Adnan Menderes University Faculty of Arts And Sciences Physics Department

PHYS 142 Physics Laboratory Electricity and Magnetism Laboratory Manual

February, 2016 AYDIN

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Contents

Introduction..........................................................................................................3 1. Laboratory 1: Electric Field & Electrostatic Potential in the Plate Capacitor...................................................................................................................9 2. Laboratory 2: Dielectric Constant of a Material.........................................13 3. Laboratory 3: Ohm’s Law...........................................................................18 4. Laboratory 4: Wheatstone Bridge...............................................................23 5. Laboratory 5: Magnetic Field of Single Coils / Biot-Savart’s Law..............27 6. Laboratory 6: Magnetic Induction................................................................32 7. Laboratory 7: Transformer...........................................................................37

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INTRODUCTION Purpose of this laboratory course is to teach electricity and magnetism by observations from experiments and prove some principles of electricity and magnetism doing experiments by using basic measuring devices and measurement techniques. This approach complements the classroom experience of Physics-162 where you learn the material from lectures and books designed to teach problem solving skills. Also with this laboratory students will learn the how experimental uncertainty plays a role in physical measurements and they will learn how can they minimize this uncertainty.

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Student Responsibilities

You must be prepared to perform the experiments by reading the lab manual and related textbook material before coming to the laboratory. Since each experiment must be finished during the lab session, familiarity with the underlying theory and procedure will prove helpful in speeding up your work. If you have questions or problems with your preparation, you can contact Laboratory Teaching Assistant (LTA), but in a timely manner. You must come to laboratory on time and you have only one Makeup Experiment chance (if you have a valid excuse and you must be documented), if you miss more than two experiments you will fail from this course, so you must come and perform all experiments. In laboratory, you should remain alert and use common sense while performing a lab experiment. You are also responsible for keeping professional and accurate record of the lab experiments in a laboratory notebook and you should report any errors in the lab manual to the teaching assistant. At the end of experiment, you must collect and clear the equipments and tables and you have to prepare an experiment report for each experiment after the laboratory, and bring it at his/her next coming.

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Grading Policy

Each experiment will be graduated upon 100 points. 1. The student has an mini exam (approximately 15 minutes) for each experiment before performing the experiment. [30 points] 2. The student will take experiment performance grades (This part also includes oral exam). [30 points] 3. The student prepare an experiment report. [40 points] Average of these total grades will be your midterm exam. Final exam include theoretical questions about each performed experiments, and will be at the end of semester.

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Laboratory Reports

The laboratory report is a kind of manuscript to communicate your experiment results and conclusions to other professionals. In this course you will write the laboratory 3

report to inform your LTA, so LTA can learn what you did and learned from the experiment. But don’t write in your report like this sentence ”In this experiment i learned the Ohm’s law · · · ”. Your laboratory report should be clear and concise. We prepare a report format as follow, you can use as a guide. In this lab probably you will work with more than one lab partners, but your report will be your individual effort.

3.1

Format of Laboratory Report

Name Surname: Student Number: Section and Experiment Date: Laboratory Teaching Assistant Name: The name of the instructor who you have performed the experiment with. Title of Experiment Purpose In this part explain the purpose of the experiment briefly. Theory In this part you can benefit from your lecture notes, books, etc. (Dont write more than one page for this part) Apparatus In this part indicate which equipment was used while you perform the experiment. Procedure In this part you will write how you perform this experiment in your own words (not from laboratory manual) Data and Calculations In this part you must write your data in order ( You can express them in a data-table format). You must write formulas that used for calculations, and your results must be written with significant numbers. You must write units of your all results in all steps of your calculations. You also plot graphs on graph paper (milimetric, logarithmic, etc.) in this part if necessary. Conclusion In this part you must make a comment on your experiment and results (and also on graphs). For example: you can evaluate and compare your results with theory, are they in agreement with physics laws, are your graphs as expected with respect to those laws? If there is error in your results, what can be the physical error causes? You must make comment also on those error causes. Questions In this part you must answer questions about performed experiment which are in laboratory manual.

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Symbols and Units of Some Fundamentals

In this course we will use SI (Syst´eme International) units for calculations. Some of the physical quantities are given in Table 1. 4

Table 1: Symbols and units of some physical quantities Electrical Field Electrical Potential Electrical Charge Electrical Current Power Current Density Magnetic Field Resistor Capacitor Inductor

Symbol ~ E V Q, q I, i P J~ ~ B R C L

SI unit (Abbreviation) Volt/meter (V/m) Volt (V) Coulomb (C) Amper (A) Watt (W) Amper/(meter)2 (A/m2 ) Tesla (T) Ohm (Ω) Farad (F) Henry (H)

Table 2: Some prefixes for powers of ten Power 10−24 10−21 10−18 10−15 10−12 10−9 10−6 10−3 10−2 10−1

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Prefix yocto zepto atto femto pico nano micro milli centi desi

Abbreviation y z a f p n µ m c d

Power 101 102 103 106 109 1012 1015 1018 1021 1024

Prefix deka hecto kilo mega giga tera peta exa zetta yotto

Abbreviation da h k M G T P E Z Y

Resistor color code

This part is written by the help of the ”Physics Laboratory Manual” which is written by David H. Loyd, Angelo State University. For resistors routinely used in electronic instrumentation, resistance is coded by a series of colored bands on the resistor. The key to the resistor color coding system is given in figure 2 above. The four bands are placed with three equally spaced bands close to one end of the resistor followed by a space, and then a fourth band. The first two bands are the first two digits in the value of the resistor, and the third band gives the exponent of the power of 10 to be multiplied by the first two digits. Thus a resistor with its first three bands labeled Yellow-Violet-Red has a value of 47×102 Ω, or 4700 Ω.

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Use of Laboratory Instruments

This part is written by the help of the laboratory manual which is written by Dr. J. E. Harriss. One of the major goals of this lab is to familiarize the student with the proper equipment and techniques for making electrical measurements. Some understanding of the lab instruments is necessary to avoid personal or equipment damage. By

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+

-

cell

battery

lamp

ac supply

switch

ammeter

voltmeter

galvanometer

resistor

potentiometer

transformer

heating element

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+

-

Figure 1: Some electrical circuit symbols.

