Lab Man 2426 So 2013

By Xiang-Ning Song

PHYSICS 2426University Physics IILaboratory Manual

Acknowledgments

I would like to express my sincere thanks to all of the people whose support, help, andassistance have been important in the completion of this lab manual.

I am grateful for the support from Ray Canham and Rita Maher. My gratitude goes toAfaf Abughazaleh, Claudiu Rusu, Fred Wittel, and Justin Song for reviewing the manualand providing so many helpful suggestions. I am especially thankful to Claudiu Rusu andJustin Song for assistance in creating some of the graphics.

Xiang-Ning Song

Richland College

Physics 2426

Table of Contents

Lab Guide 5

1. Standing Waves on a Stretched String 11

2. The Speed of Sound in Air 19

3. Electrostatic Charge 27

4. Equipotential and Electric Field Lines 37

5. Capacitors in Series and Parallel 47

6. Resistors in Series and Parallel 55

7. The RC Circuit: Measuring a Voltmeters Resistance 63

8. Magnetic Fields 73

9. Magnetic Force and Measuring the Permeability 83

10. The Oscilloscope 91

11. The AC Circuits 101

12. Laws of Reflection and Refraction 111

13. Thin Lenses and Lens Combinations 119

14. Diffraction and Interference 127

5

LAB REPORT GUIDE

I. Format of Lab Report

PRE-LAB FORMS

You are expected to have completed a Pre-Lab form for each of the experiments that wedo this semester, unless instructed otherwise by your teacher. These Pre-Lab formsconsist of basic questions designed to familiarize you with the concepts involved in thelab experiment. Lab data are recorded on separate paper during the course of the labperiod. These forms are to be turned in (deposited) on the front desk in the laboratorybefore the class begins.

COMPLETED LAB REPORTS

The lab report containing data, analysis, answers to questions, etc., is to be turned in onthe date specified by your teacher, usually at the beginning of the next lab period. Stackthese next to the Pre-Lab forms that you turn in for that days experiment. A stapler isavailable to help you make these reports a neat package.

The complete graded lab report will consist of a Pre-Lab form and final report thatare put together by the lab teacher and given a unit grade. The instructor will decide therelative weighing of each part of the lab report.

NEATNESS

All papers must be reasonably neat and organized. The margins should not have straynotes. If there is not sufficient space available on the lab forms to answer the questions,then you should write the answers on a separate sheet of paper and staple this to the labreport. The neatness, organization, and explanation of your measurements in the labreport represent the quality of your work.

REPORT FORMAT. FORMAL REPORTS

Lab report has the format of the outline below. Formal reports are more detailed, and youare to type these using a word processor. Your lab teacher will specify which labs reportsare to be formal reports.EXPERIMENT TITLEAUTHORS NAMELAB PARTNERS NAMESOBJECTIVES OF THE EXPERIMENTBASIC THEORY. Develop the calculation relations from first principles.DATA AND SAMPLE CALCULATIONS with units and appropriate significant digits.Please show only one sample of each non-trivial type.ERROR ANALYSIS. This is described in this LAB GUIDECONCLUSIONS. What have we learned? You may critique the lab experiment.

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QUESTIONS. Answer these on separate sheet of paper unless adequate space is availablein the informal reports

ORIGINALITY

Work in the laboratory is usually performed with one or more lab partners who shareyour data. You are expected to discuss the lab work and the data with partners, but pleasewrite your own sentences. You are to understand the mathematics you use in your report.You are to construct your own graphs and make independent calculations (for example, aslope). Do not copy work you do not understand.

II. Experimental Error and Data Analysis

RECORDING DATA. Uncertainty in measurements.LEAST COUNT: The smallest division on a measurement scale is called the least count.Most metric rulers have a least count of 1mm (0.1 cm). The triple beam balance that weuse to measure mass in this lab has a least count of 0.1g.

RECORDING DATA: When you record a measurement you must record all the digitsthat the measuring tool is capable of producing. As a concrete example, considermeasurements of the width, W, of this page with a standard metric (cm) scale. Aftermaking a few measurements, the smallest value that seems reasonable is

Least W = 21.49 cm

The largest value that I made (or seems reasonable) is

Largest W = 21.52 cm

I would record the width as W = W0 W = 21.5 0.02 cm. The 0.02 cm is myestimate of the limits of precision for this instrument. I feel that I can measure to 1/5th ofthe smallest division on the scale.

Similarly I have measured the length, L, and I record L= L0 L = 28.00 0.02cm. Recording L = 28 cm wont do since this implies that I dont know the digit thatfollows the 8. Another reasonable person might have measured and recorded 28.01cmor perhaps 27.98 cm.

The last digit recorded is an uncertain or estimated digit. You can use the leastcount of the measuring device, repeated measurements of a value, or other reasonableapproach to decide the uncertainty of a measurement and the corresponding precision thatyou should use to record the data. It is responsibility of the student to decide what theuncertainty of a measurement is.

Some numbers are exact numbers. How many ears do you have? We record thisas 2 and not 2.00

7

SIGNIFICANT DIGITS AND SCIENTIFIC NOTATION

As an example let us consider the size of a proton (which is a unit in the nucleusof an atom). A protons radius is about 0.000,000,000,000,0075 m. How many significantfigures (or digits) does this number have? It has 2 significant digits. The leading zeros arenot significant in the sense that they relate to the precision of the value. It is rather silly tomake the reader count all those zeros to understand the size of the number. You areexpected to write very large or very small numbers in scientific notation form. For thecase of the proton, r = 7.5 x 10-15 m. We could use an appropriate prefix to indicate themultiplier, femto f = 10-15, r = 7.5 fm.

When you record data you must write all the digits that are significant for themeasuring device and the proper units. In the above example the length of the paper, L, isrecorded to 4 significant digits. The last digit recorded is an uncertain digit.

UNCERTAINTIES FOR ARITHMETIC COMBINATIONS

When you combine numbers through arithmetic, i.e., multiplication, addition, etc., thenumber of significant digits in the result is to agree with the least precise number that wasused in the calculation. As an example, let us compute the area, A, using the data fromprevious example. The area is computed as length times width:

A0 = L0W0 = (28.00 cm)(21.50 cm) = 602.0 cm2

The area is recorded using 4 significant digits since the numbers that went into thecalculation was good to only 4 digits.

Do not simply write down all the numbers that might be on your calculator. Exactnumbers, like 602, is what the calculator yields. You have to record it as 602.0 for 4significant digits. When numbers like or (2) appear, use the appropriate keys on your

calculator to make the calculations, then use the data to determine the appropriate numberof significant digits for the final result. Do not round off before you have finishedcalculating.

How does one estimate the relative uncertainty in this area? (Relative uncertaintyis the uncertainty in a number divided by the number.) The relative uncertainty is givenby A/ A0 = (L0W + W0L)/ A0,

where W and L were both estimated to be 0.02 cm. After arithmetic, the uncertainty of area is A = 0.99 cm2, and then you can express area as A = A0 A = 602.0 0.99cm2 .

NOTE ON COMBINATION OF ERRORS: The calculation of the areas relativeuncertainty as A/ A0 = (W/ W0) + (L/ L0), using positive values, is a simple approachthat gives a larger relative error that one would expect from an analysis statistics. In thecase of a random source of measurement variations, the correct expression would be A/ A0 = ((W/ W0)

2 + (L/ L0)2)) .

8

PERCENT ERROR. PERCENT DIFFERENCE

The standard values can be found in textbooks or references. You will compute thepercent error of an experimental result using the following basic relation:

% Error = (100%)(Your Result Truth/ Truth)

Here Truth means the standard value of the measured quantity.

The % difference between two different measured results for a quantity iscomputed in much the same way. The % difference is taken as positive.

% Difference = (100%)x (Difference in Values/Average Value).

GRAPHS

Choose graph scales so that a graph is as large as practical. Label the axes of the graphwith units and numbers. Simple whole numbers are preferred. You can factor out powersof ten in the scales so that the numbers along the axes are simple whole numbers. Makethe plotted points easy to see, say by small circles or crosses. Make it easy to check theaccuracy of your plots.

As an example consider experimental data that relates the length of a simplependulum to the squared period of the motion which obeys the relation L= g/(4 2) T2.

The pendulum length is plotted against the squared period, and the slope is computed.

Linear Graph For Pendulum

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2 4 6

Period Square (s.s)

Len

gth

of

Pen

du

lum

(m)

The length values are plotted on the y-axis, and the squared time on the x-axis. Theplotted points are marked so that they can be readily seen. A straight line fits these data.

Length(m)

T(s)

T2

(s2)

0.25 1.02 1.04

0.44 1.37 1.88

0.70 1.64 2.69

0.95 1.98 3.92

1.25 2.26 5.11

9

Note that the first and last points are NOT special points. The slope is computed fromtwo points on the line that are far apart. These are not data points. Why? The graph is atool used to average all your data and two arbitrary points on the line weight all the data.You should mark the slope calculation points and list their coordinates. The slope isdefined as the ratio of (the change in the y-values) divided by (the change in the x-values).For the case illustrated, two points on the line are (0.6, 0.15) and (4.0, 0.99).

Slope = {(0.99 0.15) cm}/{(4.0 0.6)s2} = 0.247 m/s2.

(Note: the free fall acceleration is g = 42(slope) = 9.8 m/s2.)

Lets summarize the requirement for graph. It has an appropriate title. The axesare labeled with whole numbers, and the units are indicated. The data points are marked.The slope calculation points are labeled. A larger graph would be preferred in a lab report.

