# Rheostats and Potentiometers

20/07/2013 12:46

Author Name:                              Vasilis Leandrou

OBJECTIVES

This report aims to:

• Validate Thevenin’s theorem through experimental measurements.
• Became familiar of an experimental procedure to determine VTh and RTh.
• Demonstrate that maximum power transfer to a load is defined by the condition RL = RTh.

BACKGROUND THEORY

In this experiment will be used the DMM, power supply to validate Thevenin’s theorem and demonstrate that RL = RTh.

·         The DMM read resistance, voltage and current with a digital display.

·         A power supply gives a source of power, rated as maximum voltage and current output.

EQUIPMENT

·         Digital Multimeter                   (Brand: Good Will Instruments Co. Ltd, Model: GDM-8135, Serial Number: CF-922334)

·         Power supply

·         Resistors 91Ω, 220Ω, 330Ω, 470Ω, 1KΩ, 2.2KΩ, 3.3KΩ.

EXPERIMENTAL METHOD AND PROCEDURE

Part 1

The resistor values were taken. Then the Thevenin’s voltage and resistance was calculated and measured (table1.1). Then the IL was calculate by using the Ohm’s law IL=VTh / (RTh+RL), and by using the series-parallel techniques (table 1.2). The power supply was turned on. The voltage VL was measured and the IL was calculated with the original network, and then with the Thevenin’s equivalent (table 1.3).

Part 2

The power supply of 8v was connected in series with the 334Ω resistor and RL(for the follow values: 50Ω, 100Ω, 200Ω, 300Ω, 323Ω, 400Ω, 600Ω, 800Ω, 1000Ω). The value of VL was measured and the power of each resistance was calculated (table 2).

OBSERVATIONS

Table 1.1 Thevenin’s measure values

 calculate values measure values % Difference ETh 4,72v 4,71v 0,21% RTh 2,32KΩ 2,29KΩ 1,30%

Table 1.2 the current throw the RL

 ΙL (equivalent) IL (series-parallel) 1,7mA 1,75mA

Table 1.3 Thevenin Network

 VL IL (from VL) original network 0,81v 1,7mA Thevenin equivalent 0,81v 1,7mA

Table 2 Maximum power transfer

 RL VL P=VL VL / RL 0Ω 0v 0mW 100Ω 1,84v 33,85mW 200Ω 3v 45mW 300Ω 3,79v 47,88mW 323Ω 3,94v 48,06mW 400Ω 4,37v 47,74mW 600Ω 5,15v 44,42mW 800Ω 5,65v 39,9mW 1000Ω 6,01v 36,12mW

Data discussion

On the table 1.1 seeing that the difference of the calculated values and the measure values is very small.  The same thing with the current on the table 1.2

On the table 2 seeing that as the resistor values of RL approach to R1 resistor value, the power of the load resistor is increase. When RL=100Ω the P=33,85mW and when RL=323Ω the P=48,06mW.

According to the Thevenin’s theorem, any two terminal linear ac network can be substitute with a circuit that has the same value consisting of a voltage source and an impedance in series.

The Thevenin’s equivalent is made of a single dc source referred to as the Thevenin’s voltage and a single fixed resistor called the Thevenin’s resistance. The Thevenin’s resistance is the resistance between these terminals with all of the voltage and current source replaced by their internal resistance. The only is the replacement of the term resistance with impedance. Dependent and independent source are treated separately.

The open-circuit terminal voltage (Voc) of the Thevenin’s equivalent circuit is the Thevenin equivalent voltage, that is Voc = VTh. If the external terminals are short circuited the resulting is determined by Isc = VTh / RTh.

Maximum Power Transfer resulted when Thevenin’s resistance RTh is equal with the load resistance RL.

Error Analysis

The diference of the calculated values and the measured values is the formula follows: (5)

So, as an example consider the results in table 1.1 with the calculated Thevenin’s voltage and the measured Thevenin’s voltage.

0,21% = 4,72v – 4,71v x 100%

4,72v

RECOMMENDATIONS

According to the Thevenin’s theorem, any two terminal linear ac network can be substitute with a circuit that has the same value consisting of a voltage source and an impedance in series.

The Thevenin’s equivalent is made of a single dc source referred to as the Thevenin’s voltage and a single fixed resistor called the Thevenin’s resistance. The Thevenin’s resistance is the resistance between these terminals with all of the voltage and current source replaced by their internal resistance. The only is the replacement of the term resistance with impedance. Dependent and independent source are treated separately.

The open-circuit terminal voltage (Voc) of the Thevenin’s equivalent circuit is the Thevenin equivalent voltage, that is Voc = VTh. If the external terminals are short circuited the resulting is determined by Isc = VTh / RTh.

Maximum Power Transfer resulted when Thevenin’s resistance RTh is equal with the load resistance RL.