Figure 2: Resistor color code.

understanding the device’s purpose and following a few simple rules, costly mistakes can be avoided. Ammeters and Voltmeters: The most common measurements are those of voltages and currents. Throughout this manual, the ammeter and voltmeter are represented as shown in Figure 3. Ammeters are used to measure the flow of electrical current in a circuit. Theo6

Figure 3: Ammeters (A-internal resistance be very small) and Voltmeters (Vvoltmeters have ideally infinite impedance).

retically, measuring devices should not affect the circuit being studied. Thus, for ammeters, it is important that their internal resistance be very small (ideally near zero) so they will not constrict the flow of current. However, if the ammeter is connected across a voltage difference, it will conduct a large current and damage the ammeter. Therefore, ammeters must always be connected in series in a circuit, never in parallel with a voltage source. High currents may also damage the needle on an analog ammeter. The high currents cause the needle to move too quickly, hitting the pin at the end of the scale. Always set the ammeter to the highest scale possible, then adjust downward to the appropriate level. Voltmeters are used to measure the potential difference between two points. Since the voltmeter should not affect the circuit, the voltmeters have very high (ideally infinite) impedance. Thus, the voltmeter should not draw any current, and not affect the circuit. In general, all devices have physical limits. These limits are specified by the device manufacturer and referred to as the device rating. The ratings are usually expressed in terms of voltage limits, current limits, or power limits.

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Preparing Graphs

This part is written by the help of the ”Physics Laboratory Manual” which is written by David H. Loyd, Angelo State University. It is helpful to represent data in the form of a graph when interpreting the overall trend of the data. Most of the graphs for this laboratory will use rectangular Cartesian coordinates. Note that it is customary to denote the horizontal axis as x and the vertical axis as y when developing general equations, as was done in the development of the equations for a linear least squares fit. However, any two variables can be plotted against each other. When preparing a graph, first choose a scale for each of the axes. It is not necessary to choose the same scale for both axes. In fact, rarely will it be convenient to have the same scale for both axes. Instead, choose the scale for each axis so that the graph will range over as much of the graph paper as possible, consistent with a convenient scale. Choose scales that have the smallest divisions of the graph paper equal to multiples of 2, 5, or 10 units. This makes it much easier to interpolate between the divisions to locate the data points when graphing. The student is expected to bring to each laboratory a supply of good quality linear graph paper. A very good grade of centimeter by centimeter graph paper with one 7

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(a)

(b)

Displacement (m)

25

Graph (a) d(m) t(s) 7.57 1.00 11.97 2.00 16.58 3.00 21.00 4.00 25.49 5.00

20

15

10

FALSE

5

0

0

1

2

3

4

5

6

Time (s)

Displacement (m)

30

IDEAL ONE

(c)

25

20

15

10

EXCEPTABLE

5

0

0

1

2

3

4

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Graph (b), (c) d(m) t(s) 0.0 0.00 5.1 1.00 11.0 2.00 14.5 3.00 20.7 4.00 25.6 5.00 29.4 0.00

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Time (s)

Figure 4: Graph of displacement versus time; a) plotted by employing list squares fit method (Graph (a) data is used), b) False one (Graph (b) data is used), c) Exceptable one (Graph (b) data is used).

division per millimeter is the best choice. Do not, for example, ever use 1/4 inch by 1/4 inch sketch paper or other such coarse scaled paper as graph paper. In some cases special graph paper like semilog or log-log graph paper may be required. Figure 4 (a) is a graph of the data for displacement versus time from Figure 4 Graph (a) for which the least squares fit was previously made (You can learn least squares fit method from related books). Figure 4(b) is the false one, do not connect data with each other. Figure 4(c) is the exceptable one, this graph is plotted by sense of proportion according to data and theoretical knowledge. Note that scales for each axis have been chosen, to spread the graph over a reasonable portion of the page. Also note that because the data have been assumed linear, a straight line has been drawn through the data points. The straight line is the one obtained from the least squares fit to the data. For most experiments, the variables will take on only positive values. For that case the scales should range from zero to greater than the largest value for any data point. For example, in Figure 4(a) the displacement is chosen to range from 0 to 30 meters because the largest displacement is 25.49, and the time scale has been chosen to range from 0 to 6 seconds because the largest time is 5.00 seconds. Also note that the scales should not be suppressed as a means to stretch out the graph. For example, if a set of data contains ordinates that range from 60 to 90, do not choose a scale that shows only that range. Instead a scale from 0 to 100 should be chosen, and there is nothing that can be done in that case to make the graph range over more than about 30% of the graph paper. Scales should always be chosen to increase to the right of the origin and to increase above the origin.

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Experiment 1 Electric Field & Electrostatic Potential in the Plate Capacitor 1

Purpose

To analyze the relationship between the electric field strength and the voltage (electric potential) where the plate spacing is held constant, to analyze the relationship between the electric field strength and the plate spacing where the voltage is held constant and to measure the potential as a function of the distance in the manner of the plate capacitor phenomenon.

1.1

Keywords

Partial derivative, Derivative operator, Charge, Charge density, Coulomb force, electric field, electrostatic potential energy, electrostatic potential.

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Theory

According to the Maxwell’s equations; ~ ~ ×E ~ ≡ − 1 ∂B ∇ (1) c ∂t ~ ≡ [Derviative operator], E ~ ≡ [Electric field vector], B ~ ≡ [Magnetic field vector] where ∇ and c ≡ [Speed of light]. For the electro-static case (in which the charges are steady) ~ ×E ~ ≡ ~0 ∇

(2)

~ ≡ F~ /q ≡ However, in terms of F~ ≡ [Coulomb Force] & q ≡ [A test charge], E [Electric field vector] ≡ [Coulomb force per unit charge]. Thus for the electrostatics case; ~ ~ × F~ ≡ ~0 ~ ×E ~ ≡ ~0 ⇒ ∇ ~ × F ≡ ~0 ⇒ ∇ ∇ (3) q which means that the Coulomb force is a conservative force at this point. Hence, the Coulomb force can be expressed as a derivative of a scalar (i.e. it can be derived from a scalar) s.t. ~ F~ ≡ −∇U (4) where the scalar U has to be in the unit of energy according to the dimensional analysis. (Here, this scalar ”U ” with the dimension of energy is nothing but the electrostatic potential energy difference). Then, dividing the both sides of the above equation by q; F~ −1 ~ F~ ~U ⇒E ~ ≡ −∇ ~U ≡ ∇U ⇒ ≡ −∇ (5) q q q q q ~ ≡ F~ /q ≡ [Electric field vector] again. Hence; where E ~ ≡ −∇φ ~ ~ ≡ −∇ ~U ⇒ E E q 9

