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PHY 161

LABORATORY

MANUAL

CITY UNIVERSITY OF NEW YORK

COLLEGE OF STATEN ISLAND

PHYSICS & ASTRONOMY

DEPARTMENT

The City University of New York COLLEGE OF STATEN ISLAND

Department of Physics & Astronomy

PHY 161

PHYSICS LABORATORY MANUAL

Edition 2020

PHYSICS & ASTRONOMY DEPARTMENT

PHYSICS LABORATORY EXT 2978, 4N-214/4N- 215

LABORATORY RULES & REGULATIONS

When entering the laboratory premises you are entering a working professional environment therefore, you are expected to adhere to the following rules:

Food or drinks are not allowed in the laboratory.

The use of cell phones or music players is not permitted.

Behave in a professional and respectful manner towards your instructor, the technical staff and your fellow students.

Punctuality is critical. Arrive on time to each laboratory session or equipment may be removed from your workbench. Punctuality is factored into your grade.

Computers are for experiment use only such as collecting, analyzing and printing data. Do not save any data or modifications made to the experiment templates. If needed, save it to a thumb/flash drive. Web surfing, reading e-mail, playing games, streaming music/videos and printing work from other classes are not allowed.

Laboratory reports must be submitted as soon as you enter the laboratory room; otherwise, points will be deducted for lateness.

Bring a scientific calculator, a notebook and pen/pencil for each laboratory session.

Your laboratory partner and you are responsible for the equipment and workbench you use during an experiment. Please handle equipment with care, do not make any markings or write on any piece of equipment or on your workbench. Being responsible on the handling of equipment and caring for your work station is also factored into your grade.

Return or leave equipment as it was given to you when the laboratory session started. Be mindful that students from other laboratory sections use the same equipment and work stations; please cooperate to maintain everything in working conditions.

After completing an experiment and before leaving the premises check that your workbench is clean and clutter free, push in your chair and either log-off or re-start the computer.

Be sure to take all your belongings, the laboratory is not responsible for any lost items.

Your cooperation in abiding by these rules will be highly appreciated.

Thank You. The Physics Laboratory Staff

TABLE OF CONTENTS

LAB WORK 1

LABWORK 1 | 2 PHY 161

For isolated point charges, the equipotential surfaces are spheres, whereas the electric field lines are straight lines (Fig. 1).

Fig.1. Two dimensional presentation of electric field lines (red and blue arrows) and equipotential surfaces (black dotted circles) of isolated positive and isolated negative charges.

For assemblies of point charges and non-point charges, equipotential surfaces and electric field lines have more complex shapes, e.g. see Figs. 2 and 3.

Fig.2. Two dimensional presentation of electric field lines and equipotential lines of positive and negative charges placed at a short distance one from another. Two points a and b between which strength of electric field is measured are shown. The distance d (^) ab is much shorter than total length of the electric field line.

+ -

Equipotential Lines

Electric Field Lines

-^ +

Equipotential lines

Electric

field lines Va Vb

d ab

EQUIPOTENTIAL AND ELECTRIC FIELD LINES

PHY 161 LAB WORK 1 | 3

Fig.3. Two dimensional presentation of electric field lines and equipotential lines of two oppositely charged parallel plates. The uniform electric field between the plates is shown by straight parallel electric field lines

The electric field between two oppositely charged parallel plates placed at a distance much smaller than the size of the plates can be considered as uniform (Fig. 3). Note that the electric field in the areas close to the edges of the plates is not anymore uniform. For uniform electric field, there is a simple relation between the strength of electric field E and the potential difference Vab between points a and b lying on one and the same electric field line (Eq. 4):

𝐸𝐸 = −

where dab is the distance between points a and b. Although this formula is not strictly correct for non-uniform electric field, it can be used for estimation of strength of electric fields of any configuration (Fig. 2). In this case, however, the distance d (^) ab must be much less than the total length of the electric field line. Electric field can be created freely only in non-conductive media, e.g. in vacuum, air, or in insulating materials like glass or water. Electric field does not penetrate inside conductors. Thus, inside conductive materials electric field is zero. It is also true for closed hollow conductive objects, e.g. closed metal box, or closed metal cage. Since the electric field is zero, the electric potential inside conductors and conductive hollow objects is constant (Fig 4).

