General Physics Laboratory – Experiment Report …inphy.korea.ac.kr/GenPhyLab/Manual/2017_2_GenPhyLab...General Physics Laboratory – Experiment Report 2nd Semester, Year 2017 PAGE

General Physics Laboratory – Experiment Report

2nd Semester, Year 2017

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Introductory Physics Office, Department of Physics, College of Science, Korea University Last Update : 2017-10-10

Exp. #2-6 : Measurement of the Characteristics of , , and Circuits

by Using an Oscilloscope

Student's

Mentioned

Items

Student ID Major Name Team No. Experiment Lecturer

Experiment Class Date Submission Time Submission PlaceIntroductory Physics Office

Report Box #

※ Students should write down Student’s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding

contents to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor.

Instead, it is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the

time specified by Experiment Lecturers.

The Experiment Report points per each Experiment Class are evaluated by max. 50 points (basically 15 points).

Solutions of Problems in Experiment Reports are not announced to the public according to the General Physics Laboratory - Administration Rule.

If a student permits other students to pirate one’s Experiment Reports or a student pirates Experiment Reports of other students regardless of permission of original creators, the corresponding Experiment Report points and Active Participation points will be zero in case of exposure of such situation.

Unless Experiment Reports are submitted to the place due to the time specified by Experiment Lecturers, the corresponding Experiment Report points will be zero.

If the submission rate of Experiment Reports is less than or equal to two thirds, the grade of General Physics Laboratory will be F level.

In order to decide grades of General Physics Laboratory at the end of

current semester, the detailed scores of General Physics Laboratory will

be announced at Introductory Physics Office homepage. Based on the

announcement, students can raise opposition of score error. Since the

public evidence is needed for the confirmation of opposition, students

should keep one’s Experiment Reports completed evaluation by

Experiment Lecturers until the grade decision of General Physics

Laboratory.

If a student is absent from the Experiment Class because of proper

causes, the corresponding student should submit documents related to

absence causes to Introductory Physics Office regardless of cause

occurrence time until the grade decision of General Physics Laboratory.

If a student moves the Experiment Class arbitrarily without permission

of Introductory Physics Office, it is noted that the total Experiment Scores

will be zero.

Lecturer's

Mentioned

Items

Submission Time/Place Check Experiment Report Points Evaluation Completion Sign

50



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1. Objective

The peak-to-peak voltage and the frequency of alternative signals generated by the function generator are measured by using an oscilloscope and the usage

of the oscilloscope is understood through this procedure. The characteristics of various circuits composed of a resistor (), a capacitor (), and an inductor

( ) are measured by using an oscilloscope.

2. Theory

(1) Oscilloscope and function generator

1) Oscilloscope

The oscilloscope is a basic experimental instrument used in the laboratory

for various fields. Signals can be shown on the fluorescent screen of the

oscilloscope similar to the cathode ray tube in a television by sweeping the

electron beam. The values of X-axis and Y-axis in the oscilloscope are

voltages actually, but the values of X-axis corresponds to the time in most

cases. The sweep oscillator loaded inside the oscilloscope sweeps the

electron beam along the X-axis at a constant rate. Buttons and knobs in

an oscilloscope can have different names, but most of them have the same

function among various oscilloscope models. In some models with 2

channels, each signal selected can be shown or two signals can be shown

simultaneously.

① INTENSITY : It is used to control the intensity of the screen.

② FOCUS : It is used to control the focus of the electron beam.

③ TRACE ROTATION : It is used to rotate the trace in the screen which

can be biased by geomagnetism, etc.

④ TIME/DIV : It is used to set the time scale in one horizontal division. In

addition, there is the fine adjust knob of TIME/DIV, called VAR. When VAR

is rotated in the clockwise direction completely, CAL (calibration) mode is

set and the time is the same value as that indicated by TIME/DIV. When

VAR is rotated in the counterclockwise direction, the time is at max. 2.5

times longer than that indicated by TIME/DIV.

⑤ TRIGGER : If a specific voltage condition set by the trigger is satisfied, a

stationary signal can be shown on the screen.