(6)

where φ ≡ U/q ≡ [Electrostatic potential difference] ≡ [Electrostatic potential energy difference per unit cha [voltage] Thus, for two different reference points with coordinates a and b; Z b Z b ~ ~ Ed~x ≡ (−∇φ)d~ x (7) a

a

In this experiment, if it is assumed that one of the capacitor plates lies in the yz-plane in 3-dim. cartesian space and the other one is parallel to it, it can also be assumed that electric field is in the x-direction and uniform. Z b Z b Z b ~ ~ ⇒ Ed~x ≡ Edx ≡ (−∇φ)d~ x a a a Z b ⇒E dx ≡ −{φ(b) − φ(a)} ⇒ E(b − a) ≡ φ(a) − φ(b) ≡ φ a

⇒ Ed ≡ φ ⇒ E ≡ φ/d

(8)

where ”b − a ≡ d” is nothing but the distance between the parallel-plates and the ~ is ”φ(a) − φ(b) ≡ φ” is the potential difference between those plates and ”E ≡ |E|” the magnitude of the electric field vector.

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Apparatus 1. Two plates 2. Electric Field Magnitude Meter 3. Resistor 4. DC Power Supply (DC Voltage Source) 5. Two Digital Multimeters 6. Connecting Cables 7. Various Supporting Units

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Procedure

4.1

Relation Between the Magnitude of the Electric Field Eexp. (kV /m) & the Electric Potential φ(V )

1. Construct the experimental setup shown as in Fig.1. 2. Fix the separation of plates as 10 × 10−2 m. 3. Turn on the DC power supply and set the input voltage and current values 12V and 0.5A respectively. 4. Check the rotators of electric field magnitude meter and set the output of it to ”0” value adjusting the power supply and the knob-2 ”← 0 →” behind the electric field magnitude meter when there is no capacitor potential applied. 5. Set the capacitor voltage values to 50V, 80V, 100V, 120V, 150V respectively, determine the corresponding experimental value of the electric field magnitude Eexp. and record it on the Table-1 for each case. (Check the leds expressing the scaling of the electric field magnitude meter regularly during the measurements) 10

Figure 1: Experimental Setup

Table 1 Etheo. (kV /m)

Eexp. (kV /m)

φ(V ) 50 80 100 120 150

6. Turn off the DC power supply. 7. Calculating the theoretical values of the electric field magnitude Etheo. (kV /m) complete the Table-1 and determine the error percentages comparing Etheo. (kV /m) values with Eexp. (kV /m) values for each case. 8. Plot an Eexp. (kV /m) v.s. φ(V ) graph using the Table-1 and reach the distance ”d” between the plates by means of the graph. Determine the error percentage assuming that the measured value of the distance is correct.

4.2 Relation Between the Magnitude of the Electric Field Eexp. (kV /m) & the Distance d (m) 9. Set the plate distance to 2 × 10−2 m moving the plate which does not contain the electric field magnitude meter. 10. Adjust the electric field magnitude meter output to ”0” value using the knob-2 ”← 0 →” again. 11

11. Turn on the DC power supply and set the capacitor voltage (the voltage difference between the two plates of the capacitor) to 200V . 12. Determine the Eexp. (kV /m) and record it to the table-2. 13. Continue the same process for the plate distance values 4×10−2 m, 6×10−2 m, 8× 10−2 m, 10 × 10−2 m respectively.

Table 2 Etheo. (kV /m)

Eexp. (kV /m)

d (×10−2 m) 2 4 6 8 10

14. Turn off all the electronic devices and cut the power connections. 15. Calculating the theoretical values of the electric field magnitude Etheo. (kV /m) for each case complete the table-2. 16. Determine the error percentage of Eexp. (kV /m) only for the d = 8 × 10−2 m value. 17. Sketch an Eexp. (kV /m) v.s. d (m) graph and analyze the graph.

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Questions 1. What do you expect for the electric field in this experiment if the capacitor plates are completely in an ionized liquid (Liquid which is electrically conducting)? 2. Reach the magnitude of the Coulomb force which is felt by a test charge ”q” located at exactly the middle of the capacitor plates if the magnitude of the electric field is measured as 2 kV /m in this experiment. Prepared by : Onur GENC ¸.

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Experiment 2 Dielectric Constant of a Material 1

Purpose

To examine the relation between the charge ”Q” & the voltage ”φ” in the manner of plate capacitor, to determine the electric permittivity constant of the vacuum ”²0 ”, to examine the relation between the charge Q on the plate capacitor and the distance ”d” between the plates when the potential difference between the plates (voltage) ”φ” is constant, to examine the relation between the charge Q on the plate capacitor and the potential difference between the plates (voltage) when the distance d between the plates is constant.

1.1

Keywords

Charge, electric permittivity constant, Vacuum, Gauss Surface, directional area,

2

Theory

According to the Maxwell’s equations; ~E ~ ≡ ρ ∇ ² | {z 0} Differential form of the Gauss’ Law Z Z ρ ~ ~ ⇒ ∇EdV ≡ dV ; ²0

ρ ≡ [charge density (total charge over volume)] (1) dV ≡ [infinitesimal volume element]

However, according to the Divergence Theorem; I Z ~ S ~; ~ ≡ [infinitesimal surface element] ~ ~ dS ⇒ ∇EdV ≡ Ed Z ⇒

Z ~ EdV ~ ∇ ≡

I Q ~ S ~ ⇒ ≡ Ed ²0 | {z } Integral form of the Gauss’ Law

ρ dV ≡ ²0

(2)

(3)

I ~ S ~ Ed

(4)

Q ≡ [Total charge enclosed by the surface of magnitude S]

(5) As in the previous experiment, if it is assumed that one of the capacitor plates lies in the yz-plane in 3-dim. cartesian space and the other one is parallel to it, it can also be assumed that electric field is in the x-direction and uniform in this experiment too. Additionally, if it is also assumed that the area is right-handed and the Gaussian surface chosen around the capacitor plate from which the electric field is originated is cylinder of the same diameter with the capacitor plate in the manner of the symmetry of the problem; I Z ~ ~ ~ A ~ ⇒ EdS ≡ Ed (6) 13

