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Experiment 3 – Design of Simple Resistive Circuits

Report Due In-class on Wed., Apr. 4, 2017

Pre-lab must be completed prior to lab.

1.0 PURPOSE

To (i) design a simple LED circuit; and ii) investigate the concept of loading effects in a voltage divider circuit.

2.0 INTRODUCTION 2.1 Voltage Divider Circuits A voltage source is sometimes required to supply a particular voltage to a load and, in fact, it may be required to supply several loads with certain specified voltages simultaneously. Ideally, the voltage supplied should not depend on the size of the load. As a first example, consider the circuit shown in Figure 1 in which a simple voltage divider circuit is connected in series with the load. Notice the situation has been depicted in two equivalent ways. In the second schematic, the negative terminal of the source is assumed to be electrical ground. An electrical ground is a reference level from which other voltages are measured. An ideal electrical ground can absorb an unlimited amount of current without changing its potential. Here, then, conventional current flows from the positive terminal of the source, through the resistors, and back to the source, via the ground path (the closed path connection is not explicit in the schematic diagram, but it is understood).

Figure 1: Two equivalent schematics (𝑎) and (𝑏) for a simple voltage divider

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From the class notes, we know that

𝑣! = 𝑣!𝑅!

𝑅! + 𝑅!

However, this type of voltage divider has a serious disadvantage since the value of 𝑣! depends on the value of 𝑖!, and the latter will change depending on the value of the load resistance.

To help overcome the problem referred to above it is possible to construct a voltage divider with a bleeder resistor R! as shown below in Figure 2.

Figure 2: Two representations (𝑎) and (𝑏) of a voltage divider with a bleeder resistor

Strictly, the voltage across the parallel section of the circuit is obtained by voltage divide rule as,

𝑣! = 𝑣!𝑅!//𝑅!

𝑅! + 𝑅!//𝑅!

where

𝑅!//𝑅! = 𝑅!𝑅!𝑅! + 𝑅!

From equations (2) and (3), we notice that when 𝑅! ≪ 𝑅! ,

𝑣! ≈ 𝑉!𝑅!

𝑅! + 𝑅!

The advantage of this kind of voltage division is that when 𝑅! ≪ 𝑅!, the load voltage is essentially independent of the load resistance. Because the load voltage is less affected by the load resistance in this situation, we say there is better voltage regulation in this circuit (Figure 2) than in Figure 1.

(2)

(1)

(3)

(4)

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2.2 Application of the Voltage Divider Circuit Many applications require physical information such as temperature, force, pressure, flow, position, light intensity, displacement, and liquid level to be converted to voltage for display, measurement, and control purposes, or to generate alarms. The conversion of the physical variable requires the use of a sensor. If the sensor is of the type whose resistance changes with the physical variable, the voltage divider circuit can be used to convert the physical variable to a voltage signal. For example, the resistance of the resistance-temperature detector (RTD) and the light-dependent resistor (LDR) changes in response to the variation of temperature level and to the variation of light intensity, respectively. 2.2.1 Resistance-temperature detector (RTD) This sensor is commonly used for control purposes. The relationship between resistance and temperature is approximated as

𝑅 𝑇 = 𝑅! 𝑇! [1+ 𝛼!Δ𝑇]

where, 𝑅 𝑇 is the resistance at temperature 𝑇 𝑅!(𝑇!) is the resistance at temperature 𝑇! Δ𝑇 is the temperature difference (𝑇 − 𝑇!) 𝛼! is the temperature coefficient (with unit Ω/!𝐶 or /!𝐶) The sensor (RTD) can be used in a voltage divider circuit, as shown in Figure 3, to convert the resistance change due to temperature variation to voltage change for fixed values of 𝑣! and 𝑅!. The output voltage 𝑣! can be calibrated to represent temperature.

Figure 3: Application of the voltage divider circuit - RTD sensor

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Example: If an RTD has 𝛼! = 0.005/!𝐶 and 𝑅! = 500 Ω at 20 !𝐶, and 𝑣! = 12 𝑉 and 𝑅! = 500 Ω, what would be the output voltages at 50 !𝐶, 100 !𝐶, 200 !𝐶 and 1000 !𝐶.

𝑣! = 𝑣!𝑅!

𝑅!"# + 𝑅! = 𝑣!

𝑅!𝑅! 𝑇! 1+ 𝛼!Δ𝑇 + 𝑅!