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III. Basic Formulas in Data Analysis

1. Percent error: % error is used to compare your measured value with the standardvalue.

% error = {Measured Value Accepted Value/(Accepted Value)}100%

2. Percent difference: % difference is used to compare two measured values.

% difference = {Difference in Values / [Average Value]}100%={ Value1 Value2 / [ (Value1 + Value2)/2]} 100%

3. Mean value for a set of N measurements:

xav = [x1 + x2 + .....+xN] / N

4. Deviation from the mean:

Di = xi - xav

5. Mean deviation (uncertainty):

Dav = [D1 + D2 + + DN] / N

6. Record the accuracy of the mean value in terms of mean deviation:

Measured Value = xav Dav

7. Standard deviation(uncertainty):

= NDDD N /)...(22

2

2

1

8. Record the accuracy of the mean value in terms of standard deviation:

Measured Value = xav

Note: Both the mean deviation and standard deviation represent the dispersion ofexperimental measurements about the mean. They are used as terms in yourmeasured value to indicate the precision of your measurement.

11

By Xiang-Ning Song 11

Experiment 1

STANDING WAVES ON A STRETCHED STRING

EQUIPMENTPASCO Mechanical Wave DriverSine Wave Generator and its Power SupplyPulley attached to its rodUniversal Table ClampTwo patch cords with banana plug connectorsOne string (length between 1.2 and 1.5 meters)Weights and BalanceMeterstick

Figure 1: Experimental Setup

OBJECTIVESWhen you have completed this experiment, you will be able to use a mechanical vibratorand sine wave generator to produce standing wave on a stretched string. You will be ableto determine the speed of wave on the string and measure the first four harmonics on thestring.

CONCEPTSA wave is a disturbance that propagates through the space. Although the wave carriesenergy from one place to another, the medium that carry the wave do not transportthrough the space. Instead, they oscillate back and forth or up and down about their

12

equilibrium position. In this experiment, as shown in Figure 1, a mechanical vibrator andsine wave generator are used to generate waves on a stretched string.

Harmonic waves are generated on a stretched string in this experiment. When a wavevibrator is attached to the stretched string and moves up and down in simple harmonicmotion, a continuous wave on the string will have the shape of a sine or cosine curve;such a wave is called a harmonic wave.

In this experiment, transverse waves are generated along the stretched string. Althoughthe wave generated by the wave vibrator propagates along the string, every element onthe string oscillates up and down while the wave passes through it. The displacement ofevery element on the string is at the right angle to the direction of propagation of thewave; such traveling wave is referred as a transverse wave.

Standing waves are formed on a stretched string for a group of resonant frequencies inthis experiment. While the wave vibrator continuously generates harmonic waves, theincident wave traveling to the other end of string will reflect back. The incident andreflected wave have the same frequency and amplitude but traveling in opposite directionalong the string. The interference between incident and reflected waves produces astanding wave. The special feature of the standing wave is that there are fixed nodes andantinodes along the string. The node, indicated by N in Figure 2, is where the stringnever moves. The antinode, indicated by A in Figure 2, is where the string has maximumdisplacement. The antinodes are located halfway in between adjacent nodes.

1 =2L, f1= /1

2 = 1/2, f2 = 2f1

2 = 1/3, f3 = 3f1

Figure 2: A stretched string with both fixed ends oscillates in standing wave pattern.(a) The first harmonic-lowest possible frequency produces one loop of standingwave. (b) The second harmonic yields two loops. (c) The third harmonic givesthree loops.

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For a stretched string with fixed ends, standing waves can only be generated with certainfrequencies. These frequencies are called resonant frequencies, or natural frequencies,or normal modes of the string. The collection of all possible resonant frequencies arecalled the harmonic series. They are given by

fn = nf1 = n/2L n = 1, 2, 3, (1)

where f1 is the lowest frequency that can produce standing wave and is called thefundamental frequency or first harmonic, as shown in Figure 2 (a). is the speed ofwave on the string.The speed of a harmonic wave on the stretched string is given by

= fn n = tF

(2)

where f is frequency, defined as number of oscillations per unit time. is wavelength,defined as the repetition distance of wave along the waves travel, such as the distancefrom the top of one crest to the next, shown in Figure 3. The time for one completeoscillation is called period T, T = 1/f. Ft is the tension in the string. is linear massdensity, defined as mass of string divided by length of string, = m/l.

Figure 3: A stretched string with both fixed ends oscillates in third harmonics of standingwave

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PROCEDURESPart A: Measuring the Linear Mass Density of String

1. Use the meterstick to measure the total length of the string l. Record its value in

Data Table 1.2. Measure the mass of string, m, using the balance. Record it in Data Table1.3. Complete the calculation of linear mass density, = m/l, in Data Table 1.

Part B: Setting up Lab Apparatus and Predicting the Harmonic Frequencies

1. Clamp the pulley on the edge of lab table (or on a wood board if provided).2. Attach and tie the string to the wave driver.3. Stretch the string over the pulley. Adjust the distance between the tip of wave

driver and the top of the pulley to be 0.8 m (80 cm). Note: This is the length ofvibrating string, L=0.8 m, and the longest wavelength of standing wave is 1 = 2L.

4. Hang mass, M = 0.070 kg (70 g), at the end of the string over the pulley. Note:Leave this mass for the experiment of Part C.

5. Complete the calculations for three different masses in Data Table 2 for the

following quantities: tension in the string Ft = Mg; speed of wave, = tF

, is

from Data Table 1; predicted driving frequency of first harmonic, f1 = / 1 ;second harmonic, f2 = 2f1; third harmonic, f3 = 3f1; and fourth harmonic, f4 = 4f1.

Part C: Measuring First to Fourth Harmonics

1. There is a lock switch on the wave driver, unlock it. Note: Make sure you do notchange the distance, L = 0.8 m, between the tip of wave driver and the top ofpulley in the operating process.

2. Connect the wave driver and the Sine Wave Generator using the pair of bananapatch cords. Note: The polarity is not important.

3. Connect the power supply to the power input of the Sine Wave Generator. Slidethe ON/OFF switch to the right to turn it on.

4. Set the Amplitude knob about midway on the Sine Wave Generator.5. Initially adjust the frequency knobs of Sine Wave Generator to the predicted

value, f1, from Data Table 2. Then, adjust the fine tuning knob slowly to achievethe best standing wave with one loop. Record the value of frequency from thedisplay of Sine Wave Generator in Data Table 3.

6. Double the frequency on the display of Sine Wave Generator. Adjust thefrequency knob till the best two loops are observed. Record it as f2 in Data Table3. Repeat the similar procedure for 3rd and 4th harmonics.

7. Repeat steps 5 to 6 for masses 0.100 kg and 0.120 kg.8. Calculate the % difference for the 4th harmonics between values in Data Table 2

and 3.9. Turn off the Sine Wave Generator.10. Lock the wave driver and return all equipments.

15


PRE-LAB FORM


1. What is a standing wave and how are standing waves are formed?

2. Define nodes and antinodes?

3. What is the relationship between the nth harmonics and the fundamentalfrequency?

16

4. Referring to Figure 2, what is the relationship between the length of the string andwavelength?

5. Referring to the three loops of standing wave in Figure 3, calculate thewavelength and wave speed of the standing wave. The wave generator has afrequency, 24 Hz. The length of the string between wave generator and pulley is0.8 m.

17


LAB REPORT FORM


Part A: Measuring the Linear Mass Density of String

Data Table 1

m (kg)mass of string

l (m)

total length of string

= m/l ( kg/m)

linear mass density

Part B: Predicting the Harmonic Frequencies

Data Table 2

Length of String, L = 0.8 m Wavelength, 1 = 2L = 1.6 m

M (kg)Hanging

Mass

Ft = Mg(N)

Tension

= tF

(m/s)

Speed of Wave

f1 = / 1(Hz)

f2 = 2f1(Hz)

f3 = 3f1(Hz)

f4 = 4f1(Hz)

0.070

0.100

0.120* g = 9.8 m/s2 is from Data Table 1.

Part C: Measuring First to Fourth Harmonics

Data Table 3

M (kg)Hanging

Massf1 (Hz)

1st Harmonicf2 (Hz)

2nd Harmonicf3 (Hz)

3rd Harmonicf4 (Hz)

4th Harmonic% DiffFor f4

0.070

0.100

0.120

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QUESTIONS

1. Use your own words to describe the characteristics of the harmonics based onyour observation from this experiment.

2. What would be the wavelength and frequency of the tenth harmonic for theM=0.100 kg case?

3. According to the data of Data Table 2, if the tension is increased, how did thewave speed and the first harmonic change?

4. If the length between wave generator and pulley is 0.4 m and linear mass densityof the string is 4.0 g/m, what are the tension and the hanging mass values toproduce one loop of standing wave with f1 = 8 Hz?


Experiment 2

THE SPEED OF SOUND IN AIR

EQUIPMENTAir Column Resonance TubeThree Tuning Forks (< 1000 Hz)Rubber MalletBeakerThermometer

(a) (b)

Figure: (a) Experimental Apparatus (b) Standing Wave: An antinode is near theopen end. A node is at the level of water.

OBJECTIVESUpon completion of this lab you will understand the concept of resonance and relationsbetween velocity, wavelength, and frequency. You will be able to set up and operate anAir Column Resonance Tube, and measure the velocity of sound in air.

20

CONCEPTSA disturbance in an elastic medium travels with a speed given by the followingrelationship.

V =Density

ModulusElastic(1)

For a sound wave in air, the speed of the wave can be determined for a specific airtemperature using

VT = 331 273/KT (2)

where: VT = Speed of sound in air m/sTK = Absolute temperature K

The absolute temperature is determined as follows:

TK = ( 273 + TC ) K (3)

where: TC = temperature in degrees Celsius.