~ is the infinitesimal area element, defining the surface of the mathematical where dA Gauss cylinder which is parallel to the electric field. Hence; Z Z Z I I ~ S ~ ≡ Ed ~ A ~ ≡ EdA ≡ E dA ≡ EA ≡ Ed ~ S ~ Ed I ~ S ~ ≡ Q ≡ EA ⇒ Ed ²0 where A is the magnitude of the area of the plate from which the electric field is originated. On the other hand, the relation among the Capacitance ”C” of the capacitor, voltage φ on the capacitor and the total charge Q accumulated on the capacitor plate for a capacitor for which there is vacuum between the plates is expressed as Q ≡ Cφ and Ed ≡ φ from the previous experiment, thus;

and

Q φ Q Qd ≡ EA ⇒ ≡ A ⇒ ²0 ≡ ²0 ²0 d φA

(7)

Q φ φ 1 ≡ EA ⇒ ≡ A ⇒ C ≡ ²0 A ²0 C²0 d d

(8)

However, the above equations are valid for the vacuum between the capacitor plates case. If there exists a dielectric material which is not vacuum between the capacitor plates, the voltage φ on the capacitor is reduced by the relative permittivity constant ²r ≡ ²/²0 , where ² ≡ [electric permittivity constant of the dielectric material], due to the electron polarization of the dielectric material s.t. φD ≡

φ ²r

(9)

where ”φD ” is the potential difference between the capacitor plates when there is a dielectric material between them. Thus the capacitance ”CD ” of the capacitor in the presence of the dielectric material in terms of the capacitance C when there is no dielectric material comparing with respect to the same amount of charge accumulated, is; Q Q CD ≡ ≡ ²r ≡ ²r C ≡ CD (10) φD φ Then for the case φ ≡ φD using the Q ≡ Cφ the charge relation is; QD CD φD CD φ QD ≡ ≡ ≡ ²r ≡ Q Cφ Cφ Q

(11)

where ”QD ” is the charge accumulated on the capacitor plate in the existence of the dielectric material and Q is the charge accumulated on the capacitor plate in the existence of the vacuum.

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Apparatus 1. Plate Capacitor 2. Plastic Plate 3. Universal Measuring Amplifier 14

4. High Voltage Supplier (0 kV - 10 kV ) 5. Digital Multimeter 6. Connecting Cables 7. Capacitor (0.22 µF )

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Procedure

4.1

Relation Between the Accumulated Charge ”Q” & the Capacitor Potential ”φc ”

1. Construct the experimental setup shown as in the figure below.

Figure 1: Experimental Setup

2. Fix the separation of plates as 0.95 × 10−2 m. 3. Turn the high voltage supply on and adjust the potential values to φc to 0.5kV , 1kV , 1.5kV , 2.0kV , 2.5kV , 3.0kV , 3.5kV , 4.0kV respectively, determine the corresponding voltage value φ using the multimeter and record it on the table-1 for each case. (Do not forget to discharge the capacitor of 0.22µF after each measurement)

Table 1 φc (kV) φ(V ) Q(C) ²0 (C/V m)

0.5

1.0

1.5

15

2.0

2.5

3.0

3.5

4.0

4. Turn off the high voltage supply. 5. Calculate the Q values benefiting from the relation Q ≡ Cφ and record on table-1 for each case. (Note: C = 0.22µF ) 6. Plot a Q v.s. φC graph using the table-1 and reach the ”²0 ” by means of the graph. Determine the error percentage assuming that the theoretical value ”²0theo. = 8.8542 × 10−12 C/V m” of the ²0 is correct. (Note:A = 0.0531m2 )

4.2 Relation Between the Accumulated Charge ”Q” & the Plate Distance ”d (m)” 7. Turn on the high voltage supply and set it to 1.5 kV . 8. Adjust the capacitor plate distance ”d” to 0.2 ×10−2 m, 0.3 ×10−2 m, 0.4 ×10−2 m, 0.5 ×10−2 m, 0.6 ×10−2 m, 0.7 ×10−2 m respectively, determine the corresponding voltage value φ using the multimeter and record it on the table-2 for each case. (Do not forget to discharge the capacitor of 0.22µF after each measurement)

Table 2 φ (kV ) d (×10−2 m) 1/d (1/(10−2 m)) Q (C) ²0 (C/V m)

9. Turn off the high voltage supply. 10. Calculate the Q values benefiting from the relation Q ≡ Cφ and record on table-1 for each case. (Note: C = 0.22µF ) 11. Plot a Q v.s. 1/d graph using the table-2 and reach the ”²0 ” by means of the graph again. Determine the error percentage assuming that the theoretical value ”²0theo. = 8.8542 × 10−12 C/V m” of the ²0 is correct. (Note:φc = 1.5kV & A = 0.0531m2 )

4.3 The Measurement of the Permittivity Constant of the Dielectric Material (Plastic Plate) 12. Place the plastic plate between the capacitor plates. 13. Fix the separation of plates as 0.95 × 10−2 m again. 14. Turn the high voltage supply on and adjust the potential values of φc to 0.5kV , 1kV , 1.5kV , 2.0kV , 2.5kV , 3.0kV , 3.5kV , 4.0kV respectively, determine the corresponding voltage value φD using the multimeter and record it on the table3 for each case. (Do not forget to discharge the capacitor of 0.22µF after each measurement) 16

Table 3 φc (kV ) φ (V ) QD (C) Q (C) QD /Q (QD /Q)average

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

15. Turn all the electronic devices off and cut all the connections. 16. Calculate the QD values using the relation QD ≡ Cφ and record on table-3 for each case. (Note: C = 0.22µF ) 17. Complete the Q (C) row benefiting from the table-1. 18. Calculate the QD /Q ratio for each case, determine an average (QD /Q)average value and reach the electric permittivity constant ²D of the plastic plate.

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Questions 1. In this experiment in some steps the vacuum equations are used. In this laboratory, is the existence of the vacuum possible? If it is, how? If it is not, explain the situation in terms of physical arguments. 2. If the voltage φ in the experiment is measured as 0.5kV what would it be if the ”plate thickness” increases to two times of its initial value? Prepared by : Onur GENC ¸.

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Experiment 3 Ohm’s Law 1

Purpose

1. To test the validity of Ohm’s law, to construct a circuit using resistors, wires and a breadboard from a circuit diagram and to construct series and parallel circuits.

1.1

Keywords

Ohm’s law, serial connection, parallel connection, current, electric potential.