TRIGGER LEVEL / TRIGGER SLOPE : It is used to control the level of

TRIGGER voltage. It is possible to Invert the polarity of the TRIGGER LEVEL

by pushing in or pulling out the TRIGGER LEVEL knob. The function of

TRIGGER SLOPE is provided in some models.

TRIGGER MODE : It is used to select the trigger mode such as AUTO or

NORM.

TRIGGER SOURCE : It is used to select the trigger source such as INT

or EXT.

⑥ VOLT/DIV : It is used to set the voltage scale in one vertical division.

The function of VAR for VOLT/DIV is similar to that of TIME/DIV.

⑦ AC, GND, DC : It is used to select the coupling mode for the vertical

signal amplifier.

AC : The vertical signal amplifier is coupled through a condenser so

that alterative signals can pass while direct signals are blocked.

GND : The vertical signal amplifier is coupled with the ground.

DC : The vertical signal amplifier is directly coupled so that all the

signals including the alternative and direct signals can pass.

2) Function generator

Various signals with the following waveform, frequency, and amplitude can

be generated by using the function generator.

Waveform : Sine wave, square wave, triangular (sawtooth) wave

Frequency : a few Hz ~ about MHz

Amplitude : 0 ~ a few V

Signals can be added by DC offset.

Student ID Name



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(2) Characteristics of the circuit

A battery with the electromotive force , a resistor (), and a capacitor

() are connected in series as shown in Fig. 1.

Fig. 1. circuit.

1) If the switch is connected to position A at , the electric current

starts to flow through and the electric charges are stored in . As the

more electric charges are stored in , the increase of potential difference

across prevents the flow of the electric current so that the electric

current no longer flows after a sufficiently long time. For the quantitative

understanding, the sum of potential difference over the circuit gives the

following equation.

(Eq. 1)

Here, is the electric charges stored in and

is the electric

current flowing through . By solving the above equation with the initial

condition at , the following result can be obtained.

(Eq. 2)

Here, is called the capacitive time constant of the circuit. It

represents the changing rate of the electric charge and current depending

on the time. Using

and , the potential difference

across and can be found respectively.

2) If the switch is connected to position B when is sufficiently charged,

the electric charges stored in start to discharge through . As the

discharging progresses, the electric charges stored in vanish and the

electric current no longer flows. For the quantitative understanding, the

sum of the potential difference over the circuit gives the following

equation.

(Eq. 3)

By solving the above equation with the initial condition at ,

the following result can be obtained.

(Eq. 4)

Using

and , the potential difference across and

can be found respectively.


A battery with the electromotive force , a resistor (), and an inductor

( ) are connected in series as shown in Fig. 2.

Fig. 2. circuit.

1) If the switch is connected to position A at , the electric current

starts to flow through . prevents the flow of the electric current

according to Faraday's law of induction, but the electric current approaches

to the value

without the effect of . For the quantitative

understanding, the sum of potential difference over the circuit gives the

following equation.

(Eq. 5)

By solving the above equation with the initial condition at , the

following result can be obtained.

(Eq. 6)



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Here,

is called the inductive time constant of the circuit. It

represents the changing rate of the electric current depending on the time.

Using and

, the potential difference across and


2) If the switch is connected to position B when the electric current has a

constant value

, the battery can no longer provide the electromotive

force. prevents the rapid change of the electric current, but eventually

the electric current vanishes. For the quantitative understanding, the sum of

the potential difference over the circuit gives the following equation.

(Eq. 7)

By solving the above equation with the initial condition

at ,

the following result can be obtained.

(Eq. 8)

Using and

, the potential difference across and


※ Answer the following questions.

1. Derive (Eq. 8) by solving the differential equation (Eq. 7), and

then find .


An alternative voltage source with the angular frequency and the

amplitude , a capacitor (), an inductor ( ), and a resistor () are

connected in series as shown in Fig. 3.

Fig. 3. circuit.

