unsw elec1111 Lab 4 PDF

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1

Circuit theorems

Aims of this experiment The aim of this lab experiment is to investigate the following circuit theorems: 1

Thevenin’s theorem.

1

Norton’s theorem.

2

Maximum power transfer theorem.

Videos and guides for review List of suggested videos: Power supply Multimeter List of suggested guides from Appendix: 

DC power supply



Digital multimeter

Lab 4: Pre-Lab work For your pre-lab work, please answer the following questions before coming to the lab. 1

Consider the circuit of Figure 4 .1. Find the Thevenin and Norton equivalent circuits from across terminals c and d (i.e., assuming

R6

to be a load resistor), as shown

in Figure 4 .2. Show all working and sketch the equivalent circuits.

Figure 4.1: Resistive circuit for Pre-Lab 4.

Figure 4.2: Resistive circuit used to calculate Thevenin and Norton equivalent circuits from terminals c and d.

100||220 = 68.75 (68.75+330+470)||1000 = 464.883 Rth = 464.883 ohm

Vth = V3 – V4 = 3.68 v In = 3.68/464.883 = 0.00792 A

2

Find the Thevenin and Norton equivalent circuits from across terminals b and c (i.e., assuming R3 to be a load resistor), as shown in Figure 4 .3. Show all working and sketch the equivalent circuits.

Figure 4.3: Resistive circuit used to calculate Thevenin and Norton equivalent circuits from terminals b and c.

Rth = (100||220) + 470 + (1000||1500) = 1138.75 ohm Vth = 10 * (220 / (220+100)) = 6.875 v I = Vth / Rth = 0.00604 A

1

State the principle of superposition and explain how it can be used to analyse electric circuits. The superposition principle states that the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone. Superposition: − It is based on the linear property of circuits. − Only one independent source is considered at a time.

− The rest of the independent sources are set to zero (turned off). − Dependent sources are left intact since they are controlled by circuit variables. Superposition can be applied to analyse electric circuits if there are two or more independent sources in a circuit.

2

Explain how Norton’s and Thevenin’s theorems can be used to analyse electric circuits. Thevenin’s theorem provides a technique to simplify the analysis by replacing the fixed part of the circuit with an equivalent one known as Thevenin equivalent circuit. It states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source ��� in series with a resistor ���. Norton’s theorem is the dual form of Thevenin’s theorem. It provides a similar technique to simplify the analysis by replacing a linear circuit with an equivalent one known as Norton’s equivalent circuit. It states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source �� in parallel with a resistor ��.

3

Explain how a DC linear circuit or network can deliver maximum power to a resistive load. Sketch any necessary equivalent circuit and provide the maximum power transfer formula to elaborate your answer (you do not have to prove the theorem). The DC voltage source will deliver maximum power to the variable load resistor only when the load resistance is equal to the source resistance, so that we can get the maximum power by having the minimum power loss.

Pre-Lab 4

Date:

Assessor name and signature:

Mark:

Lab 4: Experimental procedure Please complete all the tasks given in this section during the lab session. Do not forget to watch the related lab videos and guides that are suggested for this lab experiment.

Required components In this experiment you will be required to use the following components:  

A breadboard.

100 Ω ,

220 Ω ,

330 Ω ,

470 Ω ,

680 Ω ,

1 kΩ , and

1.5 kΩ

resistors.

I. Thevenin’s theorem The first part of Section I of Lab Experiment 4 uses the remote lab practical setup in Error: Reference source not found. You will use this practical setup to remotely configure the circuit in Error: Reference source not found.

Figure 4.4: First remote lab setup for Section I of Lab Experiment 4.