2

Theory

One of the fundamental laws describing how electrical circuits behave is Ohm’s law. According to Ohm’s law, there is a linear relationship between the voltage drops across a circuit element and the current flowing through it. Therefore the resistance R is viewed as a constant independent of the voltage and the current. In equation form, Ohm’s law is: V = IR

(1)

Here V is the voltage applied across the circuit in volts (V ), I is the current flowing through the circuit in units of Amperes (A) and R is the resistance of the circuit with units of ohm (Ω). Equation (1) implies that, for a resistor with constant resistance, the current flowing through it is proportional to the voltage across it. If the voltage is held constant, then the current is inversely proportional to the resistance. If the voltage polarity is reversed, the same current flows but in the opposite direction. If Ohms law is valid, it can be used to define resistance as: V (2) I where R is a constant, independent of V and I. The current (I) is a measure of how many electrons are flowing past a given point during a set amount of time. The current flows because of the electric potential (V ) applied to a circuit. If one point of the circuit has a high electric potential, it means that it has a net positive charge and another point of the circuit with a low potential will have a net negative charge. Electrons in a wire flow from low electric potential with its net negative charge to high electric potential with its net positive charge because unlike charges attract and like charges repel. As these electrons flow through the wire, they are scattered by atoms in the wire. The resistance of the circuit is just that; it is a measure of how difficult it is for the electrons to flow in the presence of such scattering. Materials that have a low resistance are called conductors and materials that have a very high resistance are called insulators. Two or more resistors can be connected in series, connected one after another, or in parallel, typically shown connected so that they are parallel to one another. R=

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When two resistors R1 and R2 are connected in series, the equivalent resistance Rs is given by Rs = R1 + R2 . Thus the circuit in Figure 3.1 behaves as if it contained a single resistor with resistance Rs that is, it draws current from a given applied voltage like such a resistor. When those same resistors are connected in parallel instead, we use a different formula for finding the equivalent resistance.

Figure 1: Schematics of circuits illustrating resistors connected in series and in parallel

Table 1 Series Vs = V1 + V2 Is = I1 = I2 Rs = R1 + R2

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Parallel Vp = V1 = V2 Ip = I1 + I2 1 1 1 Rp = R1 + R2

Apparatus 1. DC power supply 2. Resistor connection board 3. Digital multimeter 4. Various resistors 5. Connecting cords

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Procedure

4.1

Part A

1. Adjust the power supply to 0 V. 2. Construct the circuit shown in figure 3.2. 3. Set the power supply to five different potential values and read off the voltage and current values from digital multimeters. Record your measurements in Table 3.2. 4. Plot V versus I graph with your data and find resistance value from slope of the graph.

19

Figure 2:

5. Calculate the error percentage of the resistor. 6. Repeat the experiment for two different resistors.

Table 2 R1 V

4.2

R2 I

V

R3 I

V

I

Part B

1. Construct the circuit shown in Figure 3.3. 2. Use two different resistors while constructing the circuit. 3. Set the power supply to five different potential values and read off the voltage and current values from digital multimeters. Record your measurements in Table 3.3. 4. Plot V versus I graph with your data and find the total resistance value from slope of the graph. 5. Calculate the error percentage of the total resistor. 6. Repeat the experiment for two different resistors.

Table 3 R1 and R2 V

R2 and R3 I

V

20

R1 and R3 I

V

I

Figure 3:

4.3

Part C

1. Construct the circuit shown in figure 3.4. 2. Use two different resistors while constructing the circuit. 3. Set the power supply to five different potential values and read off the voltage and current values from digital multimeters. Record your measurements in Table 3.4. 4. Plot V versus I graph with your data and find the total resistance value from slope of the graph. 5. Calculate the error percentage of the total resistor. 6. Repeat the experiment for two different resistors.

Figure 4:

Table 4 R1 and R2 V

R2 and R3 I

V

21

R1 and R3 I

V

I

5

Questions 1. What is the main difference between an ohmic and non-ohmic conductor? Give examples for ohmic and non-ohmic conductors. 2. The current flowing in a circuit containing three resistors connected in parallel is I = 1.0A (Figure 3.5). Find the current and voltage values of all the resistors (R1 = R2 = R3 = 15Ω).

Figure 5:

Prepared by ; S¸. G¨ok¸ce C ¸ ALIS¸KAN.

22

Experiment 4 Wheatstone Bridge 1

Purpose

To determine some unknown, connected in series and connected in parallel resistors’ resistance values by means of the Wheatstone Bridge, in the Kirchhoff’s Principles (relaying on the conservation of the charge and the energy) concept.

1.1

Keywords

Charge, electrical energy, voltage, Kirchhoff’s principles, Wheatstone bridge, resistivity.

2

Theory

For a Wheatstone Bridge circuit in the figure below;

Figure 1: Wheatstone bridge circuit when the circuit is at equilibrium (i.e. there is no current measurement in the galvanometer), it can be asserted according to physics principles that the potential difference (the voltage) between the points ”A” & ”B” equals to zero. Thus for the equilibrium case; I1 R1 ≡ I2 R2 & I3 R3 ≡ I4 R4 (1) However, according to Kirchhoff rule of incoming and outgoing current magnitudes sum up to zero at a point on a circuit, I1 ≡ I3 & I2 ≡ I4 for the equilibrium situation, hence from the above equations; I1 R1 I2 R2 R1 R2 ≡ ⇒ ≡ I1 R3 I2 R4 R3 R4

(2)

for the equilibrium case in Wheatstone Bridge. On the other hand, for a wire the resistance of the wire is expressed in terms of the resistivity of the wire ”ρ”, the

23

length of the wire ”L” and the cross-sectional area of the wire ”A” s.t. R≡ρ

3

L A

(3)

Apparatus 1. Power Supply 5 V 2. Resistor Connection Board 3. Various Resistors 4. Wire Resistor Board with Various Wires of Diameter and Material 5. Wire Length Changeable Bridge 6. Connecting Cables 7. Digital Multimeter (As Galvanometer)

4

Procedure

Construct the experimental setup shown as in the figure below.

Figure 2: Experimental Setup

4.1

Resistance Value of a Resistor

1. Connect a resistor of 10 Ω as an unknown resistor R3 and 5 Ω as the known resistor R1 to the circuit. 2. After checking all connections turn on the power supply. 3. Start to change the wire lengths ”l1 ” & ”l2 ” on the wire length changeable bridge until determining the equilibrium point (The point at which the current value is read as zero on the multimeter) and record the length values on table-1.

