lab 5 (loading effects)

5/23/2018 Lab 5 (Loading Effects)

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EEEB 111 ELECTRICAL/ELECTRONICS MEASUREMENT LABORATORY - UNITEN Exp. 5, Page 1/17

EEEB111

ELECTRICAL/ELECTRONICS

MEASUREMENT LABORATORY

Experiment 5:Loading Effects of Meters and Thevenins Theorem


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EXPERIMENT 5:

Loading Effects of Meters and Thevenins Theorem

Assessed OBE Course Objectives: CO1and CO5

OBJECTIVES

The objective of this laboratory experiment is to identify the loading effects of digital and

analogue voltmeter and to validate the Thevenins Theorem.

INTRODUCTION

Loading Effects in DC Measurements

1. The DArsonval MovementIdeally, the internal resistance of a voltmeter is infinite () while the internal resistance ofan ammeter should be zero (0) ohms to minimize its effect on a circuit when takingmeasurements.

However, because measuring instruments are not ideal, they do draw current from thecircuit thus causing an effect known as loading.

Most analog ammeters and voltmeters operate based on a current sensing mechanism

called a "DArsonval movement". In this mechanism, a wire coil wrapped around a softiron shaft is mounted between two magnetic lines, a proportionate torque is producedwhich rotates the coil and moves an attached pointer along a calibrated scale.

There is always a resistance RMassociated with the coil of a wire.

2. Analogue AmmeterA single scale ammeter may be modeled as an ideal movement (short circuit) in serieswith the movement resistance, RM. In order to create an ammeter scale with a larger full-

scale range, a shunt resistor is placed in parallel with the movement to draw off aproportionate amount of the current (Figure 5.1a). Thus the total meter resistance of amulti range ammeter is the parallel combination of the shunt resistance and the movementresistance RM (Figure 5.1b).


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Figure 5.1a: Mul t i - r ange Ammeter Figure 5.1b: Equi val entAmmet er Resi st ance

Since the ammeter is always connected in series with elements in the branch in whichcurrent is to be measured, this meter resistance Rmeter= RM// Rshunt, affects the circuit byplacing an additional series resistance in the branch where current is being measured.

Also, since the shunt resistance must become progressively smaller to construct largerscales, the meter resistance is dependent on scale.

3. Analogue VoltmeterThe DArsonval movement can be used as a voltmeter by calibrating the voltmeter scalecorresponding to the product of the current through the movement multiplied by the

movement resistance.

To increase the voltage scale, a resistor is placed in series with the movement resistance.Placing the voltmeter in parallel with the element across which voltage is to be measuredloads the circuit by placing a parallel resistor Rmeter= RM+ Rseriesacross the elements (seeFigures 5.3a and 5.4b).

This parallel resistance draws current from the rest of the circuit. Like the ammeter, thevoltmeter resistance is scale dependent.

Figure 5.2a: Ci r cui t wi t houtAmmet er

Figure 5.2b: Ci r cui t wi t h Ammeter


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Figure 5.3a: Mul t i - r ange Vol t met erFigure 5.3b: Equi val ent

Vol t met er Resi st ance

Figure 5.4a: Ci r cui t wi t hout Vol t meter

Figure 5.4b: Circuit withVol t meter

4.

Meter Scales

Many analog meters have an ohm/volt rating on the face of the meter. The meterresistance for a particular scale may be found by the following formula:

Rmeter = (/) x (full-scale voltage selected)

Figure 5.5: Meter Scal e of a anal ogue meter .

The digital voltmeter generally has very high input impedance (in the mega ohm range)so that the loading effect is minimized.

/


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Summary:

Measurement devices connected in a circuit to determine the currents or the voltages aretheoretically designed to prevent any disturbance in the behavior of the circuit.

However, in practice such perfection is impossible. It is then normal to expect thatthese measurement devices will slightly modify the voltage and the current distribution inthe circuit and introduce some errors in the measurements. This phenomenon is known asthe loading effectin a circuit.

Remarks:

When a measurement device has to be connected in a circuit, the following rules must be

respected:

1. A voltmeter must always be connected in parallel with the element(s) across whichthe voltage is to be measured.

2. An ammetermust always be connected in serieswith the element(s)through whichthe current is to be measured.

3. Make sure to verify the polarity of all voltages and the direction of all currentsbefore you connect the measurement device to avoid a deviation in the wrongdirection that might damage the meter.

4. First, select the largest range of values available on the meter and progressivelyreduce the scale (increase the sensitivity) in order to achieve the most precise reading

that is possible without taking the risk of overloading the measurement device. Thisprocedure also ensures to minimize the relative instrumental error.


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Thevenins Theorem

1. Thevenin Equivalent CircuitThevenins theorem states that a linear two-terminal circuit can be replaced by anequivalent circuit consisting of a voltage source VThin series with a resistor RTh, whereVTh is the open-circuit voltage at the terminals and RTh is the input or equivalentresistance at the terminals when the independent sources are turned off.

