Champlain - St. Lawrence
Physics 203-NYB-05
Electricity & Magnetism
Laboratory Manual
Winter 2014
Instructors
S.D. Manoli, Office #354
Stéphanie Plante, Office #342
Gwendoline Simon, Office #267
Champlain-St. Lawrence Physics 203-NYB-05
Winter 2014 Electricity & Magnetism
Table of Contents
Laboratory Program 5
I. Introduction 5
II. Laboratory Teams 5
III. Laboratory Reports 5
IV. Laboratory Rules 5
V. Timetable 5
VI. Evaluation 6
Laboratory Exercise #1 7
Voltage, Current, Resistance and Ohm’s Law 7
I. Introduction 7
II. Simple Circuits 7
III. Equivalent Resistance 8
IV. The Report 8
Laboratory Exercise #2 9
Multi-loop Circuits 9
I. Introduction 9
II. Multi-loop Circuits 9
Part A. Circuit #1 9
Part B. Circuit #2 9
III. Kirchhoff’s Voltage and Current Rules & Maxwell’s Loop Method 10
IV. The Report 10
Laboratory Exercise #3 11
Measurement of the Electric Constant 11
I. Introduction 11
II. The Experiment 11
Preliminary Setup 12
Measurements and Calculations 12
III. The Report 12
Laboratory Exercise #4 13
Introduction to the Oscilloscope 13
I. Introduction 13
II. Measurement of an AC signal 14
III. The Oscilloscope 14
IV. The TDS-210/220 Digital Real-time Oscilloscope 14
The Probes 15
The Trigger Control 15
Channel Controls 15
Vertical Controls 16
Horizontal Controls 16
Menu and Control buttons 16
The Display Area 18
V. Measurements 18
Using Autoset 18
Automatic Measurements (one channel) 18
Using Cursors 19
Measurements from Two Signals 19
VI. Challenge Circuit 20
Laboratory Exercise #5 21
RC Time Constant 21
I. Introduction 21
II. The Experiment 22
III. The Report 22
Laboratory Exercise #6 23
The High-Pass Filter 23
I. Introduction 23
II. The High-Pass filter 23
III. Report 24
Laboratory Exercise #7 25
Faraday’s Law 25
I. Introduction 25
II. The Experiment 25
III. The Report 26
Laboratory Exercise #8 27
Ampere’s Law 27
I. Introduction 27
II. The Experiments 27
Part A 27
Part B 27
III. The Report 28
Laboratory Exercise #9 29
The Charge to Mass Ratio of the Electron 29
I. Introduction 29
II. The Experiment 29
Measurements and Calculations 30
III. The Report 30
Appendix I 31
Use of Matrices in Excel 31
I. Calculating the inverse of a matrix 31
II. Multiplying matrices 31
Appendix II 33
Uncertainties 33
I. Summary by Examples 33
1. Uncertainty. 33
2. Scientific Notation. 33
3. Calculations based on measurements. 33
4. The uncertainty of an average value. 33
5. Fitting a straight line to a set of data points. 34
II. Further Reading 34
Laboratory Manual Page 4 of 34
Champlain-St. Lawrence Physics 203-NYB-05
Winter 2014 Electricity & Magnetism
Laboratory Program
I. Introduction
In this laboratory component of the Electricity and Magnetism Physics course, students will investigate experimentally some of the phenomena studied in class as well as some applications such as linear DC and AC circuits. In order to do so, students will be required to use the skills they have acquired in previous science courses. These include, but are not limited to, recording measurements and their uncertainties, calculating quantities from these measurements; the use of Excel for data analysis, written and/or oral communications of scientific procedures, results, discussions and conclusions.
II. Laboratory Teams
Laboratory work will be carried out by teams of two or three students. The instructor will inform students of the make-up of each team. Each team member will be responsible for all the material that is submitted by the team, therefore every student must demonstrate that he/she is well-prepared and must contribute to carrying out the experiment and writing the report. The instructor reserves the right to deduct marks from individuals who are not well prepared for the labs, skip all or part of a lab session and/or do not contribute adequately to the work of the team
Individual students are encouraged to keep a laboratory notebook (Cahier Canada or a hard-cover notebook) in which all the pertinent information is written down about each experiment.