24

Table 1 l1 (×10−2 m)

l2 (×10−2 m)

R1 (Ω)

R3 (Ω)

4. Turn off the power supply and remove the 10Ω resistor (as R3 in this part) from the circuit. 5. Calculate the unknown resistance value ”R3 ” and calculate the error percentage assuming that its theoretical value 10Ω is correct.

4.2

Resistance of Wires

6. Connect one of the wires of the wire resistor board to the circuit as unknown resistor ”R3 ” and record the wire type and the diameter ”d” on that wire on table-1. 7. After checking all connections again turn on the power supply. 8. Start to change the wire lengths ”l1 ” & ”l2 ” on the wire length changeable bridge until determining the equilibrium point (The point at which the current value is read as zero on the multimeter) and record the length values on table-1. 9. Continue the process for all the remaining wires on the wire resistor board.

Table 2 Wire Type

d(×10−3 m)

l1 (×10−2 m)

l2 (×10−2 m)

R3 (Ω)

r(×10−3 m)

10. Turn off the power supply. 11. Calculate the resistance ”R3 ” values for each wire type, calculate the radius ”r” and ”1/r2 ” values for constantan wire and complete the table-1. 12. Calculate the resistivity ”ρ” of the brass wire and reach the error percentage assuming that the theoretical value of it ρ = 7.00 × 10−8 Ωm is correct. 13. Plot a R3 v.s. 1/r2 for the constantan wire and analyze the graph.

25

1/r2 ( 10−61 m2 )

5

Questions 1. If the diameter of a brass wire with a length L=1m increases to two times of its initial value what can you say about the resistance? (resistivity is constant) 2. A Wheatstone Bridge such as in Figure 1 has a V = 10V . With R1 = 5.00Ω and the unknown resistor R3 at room temperature, the bridge is balanced with L1 = 34.0cm and L2 = 66.0cm. What is the value of R3 ?

Prepared by ; S¸. G¨ok¸ce C ¸ ALIS¸KAN.

26

Experiment 5 Magnetic Field of Single Coils / Biot-Savart’s Law 1

Purpose 1. To measure the magnetic flux density in the middle of various wire loops with the Hall probe and to investigate its dependence on the radius and number of turns. 2. To determine the magnetic field constant µ0 . 3. To measure the magnetic flux density along the axis of long coils and compare it with theoretical values.

2

Theory

The Biot-Savart law is an equation describing the magnetic field (B) generated by an electric current (I). It gives the magnetic field due to an infinitesimal length of current; the total field can then be found by integrating over the total length of all currents: − → µ0 I d~l × rˆ dB = 4π r2

or

− → µ0 I d~l × ~r dB = 4π r3

(1)

Figure 1: Drawing for the calculation of magnetic field along the axis of a wire loop Here rˆ is a unit vector that points from the position of the charge to the point at which the field is evaluated. r is the distance between the charge and the point at which the field is evaluated. µ0 = 1.2566 × 10−6 H/m is the permeability of free ~ is perpendicular to the direction of both I and rˆ by right space. The direction of B hand rule. The vector d~l is perpendicular to ~r so that : ~ = dB

µ0 I d~l 4π r2

27

(2)

and from the drawing, it can be written as : µ0 I d~l (3) 4π R2 + z 2 ~ can be resolved into a radial dB ~ r and an axial dB ~ z components. The dB ~z dB ~ components have the same direction for all conductor elements dl and the quantities ~ r components cancel one another out, in pairs. Therefore are added; the dB ~ = dB

Br (z) = 0

(4)

and I Bz (z) = B(z) = Because of cosθ =

dBcosθ =

µ0 I 4π

I

cosθdl R2 + z 2

(5)

µ0 IR2 2(R2 + z 2 )3/2

(6)

R R2 +z 2

µ0 IR B(z) = 4π(R2 + z 2 )3/2

I dl =

If there is a small number of small number of identical loops close together, the magnetic field is obtained by multiplying by the number of turns (n). i) At the center of loop (z=0) we obtain: µ0 nI (7) 2R ii) To calculate the magnetic field of a uniformly wound coil of length l and N turns, we multiply the magnetic field of one loop by the density of turns (N/l) and integrate over the coil length. B(0) =

Figure 2:

28

dB =

µ0 IR2 N dz 3/2 2 2 l 2(R + z )

(8)

x = R tan φ and dx = R sec2 φdφ. After a little calculation we obtain µ0 IN dB = 2l

Z

φ2

cos φdφ

(9)

φ1

Then µ0 IN µ0 IN B(z) = (sin φ2 − sin φ1 ) = 2l 2l

µ

b a √ −√ R2 + a2 R 2 + b2

¶ (10)

here a = z + l/2 and b = z − l/2. At the center of the coil (z = 0): µ0 IN B(0) = 2l

3

µ

R2 1 + l2 4

¶−1/2 (11)

Apparatus 1. Teslameter 2. Hall probe 3. Induction coils 4. Universal constanter 5. Multimeter 6. Conduction loops

4

Procedure

ATTENTION: Coil current is 0.5 A, so never touch the circuit unless the constanter is totally off ! Part A : Magnetic Field of Coil 1. Set up the experiment as shown in Figure 3. 2. Turn on the teslameter and adjust the zero point. 3. Operate the power supply at 18 V and 0.5 A. 4. Measure the magnetic field at different positions within the coils and record the results in the tables. 5. Measure the length of each coil and write to the related part on tables. (Φ is the diameter of coil) 6. Calculate the magnetic fields in the middle of different coils using equation 11 and compare with the experimental values. 29

Table 1: For 300 turns and Φ = 33mm , l=......mm z distance (cm)

0 (center)

B (mT)

Table 2: For 200 turns and Φ = 41mm , l=......mm z distance (cm)

B (mT)

0 (center)

Table 3: For 150 turns and Φ = 26mm , l=......mm z distance (cm)

B (mT)

0 (center)

7. Calculate the percentage error for magnetic field in the middle of the coils. 8. Plot the curve of magnetic field along the axis of coil for N=150.

Figure 3: Experimental set-up

Part B : Magnetic Field of Loop ATTENTION: Loop current is 5 A, so never touch the circuit unless the constanter is totally off ! 1. Set up the circuit in Figure 3. 2. Turn on the teslameter and adjust the zero point. 3. Operate the power supply at 18V and 5A. 4. Measure the magnetic field at the center of the single conductor loops with different diameters and record the results in the Table 4. 5. Plot the magnetic field at the center of single turn, as a function of the radius. 6. Measure the magnetic field at the center of the loops using the loops with a 6 cm radius and different numbers of turn. Record the data in the Table 5. 30

Table 4: For single loops Radius (cm)

Table 5: For radius r = 6cm. Number of turns 1 2 3

B (mT)

B (mT)

7. Plot the magnetic field at the center of the loops with n turns as a function of the number of turns. 8. Calculate the magnetic field constant µ0 using one of the graphs plotted for loops and find the percentage error.