= 12500

500 1+ 0.005Δ𝑇 + 500

i) 𝑇 = 50 !𝐶, i.e. Δ𝑇 = 50− 20 = 30 !𝐶. Then 𝑣!(50!𝐶) = 5.58 V

ii) 𝑇 = 100 !𝐶, i.e. Δ𝑇 = 100− 20 = 80 !𝐶. Then 𝑣!(100!𝐶) = 5 V iii) 𝑇 = 200 !𝐶, i.e. Δ𝑇 = 200− 20 = 180 !𝐶. Then 𝑣!(200!𝐶) = 4.14 V iv) 𝑇 = 1000 !𝐶, i.e. Δ𝑇 = 1000− 20 = 980 !𝐶. Then 𝑣!(1000!𝐶) = 1.72 V

2.2.2 Light dependent resistor (LDR) An LDR is a photo sensitive sensor which changes its resistance with the change in intensity of light. Its resistance falls as light intensity increases. Therefore, in darkness its resistance is very high and in light its resistance is low; i.e., its resistance can fall from 1 𝑀Ω in darkness to 500 Ω in light. A large range of applications use LDR sensor including automated rear view mirror, automatic head light dimmer, night light control, street light control, laser security systems etc. An LDR sensor can be used in voltage divider circuit, as shown in Figure 4, to convert the resistance change due to light intensity variation to voltage change for fixed values of 𝑣! and 𝑅!. The output voltage 𝑣! can be calibrated to represent light intensity.

Figure 4: Application voltage divider circuit - LDR sensor

2.3 References [1] J.W. Nilsson and S.A. Riedel, Electric Circuits, 10th edition, Pearson Learning Solutions,

2015.

[2] E. Gill, H. Heys, J. E. Quaicoe, and V. Ramachandran, Lab manuals from previous offering of courses ENGI 1040 and ENG 1333.

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3.0 PRELAB 3.1 Read the Introduction (Section 2) and Appendix A of this lab and review the concept of

voltage division from the course textbook and the class notes. 3.2 The manufacturer of a certain LED suggests an operating point of 2.2 V at 20 mA.

3.2.1 If the LED is used in the circuit shown in Figure 5, find the resistance 𝑅! that meets the design requirements.

3.2.2 What would be the minimum power rating of 𝑅!, (1/8 W, 1/4 W, 1/2 W or 1 W)?

3.2.3 How much power must the voltage source be able to provide?

Figure 5: Design of simple resistive circuit

3.3 Refer to Figure 1. The series dropping resistor (𝑅!) has a value of 1 𝑘Ω.

3.3.1 Determine the value of the load resistor 𝑅! so that 𝑣! = 7.5 𝑉 if the source voltage is 10 𝑉.

3.3.2 If the load resistance is increased by 25%, calculate the new load voltage 𝑣!.

3.4 Refer to Figure 2.

3.4.1 Design a voltage divider (i.e., find 𝑅! and 𝑅!) for the load resistance 𝑅! obtained in part 3.3.1 so that it can operate at 𝑣! = 7.5 𝑉 from a 10 𝑉 source. Assume that the bleeder current 𝑖! is 20 𝑚𝐴.

3.4.2 If the load resistance is increased by 25%, calculate the new load voltage 𝑣!. Compare this result with that obtained in part 3.3.2 Comment on the comparison.

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4.0 APPARATUS AND MATERIALS

1 Fluke 8010A Digital Multimeter (DMM) 1 Sun Equipment Powered Breadboard: Model PBB-4060B Standard Resistors: 680 Ω, 1 𝑘Ω, 1.5 𝑘Ω, 2.2 𝑘Ω, 3 𝑘Ω, 3.3 𝑘Ω, 4.7 𝑘Ω and others as calculated in design Potentiometer: 5 𝑘Ω, 200 Ω Various connecting wires and an LED

5.0 EXPERIMENT 5.0 Pre-lab Signature 5.0.1 Have your Pre-lab signed by a TA.

5.1 Design of LED Circuit 5.1.1 Familiarize yourself with the potentiometer – the teaching assistants will help. When using

the potentiometer, do not bend the wire leads – instead, put the pot in the breadboard in a place away from the other components in the circuit and use connecting wires to extend the appropriate lead to the correct point in the circuit. Adjust the resistance of the 200 Ω potentiometer (variable resistor) to the calculated value of 𝑅! calculated in Section 3.2.1. (Be sure to measure 𝑅! resistance with the potentiometer disconnected from the rest of the circuit.)