Fig. 4. Equipotential lines and electric field lines around and inside a conductive box. Surface of this box is at a potential V. Potential in every point inside the box is also at a voltage V. The electric field inside the box is zero (no electric field lines).

- - - - - - - - - - - - - - - - - - - - - -

Equipotential lines

Electric field lines

+ + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - -

V1 (^) V2 V3 (^) V4 V5 V6 V

V

+ + + + + + + + + + + +

EQUIPOTENTIAL AND ELECTRIC FIELD LINES

PHY 161 LAB WORK 1 | 5

Experimental Procedure and Calculations

1. Set up the experiment for two point charges configuration (Fig. 6a). Connect the board to the power supply which should be set to 6V as shown on Fig. 5a.
2. Set the multimeter to V�^ for voltage DC and press the Range key to set the desired display of precision. Pressing it three times will give a display of 1 decimal place as shown in Fig. 5c.
3. Plug one end of the 36” red banana-to-banana connector into the red input, labeled V, of the multimeter and place the tip adaptor on the other end of this connector. This is now your scanning probe.
4. Using the scanning probe, search for potentials along the surface of the configuration. See Fig. 5c for an example. When the desired potential is found apply enough pressure with the tip so that a mark is created on the white paper beneath. Hint: The voltages at each individual cross located in between the two charges (dots or plates) will predetermine the potentials you should be searching for.
5. Mark enough points of equal potential to reasonably determine the shape of the equipotential line. Repeat for six additional voltages making note of each value.
6. Repeat parts 4 and 5 for the remaining configurations: two parallel plates (Fig. 6b) and closed conductive surface (Fig. 6c).
7. From the points you have marked on the white paper, carefully construct the equipotential lines for each charge distribution.
8. Construct the electric field lines. Remember that electric field lines are always perpendicular to the equipotential lines.
9. For each configuration calculate the electric field strength at 3 locations of your choice.
10. Estimate the amount of electric charge on the point electrodes (the configuration on Fig. 6a) using the accumulated data.

Fig. 6. Configurations of charged metal electrodes on conductive paper: (a) two point charges, (b) two parallel plates, (c) closed conductive surface.

(a) (b) (c)

LAB WORK 1

LABWORK 1 | 6 PHY 161

Questions

1. Is it possible for two different equipotential lines to cross each other? Explain why or why not?
2. Is it possible for two different electric field lines to cross each other? Explain why or why not?
3. Where do the electric field lines begin and end? If they are equally spaced at their beginning, are they equally spaced at the end? Along the way? Why?
4. If you wanted to push a charge along one of the electric field lines from one conductor to the other, how does the choice of electric field line affect the amount of work required? Explain.
5. The potential is everywhere the same on an equipotential line. Is the electric field everywhere the same on an electric field line? Explain.
6. How much work has to be done in order to move an electric charge along an equipotential line?
7. Where do the equipotential lines begin and end? Explain.

LAB WORK 2

LAB WORK 2 | 2 PHY

(a) (b) Fig. 1. (a) Voltage applied to a conductor as a function of the induced current for an ohmic conductor. Slope of this dependence calculated as the change of voltage  V divided by the corresponding change of current  I equals resistance R of this conductor: R =  V/  I. (b) Non-ohmic conductors may exhibit complex non-linear dependences of voltage versus current.