5

Questions 1. In the figure below, point P2 is at perpendicular distance R=25.1 cm from one end of straight wire of length L=13.6 cm carrying current i=0.693 A. (Note that the wire is not long.) What is the magnitude of the magnetic field at P2 ?

2. A solenoid 1.30 m long and 2.60 cm in diameter carries a current of 18.0 A. The magnetic field inside the solenoid is 23.0 mT. Find the length of the wire forming the solenoid. 3. The figure below shows an arrangement known as a Helmholtz coil. It consist of two circular coaxial coils, each of 200 turns and radius R=25.0 cm, separated by a distance s=R. The two coils carry equal currents i=12.2 mA in the same direction. Find the magnitude of the net magnetic field at P, midway between the coils.

6

References 1. Phywe Physics Laboratory Manual

31

Experiment 6 Magnetic Induction 1

Purpose

Measuring the induction voltage as a function of : • the current in the field coil at a constant frequency, • the frequency of the magnetic field at a constant current, • the number of turns of the induction coil at constant frequency and current, • the cross-sectional area of the induction coil at constant frequency and current.

2

Theory

The basic physics phenomenon studied in this lab is the Faraday’s Law, which is the discovery of Faraday and Henry that a changing magnetic flux induces an electromotive force (emf) and thus a current in a conductor as follows : Z d dΦ ~ A ~ =− Bd (1) Uind = − dt dt Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be induced in the coil. The negative sign, which is also denoted as Lenz law, describes the tendency R of the system to oppose the change in magnetic flux. ~ A ~ so We know that Φ = B Bd Uind

d dΦ =− =− dt dt

Z ~ A ~ Bd

(2)

For n parallel conductor loops the equation can be written as : dΦ (3) dt The induced emf in a coil is equal to the negative of the rate of change of magnetic flux times the number of turns in the coil. On the other hand Ampere equation which states that in a conductor a current generates a magnetic field of which the closed field lines around the currents : I ~ · d~s = µI B (4) Uind = −n

There µ is the magnetic conductivity (a material’s constant). We consider the magH ~ d~s = Bl = µI. (There l is netic flux density in a long coil is constant, so that B the length of the coil which must be significant higher than the diameter. In air µ V ·s can be approximated by the magnetic constant µ0 = 1.26 · 10−6 A·m .) Also it can be R ~ ~ ~ written as Φ = B dA = B A. 32

~ can be approximated by the For a long coil with N turns, the absolute value of B following equation : I (5) l If an alternating current I(t) = I0 · sin wt with a frequency f = ω/2π flows through the field coil, then from equation 5, the field density in the field coil is a function of time and alternates in phase with current. B = Nµ

B(t) =

Nµ · I0 sin(2πf t) l

(6)

From equation 3, dB(t) Nµ = −nA2πf I0 cos(2πf t) (7) dt l where n is the induction coil’s number of turns and A its cross-sectional area. The induced voltage alternates with same frequency as the current but is phase-shifted by π/2. Uind = −nA

3

Apparatus 1. Field coil (750mm, 485turns/m) 2. Induction coils 3. Function generator 4. Multimeter 5. Connecting cords

4

Procedure

ATTENTION: The effect of frequency should be studied between 1 kHz and 12 kHz, since below 0.5 kHz the coil practically represents a short circuit and above 12 kHz the accuracy of the measuring instruments is not guaranteed. Part A : Measuring the induction voltage as a function of current in the field coil and calculation of magnetic constant µ 1. Set up the experiment as shown in Figure 1. 2. Tune the current in the field coil by turning up the amplitude of the sinus signal of the digital frequency generator. 3. Start with an amplitude of 0.5 V and increase to a maximum of 10 V in steps of 0.5 V. 4. Record current and induced voltage datas in Table 1 for f=10 kHz and secondary coil with n=300 turns and d = 41mm. 5. In order to vary the magnetic field, the current in the field coil has to be altered.

33

6. To calculate µ0 , we consider relation 7. The time dependence can be disregarded, if we always measure current and voltage in intervals of one period T = 1/f 7. Plot a graph Uind versus I0 and obtain magnetic constant by the help of equation 8. (The magnetic field constant is included in the slope s of the induced voltage’s linear dependence of the current. Uind = s(t) · I0 )

Uind = −nA2πf

Nµ I0 l

(8)

Figure 1: Experimental set-up for magnetic induction

Part B : Measuring the induction voltage as a function of frequency of magnetic field at constant current. 1. Choose the current in the field coil between 20 mA and 40 mA. 2. The effect of frequency should be studied between 1 kHz and 10 kHz, since below 0.5 kHz the coil practically represents a short circuit and above 12 kHz the accuracy cannot be guaranteed. 3. Increase the frequency in steps of 0.5 kHz and record datas in Table 2. 4. In order to maintain a constant current in the field coil for various frequencies, you have to adjust amplitude very accurately for each frequency. 5. Plot a graph Uind versus f, calculate the slope of the graph (Uind = s · f ) and compare it with theoretical value of s (theoretical value of s will be calculated from equation 8.)

Part C : Measuring the induction voltage as a function of the number of turns of the induction coil at constant frequency and current.

34

Table 1: f=10 kHz and secondary coil with n=300 turns and d = 41mm Amplitude (V) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 10.0

Current (A)

Table 2: I0 = 25 mA and secondary coil with n=300 turns and d = 41mm

Uind (V)

Table 3: For fixed I0 and d = 41mm n 300 200 100

Uind (V)

Frequency (kHz) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 10.0

Current (A)

Table 4: For fixed I0 and n = 300 d (mm)

I0 (A)

Uind (V)

I0 (A)

1. Choose signal-amplitude for f=10 kHz (fixed I0 ) and maintain these settings throughout the measurements. 2. Note down the induced voltage and diameter (d) for given number of turns on Table 3. 3. Plot a graph Uind versus n. Part D : Measuring the induction voltage as a function of the crosssectional area of the induction coil at constant frequency and current. 1. Choose signal-amplitude for f=10 kHz (fixed I0 ) and maintain these settings throughout the measurements. 2. Note down the induced voltage for given diameter (d) on Table 4. 3. Plot a graph Uind versus A. 35

Uind (V)

4. The cross-sectional area is the circular area enclosed by coil: µ ¶2 d A=π 2

5

(9)

Questions 1. A flat loop of wire consisting of a single turn of cross-sectional area 8 cm2 is perpendicular to a magnetic field that increases uniformly in magnitude from 0.5 T to 2.5 T in 1 s. What is the resulting induced current if the loop has a resistance of 2 Ω. 2. A 30 turn circular coil of radius 4 cm and resistance 1 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.0100t+0.0400t2 , where B is in teslas and t is in seconds. Calculate the induced emf in the coil at t=5 s.

