ELC LAB 5 212086561

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Table of Contents Introduction ........................................................................................................................................................ 2

Theory ................................................................................................................................................................. 2

Equipment used .................................................................................................................................................. 5

Procedures .......................................................................................................................................................... 5

Results ................................................................................................................................................................. 8

Discussion of results ........................................................................................................................................... 9

Analysis ............................................................................................................................................................... 9

Compare the values of VAB and IL in Norton’s experiment with those obtained in in case the circuit is

treated as Thevenin’s circuit. Is theory of source transformation verified? ...................................................... 9

When the Norton’s equivalent circuit is established and is compared with the thevenin’s equivalent circuit

they behave in exactly the same way due to the fact that they are just a source transformation of each

other. .................................................................................................................................................................. 9

On what grounds one can say that Thevenin and Norton are the source transformation of each

other?.................................................................................................................................................................. 9

Referring to the observation tables 3 and 4, how much current will be supplied by the source?

Justify your answer mathematically. .................................................................................................................. 9

The relationship between power absorbed for the networks of Figure 4 and 5, what can you infer from

it? [Hint: Talk in terms of resistance] ................................................................................................................ 10

Conclusion ......................................................................................................................................................... 10

REFERENCES ................................................................................................................................................. 11

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Introduction

Electricity is an essential part of the modern life experience, and as an engineer it is essential to know

how it behaves and responds to changes in its trajectory. This lab was divided into two parts namely

Part 1 you work with Norton`s theorem and part 2 is all about delta/ star transformations. The main

goal of the lab is to verify Norton’s Theorem and the theory of Star – Delta transformation. The

purpose is to get familiarized with lab equipment be able to make simple circuit connections and

successfully be able to extract experimental data from such connected circuit.

Theory

Basic definitions needed for the complete understanding of the content of this report :

Voltage is electrical potential energy per unit charge which is measured in joules per coulomb

which has its SI unit as volts.

Resistance is defined as the opposition within a conductor to the passage of electric current which

has its SI unit as Ohms (Ω). Carbon resistor are the components which are placed in a circuit to

oppose current flow.

Power supply is a device that supplies electric power to an electrical load.

Norton's Theorem

Norton's theorem states that any two terminal networks may be replaced by a simple equivalent

circuit consisting of a constant current source IN, shunted by an internal resistance RN,. The

Norton current IN is distributed between the shunt resistance RN and the load RL. The current

IL in RL may be found from the equation NN L NL I xRI RR = + The rules for determining the

constants in the Norton equivalent circuit are as follows:

1 The constant current IN is the current that would flow in the short circuit between the load

resistance terminals if the load resistance were replaced by a short circuit.

2 The Norton resistance RN is the resistance seen from the terminals of the open load, looking

into the original network, when the voltage sources in the circuit are replaced by their internal

resistance. Thus RN is defined in exactly the same manner as is RTH in Thevenin’s theorem.

The theory of source conversion says that the Norton and Thevenin’s circuits can be terminally

equivalent and related as follows:

Figure 1a shows the original network as a block terminated by a load resistance RL. Figure 1b

shows the Norton equivalent circuit

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Figure 1

Figure 2

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Delta-Star transformation

The delta-star resistor network can be equivalent to a network of star-delta resistors connection

and vice versa through a process of delta-star or star-delta transformation .As such, the electrical

performance of the interchangeable delta-star or star-delta resistors will be Identical.

Figure 3: Star-delta or Delta-Star Transformation

From figure 3, it can be seen that the resistance across any two terminals of equivalent Delta- Star or Star-Delta resistors are shown in steps A and B as follows:

A. Equations for the transformation from Delta (Δ) – load to Star (Y) – load as common in 3-

phase circuits

The general idea is to compute the impedance at a terminal node of the Y circuit with

impedances , to adjacent node in the Δ circuit by

Whereby represents resistances or impedances in the Δ circuit, this calculation yields the

specific formulae

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B. Equations for the transformation from Star (Y) – load to Delta (Δ) – load as common in 3-

phase circuits

The general idea is to compute impedance in the Δ circuit by

Where is the sum of the products of all pairs of impedances in

the Y circuit and is the impedance of the node in the Y circuit which is opposite the

edge with . The formula for the individual edges is thus

Equipment used

Power supply

Digital Multimeter (DMM) which serves as a Voltmeter and Ammeter

Resistor boxes

Conductors

Variable resist

Procedures

To Measure Voltage:

Change the voltage selection knob on the DMM to (DC or –V) for DC measurement. Voltage is

measured in parallel with the load and the range of your measurement can be altered by using the

Range buttons.

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To Measure Current:

Change the current outlet of the DMM to (“+” terminal) and the COM outlet (ground). Current is

measured in series you will have to break the circuit to measure current. For a current less than

200mA use the outlet (VΩA) and for current greater than 200mA use the outlet written 20A

in red else the DMM will not be accurate and may not show the current reading. You can vary the

range of your measurement by using the Range buttons.

To Measure Power Supply Voltage:

A voltmeter is always connected in parallel across your load or power supply. The “+” terminal of the

voltmeter should be connected to the “+” terminal of the Power Supply hence forth referred to as (PS)

(usually the red outlet) and the “-” terminal of the voltmeter to the “-” terminal of the PS (usually the

COM or black outlet) of the DMM.

