Name Matriculation Number Date

Name of Lab Partner(s) Group Submission Deadline

Name of Demonstrator(s)

Reminders• Before leaving the laboratory, make sure the demonstrator on duty initial on your data

table(s) together with the date!

• Submit a complete laboratory report of yours, i.e., laboratory worksheet together withExcel spreadsheet(s) within ONE week after your laboratory session to level 1 Physicslaboratory (S12-04-02) before 5.00 pm daily (see the above submission deadline). Inthe event that the above submission deadline falls on a public/school holiday or youhave a medical certificate due to illness, the submission deadline will be the next schoolday during office hours (9 am – 5 pm).

RC Circuits

Part A: Basic Operations of Oscilloscope

1A. TIME/DIV =1A. VOLTS/DIV =

1B. TIME/DIV =1B. VOLTS/DIV =

1C. TIME/DIV =1C. VOLTS/DIV =

Demonstrator’s signature / Date

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2A. TIME/DIV =2A. VOLTS/DIV =

2B. TIME/DIV =2B. VOLTS/DIV =

2C. TIME/DIV =2C. VOLTS/DIV =

Demonstrator’s signature / Date

Question A-1 In the grid labeled 2A, how many complete cycles are sketched in your fig-ure? From your sketch, what is the period of the wave? Using this period, calculate thefrequency of the wave for this sketch. Is it in agreement with the frequency used for this partof the experiment

3A. TIME/DIV =3A. VOLTS/DIV =

3B. TIME/DIV =3B. VOLTS/DIV =

Demonstrator’s signature / Date

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Question A-2 In your own words, explain why these two sketches in 3A and 3B appear asthey do. They both have the trigger level zero, but one has a positive trigger slope and theother has a negative trigger slope.

4A. TIME/DIV =4A. VOLTS/DIV =

4B. TIME/DIV =4B. VOLTS/DIV =

4C. TIME/DIV =4C. VOLTS/DIV =

Demonstrator’s signature / Date

Question A-3 Explain the appearance of sketches 4A, 4B and 4C. They all have a positivetrigger slope, but the trigger level of 4A is zero, the trigger level of 4B is positive and thetrigger level of 4C is negative.

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Generator (V) Voltmeter (V) Oscilloscope (V)

1.00

2.00

3.00

4.00

Data Table 1: Sine wave.

Demonstrator’s signature / Date

Analysis A-1 For your data in Data Table 1, perform a linear least squares fit to your datawith the peak voltage read on the oscilloscope as the vertical axis and the voltage read on thevoltmeter as the horizontal axis. Plot a graph of the peak voltage read on the oscilloscopeagainst the voltage read on the voltmeter. Also show on the graph the straight line that wasobtained by the linear least squares fit to the data as well as the error-bar of your data.

Gradient: ± (units)

y-intercept: ± (units)

Coefficient of determination:

Question A-4 For a sine wave, an alternating current voltmeter measures a root-mean-square value. Show that the peak value measured on the oscilloscope should be 1.414 timesthe voltmeter readings for the sine wave.

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Analysis A-2 Use percentage discrepancy to compare your experimental value for the ratio(root-mean-square value : peak value) for the sine wave with the theoretical value. Show yourwork.

% discrepancy = %

Generator (V) Voltmeter (V) Oscilloscope (V)

1.00

2.00

3.00

4.00

Data Table 2: Square wave.

Demonstrator’s signature / Date

Analysis A-3 For your data in Data Table 2, perform a linear least squares fit to your datawith the voltage as read on the voltmeter as the vertical axis and the peak voltage read on theoscilloscope as the horizontal axis. Plot a graph of the voltage as read on the voltmeter againstthe peak voltage read on the oscilloscope. Also show on the graph the straight line that wasobtained by the linear least squares fit to the data as well as the error-bar of your data.

Gradient: ± (units)y-intercept: ± (units)Correlation coefficient:

Question A-5 Determine the relationship between the root-mean-square and peak values forthe square wave. Show your work.

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Analysis A-4 Use percentage discrepancy to compare your experimental value for the ratio(root-mean-square value : peak value) for the sine wave with the theoretical value. Show yourwork.

% discrepancy = %

Part B: The RC Time Constant

C = (units)

Resistance R (Ω) Time constant τ (s)

#1

#2

#3

#4

#5

Data Table 3

Demonstrator’s signature / Date

Question B-1 The oscilloscope used to measure the voltage across capacitor, in general,will not be an ideal voltmeter, i.e. it will not have infinite resistance. We can then model theoscilloscope as an ideal voltmeter in parallel with an internal resistance r. Sketch the resultantRC circuit and show that the voltage across the capacitor during charging is now given by

V =V0

(r

R+ r

)[1− e−

(R+r)tRrC

]

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Analysis B-1 Perform a suitable linear least squares fit to your data: time constant τ and re-sistance R so that the internal resistance of the oscilloscope can be determined. Plot a suitablelinear graph for your data. Also show on the graph the straight line that was obtained by thelinear least squares fit to the data as well as the error-bar of your data.

Independent variable x:

Dependent variable y:

Gradient: ± (units)

y-intercept: ± (units)

Coefficient of determination:

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Analysis B-2 Determine an experimental value for the capacitance C of the capacitor fromyour results of your linear least squares fit above. Compare it with the manufactured valueusing percentage discrepancy. Show your work.

Experimental value: C = ±

% discrepancy = %

Analysis B-3 Determine an experimental value for the internal resistance r of the oscillo-scope from your results of your linear least squares fit above. Show your work.

Experimental value: r = ±

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Capacitor Resistance R (Ω) Time constant τ (s)

C and Cunknown in series

C and Cunknown in parallel

Data Table 4

Demonstrator’s signature / Date

Analysis B-4 Determine experimental values for the unknown capacitance Cunknown. Showyour work.

In series: Cunknown =

In parallel: Cunknown =

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Question B-2 Compare the precisions of your measurements for the unknown capacitanceCunknown. State clearly what quantity you used to compare their precisions. Show your work.Provide a possible reason if their precisions differ too much.

SUMMARY: Results, Discussion, and ConclusionIn this section, you are required to submit a handwritten summary. Write within the spaceprovided to you and your summary must NOT exceed 800 words. It should consist of the fol-lowing: Results, Discussion and Conclusion. You may refer to the uploaded sample summaryfor reference concerning what to write. Note that you should not only analyze your results,but also discuss their implications. State clearly where you think your uncertainties comefrom and how they may have affected your results. Suggest any appropriate changes to theexperiment that you think may improve your results.

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Last updated: January 16, 2014 1:42 pm (NSY)

Physics level 1 laboratory Semester II, 2013/14