Figure 5.6: Repl aci ng a l i near t wo- t er mi nal ci r cui t by i t s Theveni n

equi val ent

VThis the open-circuit voltage across the terminal as illustrated in Figure 5.7a. RThis theinput resistance at the terminals when the independent sources are turned off as illustrated

in Figure 5.7b.

Linear two-

terminal circuitLoad

LoadVTh

RTh

V

+

-

V

+

-

Figure 5.6a: Or i gi nal

Figure 5.6b: Theveni n Equi val ent Ci r cui t

RThLinear two-terminal

circuit

Linear circuit with

all independent

sources set equal to

zero

voc

+

-

VTh = voc RTh = Rin

Figure 5.7a: Fi ndi ng VTh Figure 5.7b: Fi ndi ng RTh


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The Thevenin equivalent circuit is useful in finding the maximum power a linear circuitcan deliver to a load. For the circuit shown in Figure 5.7, the power delivered to the loadis

P = i2RL = VThRTh + RL2

RL

Figure 5.8: Maxi mum Power Transf er Ci r cui t

For a circuit shown in Figure 5.8, VTh and RThare fixed. By varying the load resistance,RL, the power delivered to the load varies as illustrated in Figure 5.9.

Figure 5.9: Gr aph of Power del i ver ed to RL, PR ver sus RL

Maximum power is transferred to the load when the load resistance equals the Theveninresistance as seen RL= RTh.

Therefore, =

4

RL

VTh

RTh

RL

a

b


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PRE-LAB ASSIGNMENT

1. Calculate the voltage across R2, V2in the circuit of Figure 5.10.

Figure 5.10: Vol t age Di vi der Ci r cui t

2. An analogue voltmeter with a meter resistance, Rmeter= 200 kis used to measure V2.a. Re-drawthe circuit of Figure 5.10 to include the voltmeters internal resistance.

b. Calculate the voltage across R2,V2in the circuit re-drawn above.

R1= 100 k

VS=10 V

+

_

V2 R2= 100 k_


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3. Evaluate the VThand RThof the circuit shown in of Figure 5.11 at terminal A-B. Draw theequivalent circuit.

Figure 5.11: Ci r cui t t o be si mpl i f i ed t o equi val ent VTh and RTh

R3 = 3.3kR1 = 1k

R2 = 2.2kVS = 10V

A

B


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UNIVERSITI TENAGA NASIONAL

Department of Electronics and Communication EngineeringCollege of Engineering

Semester: I / II / Special Academic Year: 20 .. / 20 ..

COURSE CODE: EEEB111 EXPERIMENT NO.: 5

LAB INSTRUCTOR: DATE: TIME:

TITLE: Loading Effects of Meters and Thevenins Theorem

OBJECTIVES: The objective of this laboratory experiment is to identify the loading effects of digital

and analogue voltmeter, used in measuring voltage values and to validate the

Thevenins Theorem.

PRE-LAB: MARKS:

Q1 /1

Q2 /1.5

Q3 /1.5

EXPERIMENTAL RESULTS:

Part A : Voltmeter Loading Study

Table 5.1 /1

VSmeasured /0.5

Table 5.2 /2

Table 5.3 /1

Part B : Thevenins Theorem

Table 5.4 /1.5

VSmeasured /0.5

Table 5.5 /2

Table 5.6 /1.5

Table 5.7 /4

POST-LAB:

Part A : Voltmeter Loading Study

Q1 /1

Q2 /2

Q3 /1

Part B : Thevenins Theorem

Q1 /2

Q2

Part C : Open Ended Question/2

/2

CONCLUSIONS: /2

INSTRUCTORS COMMENTS:TOTAL:

/30

STUDENT NAME: STUDENT ID:SECTION:

GROUP MEMBER: STUDENT ID:


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EQUIPMENT1. Resistors: 100k(2), 1 k(2), 2.2 k, 3.3 k2. Decade Resistance Box3. Analogue Multimeter (VOM)4. Digital Multimeter (DMM)5. DC Power Supply6. DMM Probes x 2nos.7. Crocodile Clips Connectors x 2nos.8. Protoboard9. Wire 22 AWG x 2nos.

PROCEDURES

This laboratory experiment is to create awareness about the loading effects present in voltagemeasuring devices.

Part A: Voltmeter Loading Study

a. Refer to Figure 5.10 in Pre-Lab.b. Measure the resistance of resistors R1and R2with the DMM.c. Record the values in Table 5.1.

Table 5.1: Measured val ues of r esi st ors

ResistorsNominal Value

()Measured Value

()R1 100k

R2 100k

d. Construct the circuit in Figure 5.10.e. Set the source voltage VS= 10V, using the DMM for setting accuracy.

