuit which is given in the theory.

Figure 2: Thevenin equivalent circuit

Figure 3 : Experimental results for resistor R_{th}

Voltage (V) | Current (mA) |

1.23 | 2.34 |

2.34 | 4.56 |

3.45 | 3.23 |

4.56 | 2.34 |

5.67 | 5.67 |

6.78 | 10.33 |

Figure 4: The graph of load power dissipated

The results found to form the experiment were compared with the cal calculated values from the theoretical values. In this case, the values found were used in the calculation of the percentage error for the experimental values using the following formula:

Equation 3: Calculating the percentage error between experimental value and theoretical value

A table was created for calculated percentage error and the load resistance, Thevenin voltage resistance and Thevenin current results from the experiment which were then utilized in the analysis of the experiment.

From the percentage errors calculated, it was determined that there had been a number of experimental errors while carrying out the experiment. These experimental errors can be attributed to the human errors while measuring and recording the experimental results. They could also be attributed to worn out experimental apparatus which gives an incorrect reading. Results calculated in the theory were used in determining the validity of the results found in carrying out the experiment.

**Conclusion **

In conclusion, the experiment was carried out successfully with minimal errors. The objectives of the experiment were met where the values of the Thevenin experiment parameters were established and then compared to the theoretical values. The values were calculated for different circuits and also the value of maximum power transfer was calculated and determined. From the obtained results and the plotting of the results to compare the results, it was concluded from the findings that all resistive circuits take the simple form of the Thevenin circuit which is made up of the Thevenin resistance and the Thevenin Load.

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