For a longitudinal wave in a metal rod,

YV (4)

where: Y = Young's Modulus for the metal = Density of the metal

In this experiment a tuning fork is used to produce traveling wave of sound. This wave issent to a tube partially filled with water. When the incident wave meets the surface ofwater, the wave is reflected back. These two waves can produce standing waves. Whenstanding waves are produced in the tube, the amplitude of the resultant wave becomesvery large and the system is said at resonance. When the resonance occurs, a loud soundoccurs. Measuring the position for occurring resonance, the speed of the wave can thenbe determined experimentally using the following expression.

V = f (5)

where : f = frequency Hz, specifies the number of vibrations per unit time.


= wavelength m, is the distance between two identical parts of wavein space.

V = Speed m/s

In the Air Column Resonance Tube, the resonant length in air is adjusted by the waterlevel in the tube. See the Figure.

The vibrations will be stimulated by a tuning fork having a known frequency. For eachturning fork, the air column will exhibit two resonant points dependent on the frequencyof the sound wave and available resonant tube length. As seen in the Figure (b), thesetwo resonant points are distances of X1 and X2 from the top of the tube. Distance X1corresponds to /4 for this wave and distance X2 corresponds to 3 /4. This meansthat the length (X2 - X1) is equal to /2. Thus, the wavelength of the wave can bedetermined using the following expression.

= 2 ( X2 - X1 ) (6)

PROCEDURES

Part I: Predicting the Resonance Positions

1. Record the room temperature in Data Table 1.

2. Calculate the speed of sound using equation (2).

3. Ask your instructor to select three tuning forks and record their frequencies in DataTable 1.Note: The frequencies of the chosen tuning forks should be higher than 380 Hz.

4. Complete the calculations in Data Table 1. X1 and X2 are the predicted resonancepositions.

Part II: Measuring the Speed of Sound

1. Raise the water can to its highest position.

2. Add water to the Air Column Tube until the water level is at least 10cm below thetop.

3. Strike the first tuning fork with the rubber mallet causing it to oscillate. Hold thetuning fork directly above the air column and lower the water level until the first

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resonant point (adjust the water level around the predicted X1 ) is located. Resonanceoccurs at the position where the amplitude of the sound is a maximum. Record thislocation as X1 and the frequency of the tuning fork in the Data Table 2.

4. Repeat two more times of the procedure in step 3 for the first resonant position X1.

5. Repeat steps 3 - 4 for the second and third tuning forks.

6. Carefully pour half of water into the sink.

7. Repeat steps 3 - 5 for the second resonant point which should be located in the lowerpart of the tube. Record this location as X2 in the Data Table 2.Note: The predicted X2 is X2 = 3 X1. Lower or raise the water level around thepredicted X2.

8. Compute and record the wavelength of the sound wave using equation (6).

9. Compute and record the average of wavelength and velocity of the sound wave usingequation given in Data Table 2. Also, compute and record the % Error betweenyour measured value of V and the true value, VT, computed in Data Table 1.

10. Remove the water from the air column tube and secure this equipment.


PRE-LAB FORM


1. Write a brief definition of resonance.

2. How does the speed of sound vary with temperature?

3. Calculate the speed of sound in air at a temperature Tc = 24oC.

24

4. What are the approximate x1 and x2 values that you expect in an air columnresonance experiment performed at 24 oC with a tuning fork frequency, f=540Hz?


LAB REPORT FORM


Data Table 1: Predicting the Resonance Positions

Room Temp = _________ Co TK = ________ K

VT = 331 273/KT = ________ m/s

f(Hz)

= VT /f(m)

X1(m)

X2(m)

Data Table 2: Measuring the Speed of Sound

f(Hz)

Trial X1(m)

X2(m)

= 2( X2 - X1 )

(m)AV(m)

V= f AV

(m/s)% error

1

2

3

1

2

3

1

2

3

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QUESTIONS

1. What is the fundamental frequency?

2. How are the harmonics related to the fundamental frequency for the resonancetube used in this lab but with a fixed length?

3. Draw three patterns of the longitudinal standing waves which possibly exist insidethe resonance tube used in this lab.

4. Given the following data for aluminum, compute the speed of sound in analuminum rod.

Y = 6.90 x 1010 N/m2

= 2.70 x 103 kg/m3


Experiment 3

Electrostatic Charge

EQUIPMENT:ElectroscopeThree Rods: Ebonite, Glass, AcrylicFive Materials: Fur, Cotton, Wool, Silk, NylonCharge Sensor, Faraday Ice PailCharge Producers (one with white surface and one with blue surface)

(a) (b)

Figure 1: Experimental Apparatus: (a) Two Types of Electroscope(b) Faraday Ice Pail

OBJECTIVESUpon completion of this lab, you will investigate the nature of charging an object andverify the concepts of electrostatic interactions. This includes electrostatic chargingmethods: by friction, by contact, and by induction. It also includes the attractive andrepulsive aspects of the electric interaction, as well as properties of conductors andinsulators. A Charge Sensor computer probe is used in the investigation.

CONCEPTSElectrostatics is the study of electrical charges and their characteristics. As you willverify by this experimentation, there are two different types of electrical charges. Thesetwo types are designated positive (ex. protons) and negative (ex. electrons). Like chargesrepel each other and unlike charges attract each other.

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The Electroscope: An electroscope is a charge-detecting device with two thin goldleaves vertically suspended from a common point. When a charged object is brought near(or touch) the electroscope, the gold leaves separate, roughly indicating the magnitude ofthe charge, as shown in Figure 1(a). Unfortunately, this device is relatively insensitiveand does not have a quantitative reading.

The Charge Sensor: The Charge Sensor, as shown in Figure 1(b), is somewhat like anelectronic electroscope. It is a very sensitive electroscope. Unlike the traditionalelectroscope, the Charge Sensor can make quantitative measurements as well as indicatecharge polarity directly.

Charging by Friction: The atomic structure of all materials involves elementary positivecharges (nuclear protons) and negative charges (atomic electrons). Most objects aroundus are electrically neutral. When different types of materials are rubbed together,electrons are transferred from one to the other. The transferring charges are the negativeelectrons. The positive charges, within the atomic structures, are bound too securely to beeffected by ordinary physical or chemical processes. The object losing electronsbecomes positively charged. The object receiving electrons becomes negatively charged.In this lab you will identify which material is easy to loose electrons and the efficiency ofcharging material through rubbing.

Charging by Contact: If a primary charged object, say a negative ebony rod, makesdirect contact with the electroscopes ball, some of the charge will be shared with theelectroscope and remain after the primary charge has been removed. This charge isshown on the electroscope, because the foil continues to diverge after the primary chargeis removed.

Charging by Induction: An isolated conductor may be charged to an opposite sign of aprimary charge by a process called charging by induction. If a primary charge is broughtnear to the isolated object, that object becomes polarized, but still neutral, with the sidenearest the primary charge having the opposite sign and the side furthest the primarycharge having the same sigh of the primary charge. The second step is to ground theobject on the side furthest to the primary charge (contacting it with a conductor, say yourfinger, connected to much larger body or the earth). Charge having the same sign as theprimary charge will leave the grounded object. What happens is that the electrons eithergo from the ground to the object or go from the object to the ground. Next, the groundcontact is broken, while the primary charge is still nearby. The second object is left with acharge opposite to that of the prime charge.


PROCEDURE

Part A: Using Charge Sensor to Determine the Polarity and the Amount of Charge

1. Turn on the interface first and then turn on the computer.2. Connect the cable, Charge Sensor (set gain at one), and the Faraday Ice Pail in place,

as shown in the Figure 2. Make sure that the red alligator connector is connected withthe inner cylinder of the Faraday Ice Pail.

3. Open the DataStudio file on window. Choose the Create Experiment.4. Double click on the Charge Sensor under the Sensors window.5. Double click on the Graph icon under the Display window.

Figure 2: Faraday Ice Pail Setup

6. Ground the Faraday Ice Pail: touch the inner pail and the shield (outer pail) at thesame time with one of your finger and press the ZERO button on the Charge Sensorto discharge the sensor.

7. Rub the blue and white surfaces of the Charge Producers together several times(Dont rub too hard!).

8. Click the Start button to start recording data.9. Without touching the Pail, lower the white Charge Producer into the center of the

pail. Remove the white Charge Producer and lower the blue Charge Producer into thePail.

10. Click the Stop button. Click the Scale to Fit button (1st button on the tool bar menu)for better view of your data.

11. Click on the button (11th button on the tool bar menu). Record the polarity ( + or) and amount of charge (Q in C) in the Data Table I.

12. Rub the glass rod (smooth side) with fur. Click the Start button to start recordingdata.

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13. Without touching the Pail, lower the glass rod into the center of the pail. Click theStop button and click the Scale to Fit button.

14. Click on the button. Record the polarity ( + or ) and amount of charge (Q in C)in the Data Table II.

15. Complete the Data Table II by repeating steps 12-14.16. Identify the most positively and negatively charged rods as well as rubbing materials.

You will use them in the Part B of this lab.17. Turn off computer. You do not need computer for Part B

Part B: Using the Electroscope

1. Response of a Neutral Electroscope

a) Ground (discharge) the electroscope by touching it with your finger.b) Use the most negatively charged rod identified from Part A. Charge the rod by

friction.c) Bring the negatively charged rod near the ball of the electroscope (but do not

touch the ball). Observe what happens to the gold leaf of the electroscope.d) Repeat the procedures for the positively charged rod.e) Explain your observations in Data Table B1.

2. Response of a Charged Electroscope

a) Use the most negatively charged rod identified from Part A. Charge the rod byfriction.

b) Charge the electroscope by making contact between the negatively charged rodand the ball of the electroscope. The electroscope is now negatively charged.

c) Bring the negatively charged rod near the ball of the electroscope withouttouching it. Observe the response of electroscope.

d) Take away the negatively charged rod. Charge another rod positively by friction.Bring the positively charged rod near the ball of the same electroscope, but donot touch it. Observe the response of electroscope.

e) Explain your observations in Data Table B2.