5.1.2 On the breadboard, construct the LED circuit as shown in Figure 5. The longer terminal of the LED should be connected to the resistor 𝑅! while the shorter terminal should be connected to the negative side of the power supply. Do not connect the LED directly to the 5 V supply. Why? Measure the voltage across the LED (𝑉!"#) and the current through the LED (𝐼!"#). Record these values in Section 6.1.1.

5.1.3 Turn off the power supply and remove the LED from the circuit. Reconnect the LED in the circuit with the shorter terminal of the LED connected to 𝑅! and the longer terminal of the LED connected to the negative side of the power supply. Turn on the power supply and measure the voltage across the LED and the current through the LED. Record these measurements in Section 6.1.3.

5.1.4 Turn off the power and replace the 200 Ω potentiometer with the 5 𝑘Ω potentiometer. Set the resistance of the 5 𝑘Ω potentiometer to 200 Ω. (Be sure to measure 𝑅! resistance with the potentiometer disconnected from the rest of the circuit.) Remove the LED from the circuit and reconnect it in the circuit with the longer terminal of the LED connected to 𝑅! and the shorter terminal of the LED connected to the negative side of the power supply. Now turn on the power supply and observe the changes in the brightness of the LED while increasing the resistance value of 𝑅!. Record your observation in Section 6.1.5.

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5.2 Voltage Divider Circuit 5.2.1 On the breadboard, construct the voltage divider circuit as shown in Figure 1, using a 1 𝑘Ω

resistor for 𝑅! and a 5 𝑘Ω potentiometer as the load resistor 𝑅!. Ensure that the source voltage is 10 𝑉 after it is connected to the circuit. Adjust the potentiometer to obtain an output (load) voltage of 𝑣! = 7.5 𝑉. Measure the value of 𝑅! for this condition and record it in Section 6.2.1. (Be sure to measure the load resistance with the potentiometer disconnected from the rest of the circuit.)

5.2.2 Using the DMM as an ohmmeter, measure the following standard resistors and record the

values in Table 1 in Section 6.2.3: 680 Ω, 1.5 𝑘Ω, 2.2 𝑘Ω, 3 𝑘Ω, 3.3 𝑘Ω and 4.7 𝑘Ω. 5.2.3 With 𝑅! taking the successive measured values of the 680 Ω, 1.5 𝑘Ω, 2.2 𝑘Ω, 3 𝑘Ω,

3.3 𝑘Ω and 4.7 𝑘Ω resistors, use the DMM as a voltmeter to measure the load voltage 𝑣! across 𝑅!. Record all voltage readings in Table 1 in Section 6.2.3.

5.2.3 Construct the voltage divider circuit in Figure 2 using the values of resistors that you

determined in your design in Section 3.4.1. (Use the appropriate fixed resistor for 𝑅! and use the nearest available resistance values for those you calculated in the design for all resistances.) Measure the load voltage to verify your design and record this value in Section 6.2.6.

5.2.4 Now replace the load resistor, 𝑅!, with the successive measured values of the 680 Ω, 1.5 𝑘Ω, 2.2 𝑘Ω, 3 𝑘Ω, 3.3 𝑘Ω and 4.7 𝑘Ω resistors, use the DMM as a voltmeter to measure the load voltage 𝑣! across 𝑅!. Record all voltage readings in Table 2 in Section 6.2.8.

NOTE:

1. At the start of the lab, have a TA sign the Pre-lab.

2. Before leaving the laboratory, have your experimental results for all sections of the lab examined and signed by a TA.

3. The lab report should include the cover page (pg. 8), fully completed section 6 (pp. 9 – 13) showing the signature of a TA for the experimental results, and one (signed) pre-lab for the group.

4 Late submissions (after 9:00 am on Wednesday, Apr. 4) will be penalized and may not accepted.

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Faculty of Engineering and Applied Science Memorial University of Newfoundland

ENGINEERING 1040: Electric Circuits Experiment 3 – Design of Simple Resistive Circuits

Report Due In-class on Wed., Apr. 4, 2018

All parts of the lab must be a collaborative effort of both students.

Name Student ID

Student # 1 Student # 2

Section #: ______________________ Day of Lab: ________________________

(Mon., Tue., Wed., Thu.)