The ability of moving electrons to maneuver through a conducting material depends on the physical parameters of this material and on its temperature. Heating results in thermal agitation of moving electrons and atoms in the conductor. This agitation retards the directional motion of electrons and, consequently, increases resistance of the conductor. The current flow itself can increase temperature considerably: the greater the current in a conductor the higher its temperature. The actual dependence of resistance on temperature is a characteristic of the conducting material. It is measured by so-called temperature coefficient of resistivity α. This coefficient may be positive or negative and therefore the resistance of some conductors increases with temperature, whereas it decreases for the others. For instance, for tungsten α = +4.5×10- °C-1, for carbon (graphite) α = -5×10-4^ °C-1. The change of resistance with temperature is given by the following formula (Eq. 4): 𝑅(𝑇) = 𝑅𝑅𝑇[1 + 𝛼(𝑇 − 𝑇𝑅𝑇)] (4) where R ( T ) is the resistance at temperature T ; TRT is room temperature (usually 20°C) and RRT is the resistance at room temperature.

Apparatus

 Variable DC power supply  Ammeter (Digital Multimeter set to “mA” DC)  Voltmeter (Digital Multimeter set to “V” DC)  Tubular power rated resistor (100Ω)  Tungsten filament lamp (60W)  Carbon filament lamp (32cp)  Lamp socket

I slope R V   

y=mxm=100.5+/-0.

I

V

OHM’S LAW AND RESISTANCE

PHY 161 LAB WORK 2 | 3

 Connecting wires  Knife switch with spades

Procedure and Calculations

1. Set up the equipment as shown in Fig 2 with 100 Ω tubular resistor for R , a digital multimeter (connect to the 400 mA input and set the dial to mA, press the yellow button to switch from AC to DC) for A , and a second digital multimeter for V (set the dial to V DC). Have your connections checked by your technician/instructor before turning on the power supply! Close the circuit and set the power supply Vo to 1, 2, 4, 6, 10, 14, 18, 22, 26 and 30V, recording V and I for each step.

Fig. 2. Circuit set-up used for the study of Ohm's Law by voltmeter-ammeter method.

2. Open the circuit and replace the tubular resistor with the tungsten filament lamp for R (Fig. 3). Have your connections checked by your technician/instructor before turning on the power supply! Close the circuit and set the power supply Vo to 1, 2, 4, 6, 10, 14, 18, 22, 26 and 30V, recording V and I for each step. When working with the lamp at low voltages allow the current to stabilize before recording it.
3. Open the circuit and remove the tungsten lamp and place the carbon filament lamp for R. Have your connections checked by your technician/instructor before turning on the power supply! Close the circuit and set the power supply Vo to 1, 2, 4, 6, 10, 14, 18, 22, 26 and 30V, recording V and I for each step. When working with the lamp at low voltages allow the current to stabilize before recording it.

Switch

V A 400mA

Power supply

Voltmeter

Ammeter

Resistor

V

A R

+ -

+ -

A DC mA

V DC V

OHM’S LAW AND RESISTANCE

PHY 161 LAB WORK 2 | 5

Fig. 5. Sample data of R vs I for tubular resistor, tungsten bulb and carbon bulb.

Questions

1. Of the three objects you measured in this experiment (tubular resistor and two lamps), which are ohmic resistors and which are not? Explain.
2. What is your explanation for the fact that the current induced in the lamps does not follow Ohm’s Law?
3. What do the plots tell you about the temperature coefficient of resistivity of each object used?
4. Using formula (4) estimate the maximum temperature the filaments in the lamps reach during the measurements.
5. Predict the current, which would be induced in the resistors you measured if a voltage of 40 V could be applied.