3. Charging Electroscope by Induction

a) Ground (discharge) the electroscope by touching it with your finger.b) Bring a negatively charged rod near the ball of the electroscope (but do not touch

the ball).c) With the charged rod still near the ball on one side of the ball, ground the

electroscope by touching the other side of the ball with your finger.d) With the charged rod still near the ball, remove your finger from the ball.e) Remove the rod. Explain your observations in Data Table B3.


PRE-LAB FORM

ELECTROSTATIC CHARGE

1. List at least three properties of electric charges.

2. What is the process of charging by friction?

3. What is the process of charging by induction?

4. Explain how an electroscope can detect charge.

32

5. There are three charges q1 = 4.0 C, q2 = -3.0 C, and q3 = 6.0 C, located at x1 =0m, x2 = 0.3m, and x3 = 0.4m, respectively. Determine the electrostatic force onq3.


LAB REPORT FORM

ELECTROSTATIC CHARGE

Part A: Using Charge Sensor to Determine the Polarity and the Amount of Charge

Data Table I

Polarity of Charge +/- Amount of Charge( C)

White Charge Producer

Blue Charge Producer

Data Table II

Glass Rod (smoothside)

Acrylic Rod Ebony Rod(Black)Rubbing Materials

Polarity Q(C) Polarity Q(C) Polarity Q(C)

Fur

Silk

Cotton

Nylon

Wool

Identify:

1. The most positively charged rod: Rubbed by material:

2. The most negatively charged rod: Rubbed by material:

These two rods and rubbing materials will be used in Part B experiment.

34

Part B: Using the Electroscope

Data Table B1: Response of a Neutral Electroscope

Explain why the gold leaf of the electroscope diverges from the plate. (You can drawpictures instead of words as your explanations.)

Data Table B2: Response of a Charged Electroscope

Explain why a charged electroscope responds in a different way to negatively andpositively charged rods. (You can draw pictures instead of words as your explanations.)


Data Table B3: Charging Electroscope by Induction

Explain (1) how you can prove the sign of the charge on the ball and (2) where thecharges come from.

36

QUESTIONS

1. Without doing the experiment, please predict the outcome: If you bring oneuncharged pith ball (a very light and tiny ball), suspended by its thread near a wellcharged rod.(a)Explain the attraction of the pith ball as you bring it near the charged rod.

(b)Explain the behavior of the pith ball shortly after it touches the rod.

2. If a balloon is rubbed with soft tissue, the balloon can be hung on the wall.(1) Explain this phenomenon. (2) Why doe the balloon eventually fall?

3. There are three charges q1 = 4.0 C, q2 = -3.0 C, and q3 = 6.0 C, located at (0, 0), (0, 0.3m), and (0.4m, 0.3m), respectively. Determine the electrostatic force on q3.


Experiment 4

EQUIPOTENTIAL ANDELECTRIC FIELD LINES

EQUIPMENTElectric Potential Mapping Equipment with Electrodes and Conducting PaperDC Power SupplyDigital MultimeterLead Wires

A B

Figure 1: A: Mapping Equipotential LinesB: Experimental Setup

OBJECTIVESUpon completion of this laboratory experiment you will be able to

a. Define and use the electric potential difference concept.b. Understand the relation between electric fields and the electric potentials.c. Construct diagrams of equipotential lines and electric field lines for common

charge and conductor configurations.

38

CONCEPTS:The electric potential difference V between points C and D in an electric field E, asshown in Figure 1 A, is defined as

V = - rdED

C

= - drE

D

C cos (1)

where is the angle between E and dr. An equipotential surface is one on which allpoints have the same electric potential. It means that V equals zero on this surface. Based on equation (1), the angle, , between E and dr is 90 degree at every point on thissurface. Electric field lines are perpendicular to equipotential surfaces. In this lab youwill measure and map the equipotential surfaces. Then you will construct the electricfield lines.How do you do it? As the illustration in Figure 1, lead wires are connected from a powersource to electrode probes A and B. Current flows between these probes through aconductive paper. The probes of a sensitive voltmeter (digital voltmeter) make contact atpoints C and D on the conductive paper, and the voltage between points C and D areindicated by the voltmeter. Probe D is moved until the voltage is a zero or minimumvalue. For a fixed position of probe C there will be a line of points for probe D where thevoltmeter indicates a zero. This is an equipotential line. Equipotential lines are similar toelevation contour lines on a geological survey map. Electric field lines are drawn as linesthat connect the two voltage source electrodes and are perpendicular to the equipotentiallines.

The rules for drawing electric field lines are:1. The electric field lines begin on positive charges and end on negative charges.2. The electric field lines are perpendicular to equipotential surfaces.3. The density of electric field lines is proportional to the magnitude of the charge.4. No two field lines can cross.

Conductors: Conductor is a synonym for metal. Within a conductor the electric field E =0. V = 0 between any two points in or on a conductor. In particular, the surface of a conductor is an equipotential surface. It follows that just outside the surface E lines mustbe perpendicular to the surface and these lines terminate on the conductor.

PROCEDURE:

Part A: Mapping the Equipotential and E Lines for Two Opposite Point Charges.

1. Place source electrodes about 8 cm apart on the conductive paper, and connect theDC power supply to these probes. Setting the DC power supply at 6 V would beappropriate. Lets call the negative terminal 0 volts and the line between theterminals as the x-axis. Mark the positions of the source electrodes on the LABREPORT FORM.


2. Turn on the digital multimeter for DC voltage measurements. Make sure thatcurrent is flowing through the paper by measuring the voltage between the sourceprobes, between a probe and an arbitrary point on the paper, and between twopoints on the paper. Sometimes poor contacts with low voltage and very lowcurrent circuits can be frustrating.

3. With the negative voltmeter probe on the negative source electrode and thepositive voltmeter probe on the conductive sheet, record the voltage at positionson the x-axis at 1.0 cm, 2.0 cm, 3.0 cm, 4.0 cm, 5 cm, 6 cm, and 7 cm from thenegative source electrode.

4. Fixing the negative probe of the voltmeter at 1.0 cm from the negative electrode,determine positions of the positive probe such that the voltage between thesepoints on the conductive sheet is zero. Employ a systematic approach, such asmoving the positive probe on a radial line towards the positive/and or negativeelectrode until the voltage is zero. The voltage changes sign as you cross theequipotential line. Just a few points (about six points) are needed to draw theequipotential line with reasonable precision. Transfer these equipotential pointsonto your data paper. Smoothly connect these points to construct an equipotentialline.

5. Repeat this process for the points at 2.0 cm, 4.0 cm, 6.0 cm, and 7cm. Draw theequipotential lines on your data paper.

6. After completing the equipotential lines, draw the electric field lines witharrows. Use your judgment to decide how many lines result in a fair descriptionof the electric fields.Note: When you draw the electric field lines, you should try to construct theelectric field lines perpendicular to the equipotential lines at all points.Consult with your instructor if you do not know how to draw it.

Part B: Mapping the Equipotential and E Lines for One Positive Point Charge andOne Negative Conducting Plate.

1. Place a flat conducting plate on the conductive paper and then place the negativeelectrode on the top of the plate. Place the positive (red) electrode 8 cm apartfrom the front edge of the plate.

2. Connect the DC power supply between the electrodes. Draw the exact shape ofthe plate and the position of the source electrodes on your part B data paper. Theyshould look something like the illustration of the figure 2.

40

Figure 2: Point charge and Charged Plate3. Repeat steps 1 to 6 of Part A. Note: The x = 0 position is the front edge of the

plate.

4. Measure the potential difference between arbitrary two points on the axis of theelectrodes, but behind the plate, and separated by 2 cm.

Part C: Mapping the Equipotential and E Lines for One Positive Point Charge andOne Negative Conducting Cylinder (Washer).

1. Place a conducting cylinder (washer) on the conductive paper. Place a flatconducting plate on the top of the cylinder (same plate as used in Part B) and thenplace the negative electrode on the top of the plate. Place the positive (red)electrode 8 cm apart from the front edge of the cylinder.

2. Connect the DC power supply at 6V between the electrodes. Draw the exact shapeof the cylinder and the position of the source electrodes on your part C data paper.They should look something like the illustration of the figure 3.

Figure 3: Point Charge and Charged Cylinder

3. Repeat steps 1 to 6 of Part A. Note: The x = 0 position is the front edge of thecylinder.

4. Measure the potential difference between arbitrary two points within the cylinder.

5. Properly return all lab equipments.


PRE-LAB FORM

EQUIPOTENTIAL AND ELECTRIC FIELD LINES

1. What is an equipotential line?

2. Why are the families of electric field lines perpendicular to the equipotential lines?

3. Why is the surface of a conductor an equipotential surface?

4. Referring to Figure 1, the potential difference between the two electrodes is 6 V.(a) How many possible equipotential lines can you draw in the space between

them?

(b) How many equipotential lines do you plan to draw in this lab?

(c) How many equipotential points do you plan to locate in order to constructeach equipotential line?

42

5. A map of equipotential lines that might arise from a conductor placed betweentwo opposite point charges (+ on the far left, - on the far right) is shown in theillustration. Draw in a family of electric field lines that are consistent with theseequipotential lines.


LAB REPORT FORM

EQUIPOTENTIAL AND ELECTRIC FIELD LINES

Part A: Mapping the Equipotential and E Lines for Two Opposite Point Charges.

Position from Electrode (cm) 1 2 3 4 5 6 7

Voltage (V)

44

Part B: Mapping the Equipotential and E Lines for One Positive Point Chargeand One Negative Conducting Plate.


Voltage (V)

Potential difference between arbitrary two points on the axis of the electrodes, butbehind the plate, and separated by 2 cm: V.


Part C: Mapping the Equipotential and E Lines for One Positive Point Chargeand One Negative Conducting Cylinder (Washer).