Date of Submission: _______________________________________

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6.0 OBSERVATIONS AND COMMENTS

6.1 Design of LED Circuit 6.1.1 Measurements

𝑉!"# = ________________________ 𝐼!"# = _________________________

6.1.2 Compare the measured 𝑉!"# and 𝐼!"#. Comment on any disparities.

6.1.3 Measurements

𝑉!"# = ________________________ 𝐼!"# = _________________________

6.1.4 Comment on the observations.

6.1.5 How does the brightness of the LED change with increase of 𝑅!? Comment on this

observation.

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6.1.6 Based on the measurements and observations, state whether the following statements is TRUE or FALSE. Justify your answer.

“LED is not a linear circuit element”

6.2 Voltage Divider Circuit 6.2.1 Measurement

𝑅! = ____________________________

6.2.2 Comment on any discrepancies between the measured and calculated values in Section 3.3.1 of the Prelab.

6.2.3

Table 1: Measured load resistance and voltage for the voltage divider circuit given in Figure 1

𝑅! Ω (Standard) 𝑅!(Ω) (Measured) 𝑣!(𝑉)

680 Ω

1.5 𝑘Ω

2.2 𝑘Ω

3 𝑘Ω

3.3 𝑘Ω

4.7 𝑘Ω

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6.2.4 Plot of 𝑣! as a function of 𝑅! .

6.2.5 Comment on the results

6.2.6 Measurements

𝑣! = ____________________________

6.2.7. Compare the above measurement with the pre-lab calculation. Comment on any disparities.

Graph 1: 𝑣! vs. 𝑅! for the circuit shown in Figure 1

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6.2.8

Table 2: Measured load resistance and voltage for the voltage divider circuit given in Figure 2

𝑅! Ω (Standard) 𝑣!(𝑉)

680 Ω

1.5 𝑘Ω

2.2 𝑘Ω

3 𝑘Ω

3.3 𝑘Ω

4.7 𝑘Ω

6.2.9 Plot of 𝑣! as a function of 𝑅! .

6.2.10 Comment on the results.

Graph 2: 𝑣! vs. 𝑅! for the circuit shown in Figure 2

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6.3 Discussion 6.3.1 Discuss any technical difficulties encountered during the lab. 6.3.2 Comment on the probable applications of the voltage divider circuit. 6.3.3 State and comment on the major learning outcomes of the experiment.

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APPENDIX A – VARIABLE RESISTOR

Variable resistors come in many forms, but basically they can be separated into the linear or non- linear types. Variable resistors usually have three leads: two fixed and one moveable. If contacts are made to only two leads of the resistor, the variable resistor is being employed as a rheostat. If all three contacts are used in a circuit it is termed as potentiometer or 'pot'. The value of the overall resistance and the power ratings of variable resistors are usually stamped on their cases.

Some examples of potentiometers are shown below in Figure A.1:

Figure A.1 Example of commercially available potentiometers (https://cdn.instructables.com/FP6/LC66/IA8WFQCA/FP6LC66IA8WFQCA.MEDIUM.jpg)

The resistance between the two outer terminals, i.e. terminal 1 and 3, is fixed to a specific value. The second terminal (center terminal) is connected with a sliding or rotating contact as shown in Figure A.2. This terminal (wiper) can be moved over the whole range of potentiometer by turning a shaft arm or screw on a potentiometer. This movement changes the resistance between terminal 1 and 2 (𝑅!"), and the resistance between terminals 2 and 3 (𝑅!"). The summation of these two resistor values is equal to the total resistance of the potentiometer.

Figure A.2 Structure and Circuit symbol of potentiometer (rotary)

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Potentiometers have multiple operation modes:

• If all three terminals of a potentiometer are used in a circuit, the potentiometer is working as a voltage divider.

• If only terminals 1 and 3 are used to construct a circuit, the potentiometer is being used as a fixed value resistor.

• If the center terminal (terminal 2) and one of the outer terminal (terminal 1 or 3) are used for constructing a circuit, the potentiometer is working as a variable resistor or rheostat.

The following safety practices are commonly used when the potentiometer is used as fixed value resistor and variable resistor.

Fixed value resistor: Turn the wiper all the way towards terminal 1. Then place a short circuit line between terminals 1 and 2. Alternatively, it is possible to turn the wiper all the way toward terminal 3 and placing a short circuit between terminals 2 and 3.

Variable resistor: Place a short circuit line between the unused outer terminal and the middle terminal.