The values of the reactance of and depend on the angular frequency

of the alternative voltage source, and the electric currents flowing through

and have a phase difference of and with respect to

the voltage, respectively. Therefore, the impedance in the circuit connecting

, , and in series is given by

(Eq. 9)

In the above equation, has the minimum value and the current

amplitude has the maximum value when

.

is called the resonance frequency, and the

phenomena that the current amplitude has the maximum value at this

frequency is called the resonance. In the resonance phenomena, it is worth

investigating the change of the current amplitude depending on the

frequency. The current amplitude at the resonance frequency is

and the difference of two frequencies where the current amplitude has half

maximum is

, which is called the resonance width. As

becomes smaller, the maximum value of the current amplitude becomes

larger while the resonance width becomes narrower.

※ Answer the following questions.

2. In case of sin , find and respectively, and then

consider the meaning of the condition for .



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3. Experimental Instruments

Items Quantity Usage Clean up method

Oscilloscope 1 ea. It is used to measure alternative signals.It should be placed at the center of

the experiment table.

Function generator 1 ea. It is used to generate alternative signals.It should be placed at the center of

the experiment table.

characteristics

measurement instrument1 ea. It is used to constitute , , and circuits.

It should be placed inside the basket

of the experiment table.

Oscilloscope

-to-wall power

connection cable

1 ea. It is used to connect the oscilloscope to the wall power.It should be placed inside the basket


Function generator

-to-wall power

connection cable

1 ea.It is used to connect the function generator to the wall

power.



BNC cable 5 ea.

They are used to complete the connection among

characteristics measurement instrument, the oscilloscope and

the function generator.

They should be placed inside the

basket of the experiment table.

T connectors 2 ea. They are used to connect BNC cables.They should be placed inside the

basket of the experiment table.

Terminator

for ground1 ea.

It is used to provide the ground to characteristics

measurement instrument.





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4. Experimental Procedures

(1) Understanding of the usage of the oscilloscope

1) Measurement of the peak-to-peak voltage and the frequency of the sine

wave

① Generate a sine wave with the proper amplitude and the frequency of

kH z by using the function generator.

② Connect the signal generated by the function generator to the channel

1 of the oscilloscope.

③ Control the TIME/DIV and VOLT/DIV of the oscilloscope to observe the

signal on the screen of the oscilloscope.

④ Draw the signal shown on the screen of the oscilloscope and measure

the peak-to-peak voltage and the frequency of the sine wave.

2) Measurement of the peak-to-peak voltage and the frequency of the

square wave

① Generate a square wave with the proper amplitude and the frequency

of kH z by using the function generator.

② Connect the signal generated by the function generator to the channel

1 of the oscilloscope.

③ Control the TIME/DIV and VOLT/DIV of the oscilloscope to observe the

signal on the screen of the oscilloscope.

④ Draw the signal shown on the screen of the oscilloscope and measure

the peak-to-peak voltage and the frequency of the square wave.

(2) Measurement of the characteristics of the circuit

1) Set the resistor and the capacitor to kΩ and nF , respectively.

Generate a square wave with the proper amplitude and the frequency of

kH z by using the function generator. Connect the signal generated by

the function generator to the channel 2 of the oscilloscope.

2) Constitute the circuit as the following diagram. Connect the voltage

across the resistor to the channel 1 of the oscilloscope. Draw the signal

shown on the screen of the oscilloscope and write down the formula

describing the observed signal.


across the capacitor to the channel 1 of the oscilloscope. Draw the signal



4) Measure the capacitive time constant of circuit from the voltage

across the capacitor during charging and discharging processes respectively

and compare it to the theoretical value.



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1) Set the resistor and the inductor to kΩ and mH , respectively.

Generate a square wave with the proper amplitude and the frequency of

kH z by using the function generator. Connect the signal generated by

the function generator to the channel 2 of the oscilloscope.


across the resistor to the channel 1 of the oscilloscope. Draw the signal




across the inductor to the channel 1 of the oscilloscope. Draw the signal



4) Measure the inductive time constant of circuit from the voltage

across the resistor during increasing and decreasing processes of the

voltage respectively and compare it to the theoretical value.


1) Set the inductor and the capacitor to mH and nF , respectively.

