Exp 3

INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA REPORTS ON ECE 1101: ENGINEERING LAB - I “EXPERIMENT 3” “THEVENIN’S AND NORTON’S THEOREM AND MAXIMUM POWER TRANSFER”

No.

Evaluation Items

Marks 20%

1

Introduction

2

2

Objectives

2

3

Equipment list

2

4

Experiment Set-up

2

5

Observations & Data Analysis

6

Conclusion

TOTAL

Marks obtain

10 2

20

Date of Experiment: 17 / 01 / 2011

Date of Submission: 24 / 01 / 2011

Matric No : 1013467

Name : Mohd Syamsul Bin Ramli.

Matric No : 1017783

Name : Abdul Rahman Bin Baseair.

Matric No : 1011021

Name : Ridzuan Bin Mohamed Seth.

THEVENIN’S AND NORTON’S THEOREM Introduction: Vth is the voltage open circuit at the terminal a & b. Rth is the Rin at the terminal a & b when Vth is off and short circuit. IN is the current through terminal a & b when it is short circuited. RN = Rth Objective: • To find the current flowing in a particular resistor (variable load) of a network by application of Thevenin’s and Norton’s theorem. • To verify the theorem by comparing the simulated values to those obtained by measurement. Apparatus: o DC supply (Vs=15V) o Digital multimeters o Resistors, R1=1.8kΩ , R2=3.6kΩ , R3=820Ω , R4=R5=100Ω , RL=180Ω .

Figure 3-1 (a) Thevenin’s Theorem: Method: 1.

The supply voltage and resistance of each resistor was measured. These values were recorded in Table 3-1. RL was selected as the resistor where it was proposed to current value. 2. The circuit in figure 3-1 was constructed. The supply should not be turn on. 3. Resistor RL was removed from the network. 4. The power supply was turned on. The voltage between the points A and D of the network was measured as the Thevenin’s voltage and the value were recorded in Table 3-2. 5. The power supply was switched off. The power supply V1 was replaced with a short circuit. 6. The resistance between terminals A and D was measured as the Thevenin’s resistance and the value were recorded in Table 3-2. 7. The resistor RL was placed back in circuit with an ammeter was connected between terminals A and B or C and D. 8. The short circuit connection was removed and the power supply was placed back in the circuit. 9. The power supply was turned on. The current value flowing in the resistor RL was recorded. 10. Thevenin’s equivalent circuit inclusive of resistor RL was drawn.

(b) Norton’s Theorem: Method: 1. The circuit as shown in Figure 3-1 was constructed but the power supply remains off. 2. Resistor RL was removed from the network. RL was selected as the resistor where it was proposed to determine the current value. 3. The supply voltage was turned on. The current across the terminals A and D shown by the ammeter was read. This was Norton’s current. The value was recorded in Table 3-3. 4. The power supply was switched off. The supply was replaced with a short circuit. 5. The resistance between the terminals A and D was measured. This was Norton’s resistance. The value was recorded in Table 3-3. 6. The resistor RL was placed back in circuit with an ammeter connected between terminals A and B or C and D. 7. The power supply was placed back in the circuit instead of the short circuit. 8. The current flowing across the resistor RL was read and recorded. 9. The Norton’s equivalent circuit inclusive of resistor RL was drawn. Discussion and conclusion: The aims have successfully been achieved; the current flow in a particular resistor of a network by application of Thevenin’s and Norton Theorem has been obtained. The Thevenin’s Theorem is a process by a complex circuit reduced to an equivalent series circuit consisting of a single voltage source, a series resistance and a load resistance, RL. The Norton’s Theorem is the dual of Thevenin’s, it simplifies a complex network into a current source called the Norton Short Circuit Current. A parallel Norton Equivalent Conductance or Norton equivalent resistance and a parallel load resistance, RL was also used. The fact of the theorems was applied to the experiment successfully because the measured values approximately closer to the theoretical values and thus, the theorem have been verified. Thevenin’s Theorem is likely to be used widely in practice because it can obtain both load voltage and load current. We most likely interested in voltage and current and it is easier to have both of the values. Norton’s Theorem is the fact that based on the concept of a constant current generator. It simplifies a complex network into a current source called the Norton’s Current or the Norton Short Circuit Current. The theorems will be most applicable in the complex network circuit like those involving wye-delta transformation. It is also able to analysis a particular resistance, current and voltage. The theorems are still valid if there is more than one supply in the circuit because the sources will eventually be replaced either with a short circuit for voltage source or an open circuit for current source.

(C) Maximum Power Transfer: Introduction: •

The maximum power transfer theorem states that a resistive load will receive maximum power when its total resistive value is exactly equal to the Thevenin’s resistance of the network as “seen” by load.

Objective: •

To verify the maximum power transfer theorem

Apparatus: o o o o o

One DC voltmeter One DC ammeter One power supply Rheostats (RTH=22 Ω, RL=44 Ω) Wires and chords

FIGURE 3-2

Method: 1. 2. 3. 4. 5. 6.

The Thevenin’s Equivalent Circuit in Fig. 5-1 was constructed. 10V dc was apply from the dc power supply. The Thevenin’s rheostat was kept, Rth 5kΩ at maximum position The load rheostat RL was vary from 0Ω to 10kΩ. The voltages VL and I was measured. 11 sets of reading was taken. All the result was recorded in Table 3-4.

Analysis and deductions: The maximum power transfer theorem has been verified. By theory, the maximum power transfer is given by mathematical expression = Pmax = ( Vth / Rth+ RL)2 *RL . This means that the power transfer will be at maximum when the load resistance value equals the Thevenin resistance value of the circuit. From the test result by using a 5.1kΩ resistor (fixed) as a Thevenin resistor, obviously the highest value of power gotten is when the load resistor value is 5.0 lΩ (the nearest value to 5.1 kΩ). High voltage transmission is used in case of transmitting electric power to transmit the power to the load with the greatest efficiency by reducing the losses on the power lines. The efficiency of power transfer is defined as the ratio of the power delivered to the load to the power supplied by the source.

In practice, circuits are designed both for maximum power transfer and for high transfer efficiency, depending on the application of the circuit. For example, in communications area, it is desirable to maximize the power delivered to the load. Power utility transmits power at maximum efficiency instead of transmitting maximum power to reduce the amount of power loss during the power transmitting process therefore will save the budget spent. The conditions for maximum power transfer are the power at relatively low efficiency of 50% can be tolerated and voltage regulation is equal to 100%. There are few factors that caused the difference between the experimental and the theoretical results. The first factor is, the resistor used was not 100 % accurate to the required value of resistance. There are also few errors while setting up the circuit. There is also resistance in the apparatus and wires that are used that affected the outcome of the results.

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