III. Laboratory Reports
For some experiments, students will be required to hand in a lab report. Students will be informed of the content and structure of the laboratory reports by their instructor. Lab reports must be stapled and printed (or handwritten in ink) single-sided. Students may hand in their lab reports by email. The only caveat is that the instructor will simply open the document, print it and staple the pages together. The instructor will not reformat the document. The pages must be numbered and all tables, graphs, diagrams, equations and so on must be properly spaced, labeled, in the proper order and so on.
All work must be handed in by the due date at the beginning of the lab session. The instructor will inform students of penalties for handing in late work. If students believe that they have a valid reason for handing in work late, they must make special arrangements with the instructor before the due date. (‘The printer does not work’ is NOT a valid reason.)
IV. Laboratory Rules
Attendance in the laboratory is mandatory. Students who do not come to the lab will be given zero automatically. In the case of multi-week experiments, students will get zero if they skip even one of the lab sessions.
Students are not permitted to leave the lab before the end of the laboratory without the instructor’s permission.
V. Timetable
A complete schedule of the activities for the semester is given in the following table. The last column gives the week in which work must be handed in.
Week of / Topic / DueJan. 13 / No Lab
Jan. 20 / DC Circuits – Simple Circuits
Jan. 27 / DC Circuits – Multi-loop Circuits I / Simple Circuits
Feb. 3 / DC Circuits – Multi-loop Circuits II
Feb. 10 / Measurement of the Electric Constant / Multi-loop Circuits
Feb. 17 / DC Circuits – Lab Test
Feb. 24 / Introduction to the Oscilloscope / Measurement of eo
Mar. 3 / No Lab
Mar. 10 / RC Circuits – Time constant
Mar. 17 / RC Circuits – AC – High-Pass Filter / RC Circuits – Time constant
Mar. 24 / RC Circuits – Lab Test
Mar. 31 / Magnetism and Induction (week 1)
Apr. 7 / Magnetism and Induction (week 2)
Apr. 14 / Magnetism and Induction (week 3)
Apr. 21 / No Lab Easter / Magnetism Labs
May 2 / No Lab
The relevant documents will be placed on the Physics webpage at http://web2.slc.qc.ca/physics/ in a file called Complete Lab Manual. It is the responsibility of each student to obtain these documents and familiarize themselves with the appropriate content at the appropriate time.
VI. Evaluation
Students will be evaluated as shown in the following table:
Mid-term mark / Final MarkDC Circuits Part 1 / 30% / 10%
DC Circuits Part 2 / 30% / 10%
DC Circuits Lab Test / 40% / 15%
Electric Constant / 10%
RC Time Constant / 10%
RC Lab test / 15%
Magnetism and Induction (3 parts) / 30%
The instructor will inform students of any changes to the evaluation scheme shown above. A portion of the mark assigned for each lab report will be reserved for the quality of English.
Laboratory Program Page 6 of 34
Champlain-St. Lawrence Physics 203-NYB-05
Winter 2014 Electricity & Magnetism
Laboratory Exercise #1
Voltage, Current, Resistance and Ohm’s Law
I. Introduction
This laboratory exercise is an introduction to some of the basic quantities which characterize simple circuits such as current, resistance and voltage, and the experimental techniques used to measure them.
In this lab, students will verify that Ohm's Law,
where V is the voltage drop across a resistor R and i is the current flowing through it. In addition, Kirchhoff's voltage and current rules will be verified. The voltage rule states that the sum of the voltages around any closed loop in any circuit must be zero. The current rule states that the sum of the currents entering a junction point in a circuit must be equal to the sum of the currents leaving that junction. For reference, see chapter 26 of the textbook.
II. Simple Circuits
Your instructor will show you how to operate the voltmeter and the breadboard. Note that:
· To measure voltage, the voltmeter must be connected in parallel.
· To measure current, the ammeter must be connected in series.
· To measure resistance, the resistor must be removed from the circuit.
For each of the circuits shown below:
where Vs is the electromotive force, the emf, or the voltage supplied by the power supply.
· Measure the current coming out of the power supply.
· Measure the current flowing through each resistor.
· Measure the voltage across the power supply.
· Measure the voltage across each resistor.
· Measure the resistance of each resistor using the ohmmeter.
Verify that:
· Ohm's Law is satisfied across each resistor.
· The voltage rule is valid.
· The current rule is valid.
III. Equivalent Resistance
Any circuit, no matter how complex, can be represented schematically by the circuit diagram on the right where Requiv. = Vs/itotal. For each of the circuits of part II,
· Calculate Requiv. from the experimental measurements of V and itotal.