Voltage (V)

Potential difference between arbitrary two points within the cylinder: V.

46

QUESTIONS

1. MEANING OF ELECTRIC FIELD LINES:

a. What is the significance of the number of lines per unit area, or density of theelectric field lines?

b. What is the relation between the direction of the electric field and the electric fieldline at some point on the line?

2. UNIQUENESS OF EQUIPOTENTIAL AND FIELD LINES:

a. Explain why two equipotential lines can not cross each other.

b. Explain why two electric field lines in space can not cross. [Hint: Whatdirection(s) would the field have at the intersection point?]

3. Conductors provide shielding from electric fields. Discuss this aspect of Part Band C using your data. (Note: This experiment has limitations arising from thenature of the conductive paper and the contacts with the conductors.)


Experiment 5

CAPACITORS IN SERIES ANDPARALLEL

EQUIPMENTDigital MultimeterCapacitance MeterPASCO Electronics BoardCapacitors: 470 F (C1), 330F (C2), 100 F (C3), 10 F (C4).Lead WiresDC Power Source

Figure 1: Experimental Apparatus

OBJECTIVESUpon completion of this laboratory experiment you will be able toa. Construct capacitors in series and parallel on the circuit board.b. Measure the equivalent capacitances for different combination of capacitors and thevoltages across the capacitors.

CONCEPTSA capacitor is a device that stores electric charge. A capacitor consists of two metal platesseparated by an insulator. The charge Q on each plate of a capacitor is proportional to thevoltage V across the plates:

Q = CV (1)

48

where C is the capacitance. The SI unit of capacitance is the farad (F), 1 F = 1 C/V. Thecapacitance is a measure of a capacitors ability to store charge. Capacitors not only storecharges, but also store energy. The energy stored in the capacitor can be decided by

Uc = QV/2 = CV2/2 = Q2/(2C) (2)

The capacitors can be connected in series or parallel as shown in Figure 2.

Figure 2: (a) Capacitors in series (b) Capacitors in parallel

The following are the properties for capacitors wiringin series: in parallel:

Q = Q1 = Q2 = Q = Q1 + Q2 + V = V1 + V2 + V = V1 = V2 = 1/Ceq = 1/C1 + 1/C2 + Ceq = C1 + C2 +

where Ceq, C1, and C2 are the capacitance for the equivalent capacitor, capacitor 1, andcapacitor 2, respectively. The Q, Q1, and Q2 are the charges on Ceq, C1, and C2. V, V1,and V2 are the voltages across Ceq, C1, and C2 .

On the circuit board in this experiment you will first demonstrate the properties ofcapacitors in series only, in parallel only, and then in a combination of the two.

PROCEDURE

1. Technical Reminder: Some of the capacitors have a polarity, which means whenyou are connecting them to the board you have to pay attention to which way youconnect them. You must avoid bending the wires on the capacitor because they canbreak. If you need to bend the wire on the capacitor, make it a smooth one.

2. From the PASCO Electronics kit take out all of the gray, blue and blackcapacitors. You will use only four of capacitors. The given value of the capacitance isprinted on each capacitor. Check their polarity with yes or no. Measure the actualvalue of the capacitance of each capacitor using a Digital LCR Meter with theclosest scale and record the values in Data Table 1. The percentage error can bedetermined by subtracting the given value from the measured value, dividing by the

C1

C2

C2

C1


given value, and then multiplying by 100. Use the measured value of capacitancefor your experiment.

3. Series ConnectionConnect the C1 and C2 capacitors in series on the circuit board, as shown in Figure2(a). Measure the equivalent capacitance with a Digital LCR Meter (Make sure youknow how to use it.) and record the value on the Data Table 2. Use the measuredvalue C1 and C2 in Data Table 1 to calculate the theoretical value of Ceq.

4. Parallel ConnectionConnect the C1 and C2 capacitors in parallel on the circuit board, as shown in Figure2(b). Measure the equivalent capacitance and record the value on Data Table 2.

5. Combined Circuit OneConnect the C1, C2, C3, and C4 capacitors on the circuit board, as shown in thefollowing figure. Measure the equivalent capacitance and record the value on DataTable 2.

6. Combined Circuit Two Connect the C1, C2, and C3 capacitors on the circuit board, as shown in thefollowing figure. Measure the equivalent capacitance and record the value onData Table 2.

C4 C3

C2C1

C3 C2

C1

50

Connect a 6V DC power source on the Combined Circuit Two. Measure thevoltage across each capacitor with a digital voltmeter, complete the requiredcalculations, and record your results on Data Table 3.

V C3 C2

C1


PRE-LAB FORM

CAPACITORS IN SERIES AND PARALLEL

1. What is a capacitor?

2. Define the capacitance?

3. Describe the properties of combining three capacitors(a) in series and

(b) in parallel.

52

4.

V

Using the given circuit, where V = 6V, C1 = 470 F, C2 = 330 F, and C3 =100F, determine charges and energies stored on each capacitor.

C3 C2

C1


LAB REPORT FORM

CAPACITORS IN SERIES AND PARALLEL

Data Table 1: Identify Capacitor and Measure Capacitance

CapacitorsPolarity(Yes/No) Given Measured % Error

C1 470 F

C2 330 F

C3 100 F

C4 10 F

Data Table 2: Equivalent Capacitance

Circuit Theory Measured % Error

Series Ceq

Parallel Ceq

Combined 1 Ceq

Combined 2 Ceq

Data Table 3: Combined Circuit Two

Theory Measured % Error

V1

V2

V3

Q1

----- -----

Q2

----- -----

54

QUESTIONS

V

If V = 12 V, C1 = 470 F, C2 = 330 F, C3 = 100 F, and C4 = 10 F, calculate thefollowings:

1. the equivalent capacitance,

2. the charge stored in C2,

3. the voltage across C3.

4. the energy stored in C4.


Experiment 6

RESISTORS IN SERIES ANDPARALLEL

EQUIPMENTDigital MultimeterAmmeterPASCO Electronics BoardResistors: 100 (R1), 330 (R2), 560 (R3), 1 k (R4).Lead WiresDC Power Source


OBJECTIVESUpon completion of this laboratory experiment you will be able toa. Construct resistors in series and parallel on the circuit board.b. Measure the equivalent resistances for different combinations of resistors and thevoltages across the resistors.

CONCEPTSA resistor is a resistance device, which provides the electrical resistance to charges flow.The resistance R of a resistor is defined as

R = V/I (1)

56

where the V is voltage across the resistor and I is the current passing through the resistor.Resistors are often used to control the current level in the different parts of the circuits.There are two basic types of resistor circuits. Resistors may be connected in series or inparallel, as shown in Figure 2a and 2b, respectively.

Figure 2: (a) Resistors in Series

(b) Resistors in Parallel

The following are the properties for wiring resistorsin series: in parallel:

I = I1 = I2 = I = I1 + I2 + V = V1 + V2 + V = V1 = V2 = Req = R1 + R2 + 1/Req = 1/R1 + 1/R2 +

where Req, R1, and R2 are the resistance for the equivalent resistor, resistor 1, and resistor2, respectively. I, I1, and I2 are the currents flowing through Req, R1, and R2. V, V1, andV2 are the voltages across Req, R1, and R2.

Two types of resistors, commonly used in physics labs, are the wire-woundresistor, which consists of a coil of wire, and the composition resistor, which containscarbon. Values of resistors in ohms are normally indicated by color-coding, as shown inFigure 3. In this lab you will first recognize resistors based on their color coding. Then,on the circuit board, you will demonstrate the properties of resistors in series only, inparallel only, and construct a combined circuit.

Figure 2: Color Coding for Resistors

R1 R2

R2

R1


PROCEDURE

1. Technical Reminder: You must avoid bending the wires on the resistor becausethey can be broken. If you need to bend the wire on the resistor, make the bendsmooth.

2. Take out all of the resistors from the PASCO Electronics kit. Refer to Figure 2and select the five resistors whose values are listed in Data Table 2. Measure theactual value of the resistance of each resistor using a Digital Ohmmeter with themost closed scale and record the values in Data Table 1. The percentage errorcan be determined by subtracting the coded value from the measured value,dividing by the coded value, and then multiplying by 100. Use the measuredvalue of resistance for your experiment.

3. Series Connection

Connect the R1 and R2 resistors in series on the circuit board, as shown in Figure 2(a).Measure the equivalent resistance with the Digital Ohmmeter and record the value inData Table 2. Use the measured value R1 and R2 in Data Table 1 to calculate thetheoretical value of Req.

4. Parallel Connection

Connect the R1 and R2 resistors in parallel on the circuit board, as shown in Figure2(b). Measure the equivalent resistance and record the value in Data Table 2.

5. Combined Circuit #1

Connect the R1, R2, and R4 resistors on the circuit board, as shown in the figure.Measure the equivalent resistance and record the value in Data Table 2.

R2 R4

R1

58

6. Combined Circuit #2

Part A: Connect the R1, R2, R3, and R4 resistors on the circuit board, as shown inthe figure. Measure the equivalent resistance and record the value in Data Table 2.

Part B: Connect a 6V DC power source on the Combined Circuit #2, as shown infollowing figure. Measure the power source voltage, the total current output, andthe voltage and current across each resistor. Complete the required calculations,and record your results in Data Table 3. Attention: You have only one ammeter.Wire the ammeter properly in your circuit to measure the current flowing througheach resistor. Ammeter must be connected in series within the circuit. Doublecheck your connection for the ammeter.

R2R3 R4

R1


PRE-LAB FORM

RESISTORS IN SERIES AND PARALLEL

1. Describe the Ohms law.

2. What is the resistance?

3. Explain the difference between series and parallel connections of resistors.

4. If V = 6V, R1 = 100 , R2 = 330 , R3 = 560 , and R4 = 1 k ,

Calculate:(a) the equivalent resistance

R2R3 R4

R1

60

(b) the voltages across each resistor.