Generate a sine wave with the proper amplitude and the frequency by

using a function generator. Connect the signal generated by the function

generator to the channel 2 of the oscilloscope.


across the resistor to the channel 1 of the oscilloscope.



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3) Control the frequency of the signal generated by the function generator

and measure the current amplitude at various frequencies. Determine the

resonance frequency and the resonance width.

4) After changing the resistance of the resistor, repeat the experimental

procedures and investigate the relation between the resistance and the

resonance width.

5) If all the measurements are finished, turn off the function generator and

the oscilloscope. Finally, clean up the experiment instrument according to

the suggested method.



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5. Experimental Values

(1) Understanding of the usage of the oscilloscope

Sketch the signals shown on the screen of the oscilloscope and calculate the peak-to-peak voltage and frequency measured by the oscilloscope.

Waveform and frequency of

the signal generated by the

function generator

Sine wave, kHz Square wave, kHz

Signal shown on the screen

of the oscilloscope

Voltage (V )

Voltage (V )

Peak-to-peak voltage

measured by

the oscilloscope

DIV × V/DIV

= V

DIV × V/DIV

= V

Frequency

measured by

the oscilloscope

( DIV × s/DIV )-1

= Hz

( DIV × s/DIV )-1

= Hz



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Resistance of the resistor kΩCapacitance of the capacitor nF

Waveform and frequency of the signal generated by the function generator Square wave, kHz

Sketch the signals shown on the screen of the oscilloscope and write down the formulas describing the observed signals.

Measurement Time vs. Time vs.


of the oscilloscope

Voltage (V )

Voltage (V )

Formula

decreasing :

increasing :

charging :

discharging :

Capacitive

time constant

Theoretical value (s)Experimental value (s) Error

(%) charging discharging Average



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Resistance of the resistor kΩInductance of the inductor mH

Waveform and frequency of the signal generated by the function generator Square wave, kHz

Sketch the signals shown on the screen of the oscilloscope and write down the formulas describing the observed signals.

Measurement Time vs. Time vs.


of the oscilloscope

Voltage (V )

Voltage (V )

Formula

increasing :

decreasing :

decreasing :

increasing :

Inductive

time constant

Theoretical value (s)Experimental value (s) Error

(%) increasing decreasing Average



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Inductance of the inductor mH

Capacitance of the capacitor nF

Theoretical value of the resonance frequency Th

(kHz )

Waveform of the signal generated by the function generator Sine wave

Resistance

of the resistor

(Ω )

Peak-to-peak

voltage

across the resistor

Frequency of

the signal

generated by the

function generator

(kHz )

logExp

Resonance width

(kHz )

Quality factor

Exp

2 DIV

4 DIV

8 DIV Exp

4 DIV

2 DIV

2 DIV

4 DIV

8 DIV Exp

4 DIV

2 DIV

※ Exp : Experimental value of the resonance frequency.



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6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents

should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report

is allowed.)

※ Write down contents in terms of the following key points.

1. Regarding the error of the time constant in circuit as the error of resistance or capacitance, calculate the actual resistance or capacitance.

2. Regarding the error of the time constant in circuit as the error of resistance, calculate the actual resistance. (Use the difference between the

maximum of and .)

3. (1) By using the error of the resonance frequency in circuit, calculate the actual inductance or capacitance.

(2) By using the error of the resonance width obtained from the comparison between Ω and kΩ experiments, calculate the actual

resistance. In addition, compare it to the error analysis result of and circuits

4. Explain the meaning of the time constant in and circuits. (Relate it with the reason why the kHz square wave is used in and

circuits.)

5. Comparing the signal shown on the screen of the oscilloscope to , , and obtained from the differential equation, explain the

tendency of the value changes from the time to when the sufficiently long time passes.



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7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents

should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report

is allowed.)

8. Reference

General Physics Laboratory – Experiment Report …inphy.korea.ac.kr/GenPhyLab/Manual/2017_2_GenPhyLab...General Physics Laboratory – Experiment Report 2nd Semester, Year 2017 PAGE

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