Part 1 of the lab NORTON’S THEOREM

Connect the circuit as shown in figure 2(a) above in the theory section. Remove the RL from the circuit across which Norton equivalents have to be found out. For RN or RTH of the circuit, remove the voltage source and short circuit the open terminals. Now place an ohm meter across A and B. Verify your observation, by calculating the RTH.

For IN, retain the source back into the circuit and place an ammeter connecting the

terminals A and B. The value of the current is the short circuit current i.e. IN. Also compute the value of the Norton’s equivalent current and record it in the table. Now construct the Norton’s equivalent circuit and measure the IL and VAB. (That is vary the

supply voltage until DMM indicates the value IN )Also calculate the value of IL and VAB by

using methods other than Norton’s theorem. Record all results on the tables ( 1 and 2 ) below in the results section

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Part 2 of the lab. DELTA-STAR TRANSFORMATION

Figure 4: Resistors in Delta

Connect circuit in Figure 4:R1=3kΩ , R2=3kΩ , R3=1kΩ , R4=2kΩ , R5=3kΩ ,V1=10 VDC

Measure the voltage VAB and record in Table :3 Measure the currents I1,I2 IT ,and IAB and record in Table:3 below in the results section and

calculate power across AB

Figure 5: Resistors in Star-Connection

Connect circuit in figure 5 and adjust Ra to 1 kΩ

Measure the voltage VAB and record in Table :4 Measure the currents I1,I2 IT ,and IAB and record in Table:4 and calculate power across AB Adjust variable resistor (RA) and repeat steps (b) and (c).

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Results Part 1 results: NORTON’S THEOREM

Table 1: Resistance values Nominal Values (Ω) Measured Values (Ω)

47 46

220 271

330 327

1000 1006

Table 2: RL Ω IN

(A) RN

(Ω) I L

(A) `VAB (V)

Computed

Measured

Computed

Measured

Computed

Measured

Computed

Measured 18.1 mA 270 33.85 mA 33.4 mA 9.14

Part 2 Results. Delta-star transformation

Table3- Resistors in Delta connection

Calculated Measured I1 2.92 2.59 mA

I2 1.84 1.64 mA

IT 4.72 4.24 mA

IAB 0.36 0.32 mA

VAB 1.15 1.04 V

PAB 0.414 332.8 W

Table 4- Resistors in Star connection

Variable resistor = 1kΩ Variable resistor = 2kΩ Variable resistor = 3.23kΩ Calculated Measured Calculated Measured Calculated Measured

I1 2.727 2.72 mA 1.875 1.75 mA 1.428 1.39 mA I2 1.799 1.68 mA 1.25 1.10 mA 0.952 0.86 mA IT 4.58 4.42 mA 3.125 2.85 mA 2.38 2.23 mA IAB 0.906 3.90 mA 0.625 0.53 mA 0.476 0.41 mA VAB 0.909 6.87 V 0.625 0.66 mA 0.476 0.52 V PAB 0.824 0.85 W 0.39 0.35 mA 0.23 0.21 W

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Discussion of results

Analysis

Compare the values of VAB and IL in Norton’s experiment with those

obtained in in case the circuit is treated as Thevenin’s circuit. Is

theory of source transformation verified? (ANS)

When the Norton’s equivalent circuit is established and is compared with the thevenin’s

equivalent circuit they behave in exactly the same way due to the fact that they are just a

source transformation of each other.

On what grounds one can say that Thevenin and Norton are the

source transformation of each other? (ANS)

When the circuit has already been simplified and all that is left is a voltage source in series with a

resistance which is the thevenin’s equivalent. Now this thevenin equivalent circuit if source

transformed will result in the Norton`s equivalent circuit and vice versa.

Referring to the observation tables 3 and 4, how much current

will be supplied by the source? Justify your answer mathematically.

(ANS)

For table 3

The current generated by the source is the algebraic sum of the currents I1 and I2. Therefore 2.59+1.64mA=

4.23mA which can be verified in table three above.

For table 4

The current supplied by the source changes as the Req also changes due to the ohms law relationship which

states that R=V/I. Therefore the current supplied by the source shall be as follows

With a 1KΩ variable resistor… It= 2.72mA+1.68mA=4.4mA

With a 2 KΩ variable resistor… It=1.75mA+1.10mA=2.85mA

With the 3.2 KΩ variable resistor… It=1.39mA+0.86mA=2.25mA

Therefore as the total resistance increases so does the total current supplied decrease.

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The relationship between power absorbed for the networks of Figure

4 and 5, what can you infer from it? [Hint: Talk in terms of resistance]

(ANS)

Since the relationship between voltage and resistance to generate power is ( P=V2/R ) and due to the

different arrangements between the resistors in figures 4 and 5 will cause different values for the equivalent

resistances.

For figure 4 there shall be a smaller resistance than in figure 5. And due to the fact that the source voltages

remain the same the following conclusions can be made.

That there shall be more power dissipated in a circuit with an arrangement as in figure 4. And there

shall be less power dissipated in a circuit with an arrangement as the one in figure 5

Conclusion

In conclusion it is very well established mathematically and theoretically that the Norton`s equivalent circuit

and the thevenin`s equivalent circuit are very closely related to one another since one is a source

transformation of the other. Therefore according to ohms law the relationship between resistance voltage

and current allows us to theoretically prove the practical results that we have gotten. The delta star network

transformation aids in the simplification of the circuit for the analysis.

In addition this lab has been of immense interest as it has established some of the most common theories in

elc as true.

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REFERENCES

Bird, J. (2003). electrical circuit theory and thechnology. boston: Newnes.

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