(c) the dissipating power of each resistor.


LAB REPORT FORM

RESISTORS IN SERIES AND PARALLEL

Data Table 1: Identify Resistor and Measuring Resistance

Colors1st 2nd 3rd 4th

CodedResistance

MeasuredResistance

%Error

R1 brown, black, brown, gold 100 R2 orange, orange, brown, gold 330 R3 green, blue, brown, gold 560 R4 brown, black, red, gold 1,000

Data Table 2: Equivalent Resistance

Circuit Theoretical Measured % ErrorSeries ReqParallel ReqCombined #1 ReqCombined #2 Req

Data Table 3: Combined Circuit #2Emf V = V

Theoretical Measured % Error

V1

V2

V3

V4

Itotal

I1

I2

I3

I4

62

QUESTIONS

If R1 = 100 , R2 = 330 , R3 = 560 , R4 = 1 k , and R5 = 10 k, calculate the following:

1. the equivalent resistance,

2. the current passes R1,

3. the voltage across R5,

4. the rate of thermal energy being generated in R2.

R5

R4R2

R1

R3

V = 12V


Experiment 7

THE RC CIRCUIT: MEASURING AVOLTMETERS RESISTANCE

EQUIPMENTResistor-capacitor Circuit BoardAmmeter and VoltmeterDC Power SupplyDouble-pole, Double-throw SwitchLead WiresStopwatch

Figure: Photo: Charging and Discharging Capacitor. Insert: Circuit Schematic

OBJECTIVES

Upon completion of this lab, you will be able to understand the process for charging anddischarging a capacitor through a resistor and use Cartesian graph to determine RC timeconstant. You will have measured and calculated the resistance of a voltmeter.

64

CONCEPTS

Consider the circuit as shown in the figure. There is no charge initially on the capacitorwhen the switch is open. When the switch S is in position a at time t = 0, the capacitorbegins to charge. Kirchhoffs loop rule for the charging process is

E IR q/C = 0 (1)

where E is the voltage of the power supply and q is the charge on the capacitor. Thecharging current I through the ammeter as a function of time can be shown to be given by

I = I0 exp(-t/R) (2)

where I0 = E /R is the initial current (time t=0), exp = e =2.718 is the base of naturallogarithms, and R = RC is the time constant of the charging circuit. The current deceaseswith time. When the charge on the capacitor is such that its voltage is equal and oppositethat of the voltage source, no more current will flow.

After a long time the switch S is opened and the clock is reset. At time t = 0 switch S is inposition b. The fully charged capacitor is now discharged through the internal resistanceof a voltmeter. Kirchhoffs loop rule for discharging capacitor through the voltmeter is

q/C + IRV = 0 (3)

It can be shown that the voltage of the voltmeter changes as a function of time accordingto

V = V0 exp(-t/v) (4)

where V0 is the initial voltage, V = RVC is the time constant for the discharging circuit,and RV is the resistance of the voltmeter.

In order to measure R and V, it is convenient to replace the exponential decay equations(2) and (4) with straight line equations. Taking the natural logarithm on both sides ofequation (2) and (4), the straight line equations can be shown to be

ln(I0 /I) = (1/ R) t (5)

ln(V0 /V) = (1/ V) t (6)

Both equations have positive slopes, that are m = 1/. In this experiment you will measure I(t) and V(t) and calculate the slope from your Cartesian graph. Then you candetermine the time constant with = 1/m and the value of RV with RV = V /C.

65

PROCEDURE

Part A: Charging the Capacitor C through the Resistor R

1. Set up the circuit as shown in the Figure. The high voltage terminal (red, + ) ofthe DC power source connects with the left side of the switch, called a. Thecapacitor connects with the middle position of the switch. The voltmeterconnects with the right side of the switch, called b.

Note that the polarity is marked on the capacitor. Be sure that the capacitor isconnected with the correct polarity. You only use one side of the switch.

2. Make sure the double pole and double switch is off (at middle position).

3. Turn on the DC power source. Adjust the current notch at the middle position andadjust the output voltage is about 20V.

4. Select an appropriate ammeter scale. If E is about 20 V and R ~ 40 k, then choosethe 1.0 mA scale. If R = 10 k, then select the 10 mA scale.

5. Select 25 V scale for the voltmeter.

6. Record the values of C and R on Data Table 1. Have instructor check your circuitbefore closing the switch.

7. Close the double-throw switch to the left (position a ) to start charging thecapacitor through R.

8. Start your Stopwatch. Record the first I as I0 at t = 0. Then record one I value forevery 15 s and complete the data table 1 for all your findings.

9. Open the double-throw switch to neutral position S. Reset your Stopwatch to zero.

10. Calculate ln(I0/I) for the data table 1.

66

Part B: Discharging the Capacitor C through the Resistor Rv of Voltmeter

1. Close the double-throw switch to the right (position b) to start discharging thecapacitor through Rv.

2. Start your Stopwatch. Record the first V as V0 at t = 0. Then record one V valuefor every 10 s and complete the data table 2 for all your findings.

3. Calculate ln(V0/V) for the data table 2.

4. Disconnect the elements and measure the resistance of voltmeter Rv using theohms meter. Record your finding.

5. Upon completion, properly put away the equipment.

67

PRE-LAB FORM

THE RC CIRCUIT: MEASURING A VOLTMETERSRESISTANCE

An unknown capacitor in a circuit in series with a resistance of 100 k is charged with a 50 V dc power source. When the switch is closed, the current-time data were recorded.

t (s) 0 10 20 30 40 50 60 70 80 90I (mA) I0=41 34 27 22 18 15 12 9.9 8.2 6.7

ln(I0/I)

(a) Calculate ln(I0/I) and complete the above table.

(b) Plot the ln(I0/I) (on y-axis) against time t on a graph paper. Draw a straightline to fit the data. Choose two points on this line to calculate the slope m.

(c) Then calculate the time constant using R = 1/m and capacitance C usingR = RC.

68

Plot the ln(I0/I) (on y-axis) against time t on the graph paper.

69

LAB REPORT FORM

THE RC CIRCUIT: MEASURING A VOLTMETERSRESISTANCE

Data Table 1: Charging the Capacitor C through the Resistor R

Capacitance: C = mF, Resistance: R = k.

t (s) 0 15 30 45 60 75 90 105 120 135I

(mA)I0=

ln(I0/I)

t (s) 150 165 180 195 210 225 240 255 270 285

I (mA)

ln(I0/I)

Data Table 2: Discharging the Capacitor C through the Resistor Rv of Voltmeter

t (s) 0 10 20 30 40 50 60 70 80 90V (V) V0=

ln(V0/V)

t (s) 100 110 120 130 140 150 160 170 180 190

V (V)

ln(V0/V)

Resistance of voltmeter measured by the ohms meter: Rv = k.

70

CALCULATIONS1. Cartesian Graph for Charging the Capacitor C through the Resistor Ra. Plot the ln(I0/I) (on y-axis) against time t on the graph paper. Draw a straight line

to fit the data. Choose two points on this line to calculate the slope m and showyour work here.

b. Calculate the time constant using R = 1/m. Compare this experimental valuewith R = RC by calculating the percent error.

71

2. Cartesian Graph for Discharging the Capacitor C through the Resistor Rv ofVoltmeter

a. Plot the ln(V0/V) (on y-axis) against time t on the graph paper. Draw astraight line to fit the data. Choose two points on this line to calculate theslope m and show your work here.

b. Calculate the time constant using V = 1/m. Determine the internalresistance of voltmeter RV using V = RVC and compare this value withthe ohmmeters result by computing the percent difference. Show yourwork here.

72

QUESTIONS

1. For the charging process, show that if I = I0 exp(-t/R),then ln(I0 /I) = (1/ R) t.

2. For the discharging process, show that if V = V0/2, then time t1/2 = ln2 V .This time t1/2 is called the half life for the discharging process.

3. If the half life was found to be 40s in a discharging experiment, what is thetime required for the voltage to fall from 24.0 V to 3.0 V?

4. Using the equation (3), prove q(t) = q0 exp(-t/v).


Experiment 8

MAGNETIC FIELDS

EQUIPMENTTwo Bar Magnets, Horseshoe Magnet, and Ring MagnetCompassIron-Filings PlatePASCO Magnetic Field SensorPASCO Power AmplifierPASCO Primary CoilPatch Cords

Figure 1: Mapping Magnetic Field

OBJECTIVESUpon completion of this laboratory experiment you will be able to:a. Use a magnetic compass to map the fields of a bar magnet and a horseshoe magnetb. Map the magnetic field of a bar magnet and the field of a horseshoe

magnet using iron filings.c. Measure the magnetic field strength of both of a bar and a horseshoe magnet.d. Measure the magnetic field strength inside a solenoid and compare it with atheoretical value based on the current through the solenoid.

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CONCEPTS

When studying magnetism, like gravitation and electricity, it is helpful to think interms of fields. We say there is a magnetic field surrounding a magnet. We canvisualize a magnetic field in terms of magnetic field lines. A line whose tangentialdirection at any point is the same as the direction of the magnetic field at that point iscalled magnetic field line (or lines-of-force).

The direction of magnetic lines-of-force can be visualized as those lines in which acompass needle aligns itself at each point in the field. The spacing between the fieldlines indicates the strength of the field at a specific point, where lines close togetherindicate a strong field and lines farther apart indicate a weaker field. By beginning atsome convenient point near one pole of a magnet, a field line can be mapped as aseries of short line segments. The plotting of a magnetic field line using a group ofcompasses is illustrated in the Figure 1. Now imagine that you draw two dots on bothends of each compass and connect the dots one by one to form a smooth line, onemagnetic field line is mapped. In this lab you will use one compass to follow thesame way as the group of compasses to map the magnetic field lines, as shown in theinsert of Figure 1.

