lab 5 (loading effects) copy

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EEEB 111 ELECTRICAL/ELECTRONICS MEASUREMENT LABORATORY - UNITEN Exp. 5, Page 2/17

EXPERIMENT 5:

Loading Effects of Meters and Thevenins Theorem

Assessed OBE Course Objectives: CO1 and 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 Movement

Ideally, the internal resistance of a voltmeter is infinite () while the internal resistance of an ammeter should be zero (0) ohms to minimize its effect on a circuit when taking measurements. However, because measuring instruments are not ideal, they do draw current from the circuit 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 soft iron shaft is mounted between two magnetic lines, a proportionate torque is produced which rotates the coil and moves an attached pointer along a calibrated scale. There is always a resistance RM associated with the coil of a wire.

2. Analogue Ammeter A single scale ammeter may be modeled as an ideal movement (short circuit) in series with 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 a proportionate amount of the current (Figure 5.1a). Thus the total meter resistance of a multi range ammeter is the parallel combination of the shunt resistance and the movement resistance RM (Figure 5.1b).


Figure 5.1a: Multi-range Ammeter Figure 5.1b: Equivalent

Ammeter Resistance

Since the ammeter is always connected in series with elements in the branch in which current is to be measured, this meter resistance Rmeter = RM // Rshunt, affects the circuit by placing an additional series resistance in the branch where current is being measured. Also, since the shunt resistance must become progressively smaller to construct larger scales, the meter resistance is dependent on scale.

3. Analogue Voltmeter The DArsonval movement can be used as a voltmeter by calibrating the voltmeter scale corresponding 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 measured loads the circuit by placing a parallel resistor Rmeter = RM + Rseries across the elements (see Figures 5.3a and 5.4b). This parallel resistance draws current from the rest of the circuit. Like the ammeter, the voltmeter resistance is scale dependent.

Figure 5.2a: Circuit without Ammeter

Figure 5.2b: Circuit with Ammeter


Figure 5.3a: Multi-range Voltmeter

Figure 5.3b: Equivalent Voltmeter Resistance

Figure 5.4a: Circuit without Voltmeter

Figure 5.4b: Circuit with Voltmeter

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

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

Figure 5.5: Meter Scale of a analogue meter. The digital voltmeter generally has very high input impedance (in the mega ohm range) so that the loading effect is minimized.

/


Summary:

Measurement devices connected in a circuit to determine the currents or the voltages are theoretically designed to prevent any disturbance in the behavior of the circuit. However, in practice such perfection is impossible. It is then normal to expect that these measurement devices will slightly modify the voltage and the current distribution in the circuit and introduce some errors in the measurements. This phenomenon is known as the loading effect in 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 which

the voltage is to be measured. 2. An ammeter must always be connected in series with the element(s)through which

the current is to be measured.

3. Make sure to verify the polarity of all voltages and the direction of all currents

before you connect the measurement device to avoid a deviation in the wrong direction that might damage the meter.

4. First, select the largest range of values available on the meter and progressively

reduce 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. This procedure also ensures to minimize the relative instrumental error.


Thevenins Theorem 1. Thevenin Equivalent Circuit

Thevenins theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh, where VTh is the open-circuit voltage at the terminals and RTh is the input or equivalent resistance at the terminals when the independent sources are turned off.

Figure 5.6: Replacing a linear two-terminal circuit by its Thevenin

equivalent

VTh is the open-circuit voltage across the terminal as illustrated in Figure 5.7a. RTh is the input resistance at the terminals when the independent sources are turned off as illustrated in Figure 5.7b.

Linear two-

terminal circuit

Load

Load VTh

RTh

V +

-

V +

-

Figure 5.6a: Original

Figure 5.6b: Thevenin Equivalent Circuit

RTh

Linear two-terminal circuit

Linear circuit with

all independent sources set equal to

zero

voc +

-

VTh = voc RTh = Rin

Figure 5.7a: Finding VTh Figure 5.7b: Finding RTh


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

P = i2RL = VThRTh + RL2 RL

Figure 5.8: Maximum Power Transfer Circuit

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

Figure 5.9: Graph of Power delivered to RL, PRL versus RL

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

Therefore, = 24

RL

VTh

RTh

RL

a b


PRE-LAB ASSIGNMENT 1. Calculate the voltage across R2, V2 in the circuit of Figure 5.10.

Figure 5.10: Voltage Divider Circuit

2. An analogue voltmeter with a meter resistance, Rmeter = 200 k is used to measure V2.

a. Re-draw the circuit of Figure 5.10 to include the voltmeters internal resistance.

b. Calculate the voltage across R2, V2 in the circuit re-drawn above.