Figure 4.5: Resistive circuit for Lab Experiment 4. 4

R6 to be the load resistor and configure the relays to measure the voltage across R6 and the current through it ( V L and I L ). Then calculate the power consumed ( PL ). In Error: Reference source not found, consider

V6 = 2.9 v I6 = 1.879 mA P = V*I = 0.0054491 w

5

Configure the relays to remove

R6

from the terminals c and d (the terminals

clearly become an open circuit). Now measure the open circuit voltage across terminals c and d. What does this voltage represent? V5 = 3.47 v = Vth

6

Compare the measured open circuit voltage with the voltage that you calculated in Lab 4: Pre-Lab work question 1. Provide any necessary explanations and comments. From pre-lab: V = 3.68 v, V(measured is 3.46 v), the slight difference is due to the power dissipation in the connection of the real life measuring equipment

7

Now configure the relays to short-circuit terminals c and d and measure short-circuit current, between terminals c and d (where

R6

I N , the

was connected).

7.9640 mA

ASK YOUR DEMONSTRATOR TO COME CHANGE THE LAB PRACTICAL SETUP NOW The next part of Section I uses the remote lab practical setup in Error: Reference source not found. You will use this practical setup to remotely configure the circuit in Error: Reference source not found and measure the input resistance of the circuit by opening/closing the relevant relay switches.

Figure 4.6: Second remote lab setup for Section I of Lab Experiment 4. 8

Measure the Thevenin resistance

RTh

by appropriately disabling all independent

sources in your circuit. Compare the result with the

RTh

that you calculated in Lab

4: Pre-Lab work question 1. Provide any necessary explanations and comments. Measured: 460.920 ohm Pre-lab: 464.883 ohm Power dissipation in the real life circuit is inevitable, so it’s normal to have measured resistance sightly lower than the theoretical result.

ASK YOUR DEMONSTRATOR TO COME CHANGE THE LAB PRACTICAL SETUP NOW The remainder of Section I uses the remote lab practical setup in Error: Reference source not found. You will use this practical setup to remotely configure a Thevenin equivalent circuit of Error: Reference source not found.

Figure 4.7: Third remote lab setup for Section I of Lab Experiment 4. 9

Sketch the Thevenin equivalent circuit and configure this circuit on a breadboard by opening/closing the relevant relays in the remote lab setup in Error: Reference source not found. Measure the voltage across the load and compare it to the voltage you measured in question 1. Provide any necessary explanations and comments. 7.612 v

II. Norton’s theorem 10 Calculate

IN=

V Th RTh

for the circuit in Error: Reference source not found and

compare it to the measured value obtained in question 4. Calculated: In = 3.47 / 460.920 = 0.00753 A Measured value from Q4: 7.9640 mA = 0.00796 A

III. Maximum power transfer ASK YOUR DEMONSTRATOR TO COME CHANGE THE LAB PRACTICAL SETUP NOW Section III uses the remote lab practical setup in Error: Reference source not found. You will use this practical setup to remotely configure the circuit in Error: Reference source not found and measure the voltage and current of the load by opening/closing the relevant relay switches.

Figure 4.8: Remote lab setup for Section III of Lab Experiment 4. 11 For Error: Reference source not found, measure the voltage across and the current flowing through it (

PL ) for the different values of

RL

( VL )

I L ), and then calculate the power consumed ( R L by opening/closing the relevant relays. Write

down all your measurements and calculations in the Table.

Figure 4.9: Resistive circuit to examine maximum power transfer theorem.

Load

resistor

RL

Ω

Load

voltage

VL

Load

current

IL

Load

power

PL

100 Ω

1.933 V

0.0177 A

0.0342 W

220 Ω

3.4 V

0.0146 A

0.0496 W

470 Ω

5.2 V

0.0107 A

0.0556 W

6.06 V

0.0086 A

0.0521 W

7.4 V

0.00605 A

0.0448 W

12 Plot the variation of the load power

PL

with respect to the variation of the load

R L using the collected data. Identify at what point the power is resistor maximum. Calculate the theoretical value for the maximum power transferred for the circuit of Error: Reference source not found and compare it with your experimental value.

Lab work 4

Date:

Assessor name and signature:

Mark:...