Measured VS=___________

f. Measure the voltage across R2, V2with the DMM and VOM using 10V scale.g. Record the results in Table 5.2.


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Table 5.2: Measur ed val ues of V2

Measured Voltage (V)

DMM VOM 10 V scale

V2

Most DMMs have an internal impedance of 10M or greater. For the VOM, however, theinternal resistance can be found on the scale used from the ohm/volt rating.

h. Find the ohm/volt rating (/V) on the VOM.i. Then, calculate the Rmeterfor the VOM on the 10V. Use the following formula:

Rmeter = (VOMs(ohms)

V(

volts)ratings) x (full-scale voltage selected)

j. Record the results in Table 5.3.Table 5.3: Met er s i nt er nal r esi st ances

Meter

resistanceDMM () VOM 10V scale

()Rmeter 10 M

Part B: Thevenins Theorem

Thevenin Equivalent Circuit

a. Refer to Figure 5.11 in Pre-Lab.b. Measure the resistance of resistors R1, R2and R3and record in Table 5.4.c. A resistor act as load, RL, is to be connected at terminal A-B. Use 1k for RL.

Measure and the record the resistance of RL in Table 5.4.

d. Set VSto 10V. Measure V

Sand record it here. V

S= ____________

Table 5.4: Resi st ance of Ci r cui t of Fi gur e 5. 11 and RL

ResistorsNominal Value

()Measured Value

()R1 1k

R2 2.1k

R3 3.3k

RL 1k


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e. Construct the circuit as per Figure 5.11. Connect RLat Terminal A-B.f. Measure voltage across RL (VR) and record in Table 5.6.g. Based on the measured value of VS, R1, R2and R3, calculate the VThand RTh.Show

the calculation. Get your instructors verification on the calculation.

Table 5.5: Cal cul at i on of RTh andVTh

Thevenin Resistance,RTh() Thevenin Voltage, VTh(V)

Based on

measured

value of

VS, R1,

R2and R3

h. Construct the equivalent Thevenin circuit using the VThand RThcalculated. For RThuse decade resistor box. Use the same RLused previously.

i. Measure voltage across RL (VR) and record in Table 5.6Table 5.6: Measur ed val ues of VR

VRLCircuit of

Figure 5.11

VRLEquivalent

Thevenin circuit

VR


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Maximum Power Transfer

a. Set the value of RLto 500 using the decade resistor box. Measure RLand record inTable 5.7.

b. Construct the circuit shown in Figure 5.12. R1 = 3.3k and VS= 7V are closestvalues to reflect the the VThand RThcalculated in Table 5.5.

c. Measure the voltage across RL, VRand record in Table 5.7. Calculate the PRusingthe formula given in Table 5.7. You are required to use measured value of RLfor the

calculation of PR.

Figure 5.12: Maxi mum Power Transf er Ci r cui t

d. Repeat the previous procedures for all the values of RLas in Table 5.7.Table 5.7: Measured val ues f or VR and PR

RL()Measured Value RL

()VR(V) PR =

VR (W)

500

1k

2k

3k

4k

5k

6k

7k

8k

R1= 3.3k

VS= 7V

VR

+RL0-10 k


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POST-LAB ASSIGNMENT:

Show workings of all calculations.

Part A: Voltmeter Loading Study

1. Calculate the ideal value of voltage V2. Use only the DMM measured R1, R2 and VSvalues.

2. With the internal resistance found in Table 5.3 calculate the theoretical value of V2 forDMM and VOM on 10 V scale. Use only the DMM measured R1, R2 and VS values.Record in Table 5.8.

Table 5.8: Cal cul at ed val ues of V2

Voltage calculated (V)

DMM VOM 10V scale

V2

3. What is the effect towards the value of a measured current, IRNflowing through a resistor,RN using an ammeter? Explain.

__________________________________________________________________

__________________________________________________________________

__________________________________________________________________


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Part B: Thevenins Theorem

1. Plot a graph of PRversus RLon the graph paper provided. Use appropriate scale forX-axisand Y-axis.

2. Referring to the graph, what is value of RLresulted in maximum power transfer to RL.Record the value in Table 5.8

Table 5.8: Val ues of RL r esul t i ng i n maxi mum power t r ansf er

Maximum

Power

Transfer

Measured Value

(From Graph PRversus RL)

Theoretical

value % Error

RL

Part C: Open Ended Question

1. How can we understand that the digital multimeter has higher internal resistancecompared to analog multimeter? Briefly explain.

CONCLUSIONS:

Identify TWO (2) main understandings that you have gained from this experiment.


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lab 5 (loading effects)

Documents

parallel resistance

shunt resistance

thevoltmeter resistance

themovement resistance

resistance rmassociated

ammeter scale

meter resistance rmeter

additional series resistance