R1 = 100 k

VS =10 V

+

_ V2

R2 = 100 k _


3. Evaluate the VTh and RTh of the circuit shown in of Figure 5.11 at terminal A-B. Draw the equivalent circuit.

Figure 5.11: Circuit to be simplified to equivalent VTh and RTh

R3 = 3.3k R1 = 1k

R2 = 2.2k VS = 10V

A B


UNIVERSITI TENAGA NASIONAL

Department of Electronics and Communication Engineering College 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 VS measured /0.5 Table 5.2 /2 Table 5.3 /1 Part B : Thevenins Theorem Table 5.4 /1.5 VS measured /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:


EQUIPMENT

1. Resistors: 100k(2), 1 k(2), 2.2 k, 3.3 k 2. Decade Resistance Box 3. Analogue Multimeter (VOM) 4. Digital Multimeter (DMM) 5. DC Power Supply 6. DMM Probes x 2nos. 7. Crocodile Clips Connectors x 2nos. 8. Protoboard 9. Wire 22 AWG x 2nos.

PROCEDURES This laboratory experiment is to create awareness about the loading effects present in voltage measuring devices. Part A: Voltmeter Loading Study

a. Refer to Figure 5.10 in Pre-Lab. b. Measure the resistance of resistors R1 and R2 with the DMM. c. Record the values in Table 5.1.

Table 5.1: Measured values of resistors

Resistors

Nominal 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, V2 with the DMM and VOM using 10V scale.

g. Record the results in Table 5.2.


Table 5.2: Measured values 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, the internal 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 Rmeter for 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: Meters internal resistances Meter

resistance DMM () 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, R2 and R3 and 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 VS to 10V. Measure VS and record it here. VS = ____________

Table 5.4: Resistance of Circuit of Figure 5.11 and RL

Resistors

Nominal Value

()

Measured Value

() R1 1k

R2 2.1k

R3 3.3k

RL 1k


e. Construct the circuit as per Figure 5.11. Connect RL at Terminal A-B.

f. Measure voltage across RL (VRL) and record in Table 5.6.

g. Based on the measured value of VS, R1, R2 and R3, calculate the VTh and RTh. Show the calculation. Get your instructors verification on the calculation.

Table 5.5: Calculation of RTh and VTh

Thevenin Resistance,RTh ()

Thevenin Voltage, VTh (V)

Based on measured value of VS, R1,

R2 and R3

h. Construct the equivalent Thevenin circuit using the VTh and RTh calculated. For RTh

use decade resistor box. Use the same RL used previously.

i. Measure voltage across RL (VRL) and record in Table 5.6

Table 5.6: Measured values of VRL

VRL Circuit of Figure 5.11

VRL Equivalent

Thevenin circuit VRL


Maximum Power Transfer

a. Set the value of RL to 500 using the decade resistor box. Measure RL and record in

Table 5.7.

b. Construct the circuit shown in Figure 5.12. R1 = 3.3k and VS= 7V are closest values to reflect the the VTh and RTh calculated in Table 5.5.

c. Measure the voltage across RL, VRL and record in Table 5.7. Calculate the PRL using the formula given in Table 5.7. You are required to use measured value of RL for the calculation of PRL.

Figure 5.12: Maximum Power Transfer Circuit

d. Repeat the previous procedures for all the values of RL as in Table 5.7.

Table 5.7: Measured values for VRL and PRL

RL ()

Measured Value RL ()

VRL (V) PRL = VRL2RL (W) 500

1k

2k

3k

4k

5k

6k

7k

8k

R1= 3.3k

VS = 7V VRL +

RL 0-10 k


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 VS

values.

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

Table 5.8: Calculated values of V2

Voltage calculated (V) DMM VOM 10V scale

V2

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

__________________________________________________________________

__________________________________________________________________ __________________________________________________________________


Part B: Thevenins Theorem 1. Plot a graph of PRL versus RL on the graph paper provided. Use appropriate scale for

X-axis and Y-axis.

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

Table 5.8: Values of RL resulting in maximum power transfer Maximum Power

Transfer

Measured Value (From Graph PRL versus RL)

Theoretical

value

% Error

RL

Part C: Open Ended Question 1. How can we understand that the digital multimeter has higher internal resistance

compared to analog multimeter? Briefly explain.

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


EEEB111Electrical/ElectronicsMeasurement LaboratoryAssessed OBE Course Objectives: CO1 and CO5ObjectivesIntroductionSummary:

PRE-LAB ASSIGNMENT2. Decade Resistance Box5. DC Power Supply

R1RmeterR1Based on measured value of VS, R1, R2 and R3VRL500RL

lab 5 (loading effects) copy

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