· Find a relationship between Requiv and the values of the resistors that were used to construct the circuit.
· Using only Vs and the values of the resistances, calculate the values of the currents flowing through each resistor theoretically.
Can you formulate general rules for the calculation of Requiv for configurations of resistors in a circuit? For help, consult the textbook.
IV. The Report
For each circuit,
· Submit a circuit diagram giving the values of the resistors as well as the voltage from the power supply.
· In ONE APPROPRIATE table, give the values of the measured voltages across the resistors, the measured currents flowing through them and the theoretical values of the currents flowing through them.
· Give the measured and theoretical values of Requiv. For the latter, show the calculation.
Include a short conclusion.
Laboratory Exercise #1: Voltage, Current, Resistance and Ohm’s Law Page 8 of 34
Champlain-St. Lawrence Physics 203-NYB-05
Winter 2014 Electricity & Magnetism
Laboratory Exercise #2
Multi-loop Circuits
I. Introduction
Using the techniques for measuring current, voltage and resistance as well as Kirchhoff’s voltage and current rules, complex circuits can be analyzed and designed. The purpose of this exercise is to be able to predict the current flowing through and the voltage across all resistors in a given circuit. This can be done using the concept of equivalent resistance. For resistors in series,
for N resistors in series, remembering that resistors in series are defined as those which have the same current flowing through them. For resistors in parallel,
for N resistors in parallel, remembering that resistors in parallel are defined as those which have the same voltage across them.
However, in some cases, the configuration of resistors does not lend itself to analysis using the concept of resistors in series or in parallel. In this case, Maxwell’s loop method can be used to predict the current flowing through, and hence the voltage across, each resistor.
II. Multi-loop Circuits
Part A. Circuit #1
Build the circuit shown on the right:
· Measure the resistance of each resistor using the ohmmeter.
· Measure the voltage across the power supply.
· Measure the current flowing through each resistor.
· Measure the voltage across each resistor.
· Calculate the equivalent resistance of the circuit.
Using the measured values of the resistance of each resistor:
· Calculate the theoretical equivalent resistance of the circuit.
· Calculate the current flowing through R1.
· Calculate the voltage across R2 and R3.
· Calculate the currents through R2 and R3.
· Compare the measured and theoretical values. Do they agree?
Part B. Circuit #2
Build the circuit shown on the right:
· Measure the resistance of each resistor using the ohmmeter.
· Measure the voltage across the power supply.
· Measure the current flowing through each resistor.
· Measure the voltage across each resistor.
· Derive the loop equations using Maxwell’s loop method, see below.
· Solve the equations using Excel.
· Calculate the current flowing through each resistor.
· Calculate the voltage across each resistor.
· Compare the measured and calculated values. Do they agree?
· Is it possible to calculate an equivalent resistance for this circuit? Can you derive a measured equivalent resistance for this circuit? (see previous laboratory exercise)
III. Kirchhoff’s Voltage and Current Rules & Maxwell’s Loop Method
Any multi-loop circuit can be analyzed using Kirchhoff’s voltage and current rules. Given a set of resistors arranged in a certain configuration and an input voltage, it is possible to predict the current that will flow through each of the resistors and hence the voltage across each resistor even if it is not possible to calculate equivalent resistances. This usually involves solving N equations in N unknowns where N is usually greater than 2. In this part of the lab exercise, you will be shown how to derive such equations from Kirchhoff’s voltage and current rules and how to solve them using Excel. You will apply this method in order to solve for the currents flowing through circuits 1 and 2 described previously. You will use the same values of R and the input voltage that you have measured previously.
Another such technique is called Maxwell’s loop method and it is described here. For a given multi-loop circuit:
· For every closed loop in the circuit, select a hypothetical current. Make sure that all the hypothetical currents flow in the same sense, clockwise or counterclockwise. Every resistor should have at least one hypothetical current flowing through it.
· For each closed loop, apply Kirchhoff’s voltage rule. When using Ohm’s Law, ensure that the net current through each resistor is used.
· There should be N equations in N unknowns, where N is the number of hypothetical currents.
· Reorganize these equations in terms of the N unknowns.
· Express these equations in matrix form.
· Enter these matrices in Excel and solve. Your instructor will show you how to enter matrices in Excel and how to perform the necessary calculations, see Appendix I.