6

References 1. Phywe Physics Laboratory Manual

36

Experiment 7 Transformer 1

Keywords

Faraday’s law, Magnetic flux, AC voltage, Transformer.

2

Purpose

The secondary voltage on the open circuited transformer is determined as a function 1. of the number of turns in the primary coil, 2. of the number of turns in the secondary coil, 3. of the primary voltage. The short-circuit current on the secondary side is determined as a function 1. of the number of turns in the primary coil, 2. of the number of turns in the secondary coil, 3. of the primary current. With the transformer loaded, the primary current is determined as a function 1. of the secondary current, 2. of the number of turns in the secondary coil, 3. of the number of turns in the primary coil.

3

Theory

This theoretical part is written by the help of the book “Physics Principles with Applications” (Douglas C. Giancoli). Principle: An alternating voltage is applied to one of two coils (primary coil) which are located on a common iron core. The voltage induced in the second coil (secondary coil) and the current flowing in it are investigated as functions of the number of turns in the coils and of the current flowing in the primary coil. A transformer is a device for increasing or decreasing an ac voltage. A transformer consists of two coils of wire, known as the primary and secondary coils. The two coils can be interwoven; or they can be linked by a soft iron core (laminated to prevent eddy current loses). The idea in either case is that the magnetic flux produced by a current in the primary should pass through the secondary coil. When an ac voltage is applied to the primary, the changing magnetic field it produces will include an ac voltage of the same frequency in the secondary. However, the voltage will be different

37

according to the number of loops in each coil. From Faradays law the induced voltage in the secondary is Us = −Ns

dφ dt

(1)

where Ns is the number of turns in the secondary coil, and dφ dt is the rate at which the magnetic flux changes. The input primary voltage, Up , is also related to the rate at which the flux changes; dφ (2) dt where Np is the number of turns in the primary coil. We have assumed there are no losses so that all the flux produced in the primary reaches the secondary. We divide these two equations to find Up = −Np

Up Ns = Us Np

(3)

This transformer equation tells how the secondary (output) voltage is related to the primary (input) voltage. Although voltage can be increased (or decreased) with a transformer, we dont get something for nothing. Energy conservation tells us that the power output can be no greater than the power input. A well-designed transformer can be greater than 99 percent efficient, so little energy is lost to heat. The power input thus essentially equals the power output; since power P = U I, we have Up Ip = Us Is

4

or

(Is /Ip ) = (Np /Ns )

(4)

Apparatus 1. Multitab transformer 2. Coils (140 turns, 6 tappings) 3. Iron cores 4. Rheostat 5. Digital multimeters 6. Clamping device 7. Connecting cords

5

Procedure 1. Set up the experimental system as shown in Figure 1. 2. The multi-range meters should be connected as shown in Figure 2, while the voltmeter can be used through a double-pole two-way switch for the primary and secondary circuit. The iron yoke should be opened only when the supply is switched off, as otherwise excessive currents would flow. 38

Figure 1: Experimental set-up for investigating the laws governing the transformer.

Figure 2: Connection of the multi-range meters.

3. When loading the rheostat, the maximum permissible load of 6.2 A for 8 minutes must not be exceeded. 4. At constant supply voltage, the primary current is adjusted using the rheostat in the primary circuit, with the secondary short-circuited. When the transformer is loaded, the rheostat is used as the load resistor in the secondary circuit.

5.1

Part 1:

1. Measure the secondary voltage for same turns (Np = Ns = 140) and record the data in Table 1.

39

2. Draw graph of secondary voltage on the unloaded transformer as a function of the primary voltage. 3. Make a comment for your graph.

5.2

Part 2:

1. Fixed the primary voltage at 15 V (Up =15V) and turns N at 140 (Np =140). 2. Measure the secondary voltage for given Ns turns in Table 2. 3. Fixed Ns =140 and alter Np like table and measure secondary voltage. 4. Plot a graph for U versus N . Make a comment for your graph.

5.3

Part 3:

1. Similar with Part 1 for same turns measue the secondary current for values in table (Np = Ns =140).. 2. Plot a graph for Ip versus Is . Make a comment for your graph.

5.4

Part 4:

1. Similar with Part 2 fixed the current (Ip =2A) for primary. 2. For alternating Ns and fixed Np =140, measure the secondary current. 3. For alternating Np and fixed Ns =140, measure the secondary current. 4. Plot a graph for Is versus N . Make a comment for your graph.

Table 1: Determination of secondary voltage for same turns Up (V) 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Us (V)

Table 2: Determination of secondary voltage for various turns Ns (Np = 140) 14 42 84 112 140

Us (V)

Np (Ns = 140) 42 84 112 140

40

Us (V)

Table 3: Determination of secondary current for same turns Ip (V) 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Is (V)

Table 4: Determination of secondary current for various turns Ns (Np = 140) 14 42 84 112 140

6

Is (A)

Np (Ns = 140) 42 84 112 140

Is (A)

Questions 1. What is a transformer? How does a transformer work? (Hint: what is the main physical principle? think it!) 2. A transformer for a transistor radio reduces 120 V ac to 9 V ac (Such a device also contains diodes to change the 9 V ac to dc). The secondary contains 30 turns and the radio draws 400 mA. Calculate (a) the number of turns in the primary, (b) the current in the primary, and (c) the power transformed. 3. Transformer operates only on ac. However, if a dc voltage is applied to the primary there will be an induced current in the secondary. How is it possible? Explain it with physical laws.

7

References 1. Douglas C. Giancoli, Physics Principles with Applications, Prentice-Hall, INC. Englewood Cliffs, New Jersey 07632. 2. PHYWE, Physics University Experiments, 2013.

41