• PHY
• LAB WORK 1: EQUIPOTENTIAL AND ELECTRIC FIELD LINES ...................................................1- RECOMMENDED LAB WORKS #
• LAB WORK 2: OHM’S LAW AND RESISTANCE .........................................................................2-
• LAB WORK 3: RESISTIVITY ....................................................................................................3-
• LAB WORK 4: CONNECTION OF RESISTORS AND CAPACITORS IN SERIES AND IN PARALLEL ....4-
• LAB WORK 5: DIRECT CURRENT METERS ...............................................................................5-
• LAB WORK 6: KIRCHHOFF’ S RULES .......................................................................................6-
• LAB WORK 7: SOURCES OF ELECTROMOTIVE FORCE IN DIRECT CURRENT CIRCUITS ...............7-
• LAB WORK 8: RC CIRCUITS ....................................................................................................8-
• LAB WORK 9: MAGNETIC FIELD CREATED BY A CURRENT CARRYING WIRE ...........................9-
• LAB WORK 10: MAGNETIC FIELD IN A SLINKY SOLENOID .....................................................10-
• LAB WORK 11: ALTERNATING CURRENT CIRCUITS ..............................................................11-
• LAB WORK 12: REFLECTION AND REFRACTION ....................................................................12-
• LAB WORK 13: SPHERICAL MIRRORS AND LENSES ...............................................................13-
• LAB WORK 14: FORMATION OF IMAGES BY A CONVERGING LENS ........................................14-
• APPENDIX 1: PREPARING A LABORATORY REPORT A- APPENDIX #
• APPENDIX 2: SAMPLE LABORATORY REPORT A-
• APPENDIX 3: VERNIER GRAPHICAL ANALYSIS 3.4 AND BASIC GRAPHING GUIDELINES A-
• APPENDIX 4: TECHNICAL NOTES - VERNIER LABQUEST 2 INTERFACE A-
• APPENDIX 5: TECHNICAL NOTES - SENSORS AND PROBES A-
• APPENDIX 6: MULTIMETERS AND POWER SUPPLIES A-
• LAB WORK
• LAB WORK 2 | 6 PHY

LAB WORK 3

LAB WORK 3 | 2 PHY 161

In order to better understand the relationship between the parameters in Eq. 2, see the interactive applet: http://phet.colorado.edu/sims/resistance-in-a-wire/resistance-in-a-wire_en.html

The resistivity of a conductor can be found by measuring its resistance and its dimensions. If a piece of wire of length L and diameter d is used as the conductor (Fig. 1), its resistivity can be calculated using formula (Eq. 3):

𝜌𝜌 =

Apparatus

• Variable DC power supply
• Resistance board with three wire resistors ( R ) of different diameter, d
• Digital multimeter ( V )
• Digital multimeter ( A )
• 10 0 Ω tubular ballast resistor ( Ro )
• Connecting wires
• SPST switch

Procedure and Calculations

Part I:

1. Set up the equipment as shown in Fig 2, connecting to Wire 1 first. Keep the circuit open (switch lever is up). Set the power supply to 10V. Set the voltmeter to mV and the ammeter to mA, press the yellow key for DC current. Record the diameter d, of the wire. Have your connections checked by your instructor/technician before turning on the power supply!

Fig. 2a – Circuit Set-up

Ro

Power Supply

R

0 cm 65 cm

- +

+ -

V A

A DC mA 400mA Vo

+

+

- - Switch Multimeter to measure voltage

Multimeter to measure current

V DC mV

RESISTIVITY

PHY 161 LAB WORK 3 | 3

Fig. 2b. Instruments and components posing for the circuit set-up photo.

2. Open the template Resistivity.ga to enter and analyze data.
3. When ready to start close the circuit and record the current I , which will remain constant thereafter.
4. Lift the red probe from the red post of the wire and tap the wire at the 5 cm mark, record the voltage V. Continue to obtain voltages for various lengths starting from 5 cm to 65 cm in steps of 5 cm. Be sure to make good contact with the wire to so that the voltage reading is stable. See Fig. 3 below for sample readings at the 50 cm mark.

Fig. 3. Sample reading of I and V as a function of length

5. When done with Wire 1 open the circuit. Move the connecting wires leading into the red and black posts of the wire, to the posts of the second wire. Be sure to record the diameter.
6. Close the circuit and record the current. Repeat procedure 4.
7. Repeat for the third wire.
8. Based on the recorded data, compute R in ohms, for each length L.