Another picture of the magnetic field lines can be obtained by placing a piece ofpaper over a magnet and then scattering iron filings on the paper. In this lab you willuse a transparent case that is filled with iron filings in a fluid instead of paper. Theiron filings become little magnetic needles in the field and orient themselves like littlecompasses. Therefore, one can observe a visual representation of the direction andintensity of the magnetic field. The following picture shows the pattern of iron filingsaround a bar magnet.

Figure 2: Magnetic Field of a Bar magnet

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The magnetic field lines for two unlike and two like magnetic poles near eachother are illustrated using iron filings as shown in the following pictures.

Figure 3: Magnetic Field (a) Between Unlike Poles and (b) Between Like Poles

In this experiment you will start mapping the magnetic field using a compass (PartA). Everyone has to map at least one magnet. You will map the magnetic field using aplate with iron-fillings (Part B) in a working group. You will use a magnetic fieldsensor to measure the magnetic field strength at a pole position of your magnet (PartC). You will measure the magnetic field strength at the middle of a solenoid andcompare it with a theoretical value based on the current through the solenoid (Part D).

PROCEDURES

Part A: Mapping Magnetic Field Using a Compass

1. Using the two bar magnets, demonstrate the force of attraction and repulsionof unlike and like magnetic poles in your working group.

2. Place a bar magnet on a sheet of paper, draw the outline of the magnet, andindicate the north and south poles. Then, using the compass method as shown inthe insert of Figure 1, neatly map the field of the bar magnet. Map at least threemagnetic field lines on each side of the bar. Show each point along the field linesthat is determined by the compass.Note: Every one has to map at least one magnet (bar or horseshoe).

3. On a second sheet of paper, repeat step 2 for the horseshoe magnet. Plot at leastthree magnetic field lines for this magnet.

Part B: Sketching the Pattern of Iron Filings around Magnet

1. Hold the Iron-Fillings Plate firmly with both hands. Slowly rotate and shakethePlate until the iron fillings are uniformly distributed in the plate.

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2. Place the bar magnet on the top of the Iron-Fillings Plate. The iron fillings willmove under the magnetic force and show the magnetic field pattern. Draw a neatsketch illustrating the field pattern observed on the space in your Lab Report PartB.

3. Repeat steps 1 and 2 for two bar magnets end-to-end with the north pole of oneabout 2 to 3 cm from the south pole of the other. The obtained magnetic fieldshould be similar as Figure 3(a). Sketch the results in the data section.

4. Repeat step 1 and 2 for the two bar magnets north poles near each other. Thespacing between the like poles is about 2 to 3 cm. The obtained magnetic fieldshould be similar as Figure 3(b). Sketch the results.

5. Repeat step 1 and 2 for the horseshoe magnet. Sketch the results in the datasection.

6. Experimentally determine the distance from the end of your bar magnet such thatits field and the earths magnetic field are approximately equal. Record yourmeasured results in the data section (Question (e)) and describe the procedure usedto get these results.

Part C: Measuring Magnetic Field Strength of a Magnet

1. Connect the Science Workshop interface to the computer, turn on theinterface, and turn on the computer.

2. Connect the Magnetic Field Sensor to Analog channel A on the interface.3. Run DataStudio program. Click on 'Create Experiment'.4. Double click on 'Magnetic Field Sensor' from the sensor menu.5. Double click on 'Digits' from the display menu.6. On the top of the PASCO magnetic field sensor, set the 'Range Select' switch

to 1X and the 'Radial/Axial' switch to 'Axial'.7. Place a bar magnet on table. Move the sensor away from the magnet, push

'TARE' button on the sensor. Click the 'Start' button in DataStudio. Thereading on Digits Display should show Zero Gauss.

8. Move the sensor probe toward north pole of the magnet and observe thechanging value on the Digit Display.

9. When the tip of the probe rests on the surface of magnetic north pole, recordthe reading value on Data Table of Part C.

10. Repeat 7 to 9 for magnetic south pole.11. Repeat 7 to 10 for horseshoe magnet.

Part D: Measuring the Magnetic Field of a Solenoid

1. Keep the Magnetic Field Sensor into Analog Channel A. Connect the PowerAmplifier to Analog Channel B of the interface.

2. Connect two wires between the signal output of the Power Amplifier and theinput jacks on the solenoid (using the primary coil only).

3. Run DataStudio program. Click on 'Create Experiment'.

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4. From the sensor display double click on 'Magnetic Field Sensor' for Achannel. Then perform the same procedure to choose the Power Amplifierfor B channel.

5. On the Signal Generator window, change Sine Wave to Square Wave,type 10V under the Amplitude, and Type 0.01 Hz under the Frequency.

6. Double click 3.14 Digits from the Display menu. Choose Magnetic FieldStrength (1X) and click OK. The Digits 1 display is used to show themagnetic field measurement.

7. Double click 3.14 Digits again. Choose Output Voltage as the Digits 2Display of voltage on the coil. Move the Digits 2 Display to differentlocation (click, hold, and drop the Display with the mouse.).

8. Repeat Step 7 to choose Digits 3 Display for the Current ChB through thecoil.

9. Insert the magnetic field sensor completely into the solenoid. Click Startbutton to measure B at the middle inside solenoid. If the voltage shows +10V,record values of B and I in the first row of Data Table otherwise in the secondrow.Note: You should hold the sensor parallel to the axial of solenoid. Do notclick on the Stop button before you finish the entire measurement.

10. Move the magnetic field sensor out of the solenoid until its tip rests at the endof the solenoid, for example left end. If the voltage shows +10V, record valueof B (at Left End of Solenoid) in the first row of Data Table otherwise in thesecond row.

11. Repeat step 10 for measuring B at the other end of solenoid.12. Repeat steps 9 to 11 for the row of -10 V. (Note: Wait for the Square

Wave to switch V from +10 V to -10 V.)13. Properly return all lab equipments.

Note: After you finish this lab, you should properly return all the magnets withiron keeper on and correct polarity, as shown in the following figure.

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PRE-LAB FORM

MAGNETIC FIELDS

1. Describe how to map the magnetic field lines.

2. List at least four properties of magnetic field lines.

3. Do lines of magnetic field cross each other? Explain.

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LAB REPORT FORM

MAGNETIC FIELDS

Part A: Mapping Magnetic Field Using a Compass

1. Based on your observations of the two bar magnets in Part A,

Like magnetic poles _____________________________ .

Unlike magnetic poles ____________________________.

2. Include the map of the magnetic field for the bar magnet and the map of themagnetic field for the horseshoe magnet in your report.

Part B: Sketching the Pattern of Iron Filings around Magnet

In the space below, neatly sketch your observations of the magnetic field patternsusing the iron-filings plate.(a.) Bar magnet

(b) Two Bar magnets:North pole faces to south pole.

(c) Two Bar magnets:North pole faces to north pole.

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(d) Horseshoe Magnet:

(e) Distance measured in step : _________________ cm

Describe the procedure used to get this result and draw a sketch to illustrate thisprocedure.

Part C: Measuring Magnetic Field Strength

Magnetic Field Strength (Unit in Gauss)MagnetNorth Pole South Pole

Bar Magnet

Horseshoe Magnet

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Part D: Measuring the Magnetic Field of a Solenoid

VI

(A)B at middle ofsolenoid (G)

+ B at Left End ofSolenoid (G)

B at Right End ofSolenoid (G)

10 V

-10 V

CALCULATIONSBin = 0nI (T) where 0 = 4 x10

-7 Tm/A, n = N/L = 2920 turns/0.11m. N is thenumber of turns of the solenoid. L is the length of the solenoid. 1Tesla = 104 Gauss

1. Calculated Value of Bin.

2. Using the average of B at the middle of solenoid as BExperiment,calculate the percent error.

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QUESTIONS1. What is the meaning of a negative value of the magnetic field reading?

2. Draw the possible magnetic field lines for the following combination ofmagnets:

3. Review your data. List at least three of your findings about magneticfield lines.

4. A long solenoid, of length 15 cm, has 3000 turns. The coil carries acurrent of 0.80A. What is the value of the magnetic field inside thesolenoid?

S

S

N N


Experiment 9

MAGNETIC FORCE AND MEASURINGTHE PERMEABILITY

EQUIPMENTMagnetic Force ApparatusElectrical Lead WiresPower Supply (Big Green) and AmmeterMicro Weights (10 to 100 mg)Vernier Caliper, Meter Stick

Figure 1: Magnetic Force Apparatus Setup

OBJECTIVESUpon completion of this experiment you will be able to

a. Set up and operate the magnetic force apparatus.b. Examine the relation between magnetic force and current.c. Determine the permeability of free space.

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CONCEPTSIn this experiment you will use a Magnetic Force Apparatus to determine the permeabilityof free space. The device is shown in the figure 1. The bottom conducting rod is fixed. Thetop conducting rod is free to move and is initially balanced by a counter balance, so Fneti =0. When an extra weight, W, is added on the top rod, an upward magnetic force, Fm, isneeded to reestablish the balance. That is

Fm W = 0 (1)

Figure 2: Magnetic force and weight

Referring to the figure 2, the magnetic field B at a distance r from a long straight current I1is given by

B = 0I1/(2r) (2)

where 0 is the permeability in free space. The given value of 0 is 410-7 Tm/A. A second

parallel conducting rod with current, I2, having a length L and at the distance r above thefirst current experiences an upward magnetic force given by

Fm = I2LB (3)

According to equation (1) this upward magnetic force is needed for balancing thedownward weight. Combining equations (1), (2), and (3) and using the fact I1 = I2 = I, thebalance relation is given by

Fm = 0I2L/(2r) = W (4)

where r is the distance between the center to center of the two conducting rods. From thefigure 2, r can be determined by

r = D + d (5)

where D is the diameter of the rod and d is the gap between the two rods.


PROCEDURE

1. Measure the interacting length L of the top rod, referring to the Figure 1. Measurethe diameter D of the bottom rod with Vernier Caliper and record your findings.

2. Set up the magnetic force apparatus and connect the circuit as the illustration of theFigure 1. Dont turn on the power. The power control knob of the green lab powersupply should be turned to zero position. Choose the 10 A scale for the ammeter.

3. Have your instructor check the circuit.

4. Adjust the two interacting conductors to be parallel. Note: There are four adjustingscrews for this purpose, two at the ends of bottom rod for leveling and two at theback ends of the top rod for twisting. You may not get the perfect parallel condition.Do the best that you can.

5. Adjust the counter balance so that the equilibrium gap, d, is about 1mm. Note: Noneed to measure it. When you barely see the opening gap (no position of the tworods in touch), it will be fine. The balanced rod must be able to rotate freely. If youadd a small weight, the gap should be closed. When the weight is removed, the rodshould return to its equilibrium position.

6. Without touching the top rod, carefully place a small mass, m = 40 mg (4010-6kg),on the pan, somewhat depressing the top conductor to close the gap.

7. Turn on the power supply and flip the toggle switch to range A. Slowly turn thevoltage control knob up till the exactly same equilibrium gap to be restored.Record the current value I in the Data Table 2.

8. Repeat steps 6 and 7 five more times for 50 mg, 60mg, 70 mg, 80mg, and 90mg. Alab partner is to keep a close eye on the ammeter so that a maximum currentof 10 A is not exceeded. Record your findings in the Data Table 2.

9. Complete the required calculations in the Data Table 2.

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PRE-LAB FORM

MAGNETIC FORCE AND MEASURING THE PERMEABILITY

The two anti-parallel currents shown in the illustration have a common diameter D =0.33 cm, spacing between them d = 0 .1cm, a common interacting length L = 25.0 cm,and each carrying the same current I = 8.0 A.

1. The lower current is into the paper. What is the direction of the magnetic field dueto this current at the position of the upper current?

2. What is the direction of the force on the top current-carrying rod?

3. Calculate the magnitude of the force on the upper current-carrying rod.

4. Determine the mass (in milligrams, mg) whose weight on the top conductorwould just equal the force calculated in the question above.


LAB REPORT FORM

MAGNETIC FORCE AND MEASURING THE PERMEABILITY

Data Table 1: Dimensions

L (cm) D (cm) d (cm) r = D + d

0.1

Data Table 2: Force and Current Data

m (10-6kg) W (N) I (A) I2L/(2r)

40

50

60

70

80

90

CALCULATIONS1. Show one sample calculation for the weight W=mg.

2. Show one sample calculation for I2L/(2r) using the data from DataTable 1&2.

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3. Cartesian Graph for the determination of the permeability of free space:

a. Plot the W (on y-axis) against I2L/(2r) on the graph paper. Draw a straight lineto fit the data. Choose two points on this line to calculate the slope m= 0 and showyour work here. (Recall equation (4) W=0I

2L/(2r). It is a straight line equation.)

b. Compare this experimental value 0 with the given value, 4x10-7 N/A2 , by

calculating the percent error.


QUESTIONS1. What are the major sources of error?

2. Referring to the illustration, derive the balance equation W=0I2L/(2r).

3. The SI units for 0 is sometimes given as Tm/A. Our experimental units are N/A2.

You are to show that these are equivalent in two steps:a. Use the magnetic force equation, Fm = ILxB, to show that the unit for the

magnetic field, the tesla (T), is related to the Newton and the amp by T =N/(Am).

b. From the relation for a magnetic field due to a long straight current, B =0I/(2r), show that the units of 0 are N/A

2.

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4. The two anti-parallel currents shown in the illustration have a common diameter D= 0.33 cm, spacing between them d = 0 .1cm, a common interacting length L = 25.0cm. If the top rod has a mass 17.0 g and carries current I2 = 8.0 A out of the paper asshown in the diagram,

a. What is the direction and magnitude of magnetic field needed to lift this rodvertically upward?

b. What is I1 needed to produce this magnetic field?(Note: The result might surprise you. This is why this lab can not do thisway.)


Experiment 10

THE OSCILLOSCOPEEQUIPMENTOscilloscopeTwo BNC-Alligator CablesConnecting WiresDigital MultimeterDC Power SupplyFunction GeneratorRLC Circuit Board


OBJECTIVESUpon completing this set of lab exercises you will be able to

a. Set up and operate an oscilloscope.b. Measure DC and AC voltages.c. Measure the periods and frequencies of sinusoidal signals.d. Determine RC Time Constant Using Oscilloscope.

CONCEPTSAn AC voltage signal at t moment can be expressed as

V(t)=VPsin(2ft), (1)

where VP is the peak voltage, f is frequency of the voltage signal. The RMS voltage,VRMS, can be determined by

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VRMS = VP/ 2 . (2)

The AC voltmeter can only measure the RMS voltage, VRMS. The oscilloscope can notonly measure the VP and VRMS but also display the graph of voltage versus time on itsscreen. It is a useful tool to measure the peak voltage, period, and frequency of an ACsignal. The illustration of Figure 2 shows the basic features of the cathode ray tube (CRT)that is the heart of the oscilloscope. The three basic parts of a CRT are the Electron Gun,the Beam Deflection Circuitry, and the Fluorescent Screen. The functions of each aredescribed below.

Figure 2: Cathode Ray Tube of an Oscilloscope

1. The Electron Gun generates a narrow beam of electrons which is directed along thelength of the tube.

2. The Beam Deflection Circuitry develops an electrostatic field such that when avoltage is applied across the horizontal deflection plates the electron beam will bedeflected toward one plate or the other. This causes the beam to move back and forthhorizontally across the tube. Likewise, the vertical deflection plates deflect the beamup and down depending on the polarity and magnitude of the applied voltage.

3. The electronic beam strikes the Fluorescent Screen which results in the generation ofa spot of light on the surface of the tube indicating the location of the beam. Theoverall effect is that the light spot moves on the screen in a manner dependent uponthe voltages applied to the horizontal and vertical deflection plates. The usergenerally controls the horizontal deflection with the oscilloscopes internalelectronics designed so that the beam sweeps across the screen in direct proportionalto the time. An external signal being investigated usually determines the verticaldeflection. Thus, V(t) can be measured on y-axis on the screen of the scope. Time, t,can be determined from the x-axis.

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1

2

3456

7 8

910

11

12131415

18

17

16

2021

19

22

24

23

2526

27

28

Figure 3: Oscilloscope

PROCEDURE

Part A: Initial Set-Up Oscilloscope (Refer to Figure 3)

1. Press the Power On switch (5) to turn on the oscilloscope.2. Set the CH 1 switch (14) to GND. (This will be changed when measurements are

made.)3. Set the mode switches (9) and (11) to CH 1 and ALT.4. Set the CH 1 VOLTS/DIV switch (12) to 1 ( at the 1X window). The inner knob

(13) is to be turned fully clockwise.5. Set the source switches (27) on CH 1.6. Set the SEC/DIV switch (18) to 1 ms. Turn the inner knob (19) fully clockwise.7. You should now see a line trace on the oscilloscope. Adjust the VERTICAL

POSITION (7) and HORIZONTAL POSITION (16) to center the trace on thescope screen.

8. Adjust the INTENSITY (1) and FOCUS (3) knobs to get the best trace.9. Set the CH 1 AC-GND-DC switch (14) to DC.10. Using the VERTICAL POSITION (7) knob, position the straight line trace to

the bottom line of the screen. The oscilloscope is ready to measure DC signals.

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DC Power

Supply

Figure 4: DC Voltage Measurements Setup

Part B: DC Voltage Measurements (Refer to Figure 3 and 4)

1. Make sure that the DC power supply is off. Connect an oscilloscope cable fromthe CH1 input connector (15) to the DC power supply and the digital voltmeter.Note: Make sure that the wiring connectors are linked from red to red and black toblack.

2. The digital multimeter should be set to the DC voltmeter mode, and on anappropriate scale. Turn on this digital voltmeter and the DC power supply.

3. Using the oscilloscope as a voltmeter, determine the voltage output of the DCpower supply when the output values of the DC power supply are 1.5, 3, 4.5, 6, 9,and 12 V. To do this set the CH 1 VOLTS/DIV mode switch (12) to anappropriate value to get a large deflection on the oscilloscope for each powerknob setting. Record the oscilloscope readings and the digital voltmeter readingsin Data Table 1. Note: The VOLTS/DIV decides the vertical scale in volt perdivision. This is major division about one cm on the screen. One major division isdivided into five subdivisions. Alternate the CH 1 AC-GND-DC switch (14)between GND and DC to read the #DIV for each measurement.

4. Calculate the voltage measured by the oscilloscope using: DC Voltage = # DIVVOLTS/DIV.

5. Turn off the DC power supply and remove it from the circuit.

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FG: A

FG: C

FG: B

5

1 (at rear end)

1

1

2

2

2

3

3

3

34

4

4

5

5

5

5

5

Figure 5: AC Voltage Measurements Setup: There are three kinds of FunctionGenerators (FG) in the lab. Please use only one of them.

Part C: AC Voltage Measurements (Refer to Figure3 and 5)

1. Set the CH 1 VOLTS/DIV mode switch (12) to 1 (in the 1X window).2. Set the time base SEC/DIV switch (18) to 0.5 ms (in ms window).3. Set the CH 1 AC-GND-DC switch (14) to AC.4. Adjust the VERTICAL POSITION (7) so that the trace is in the center of

Lab Man 2426 So 2013

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