Lab report-物理实验报告（英文）

Investigation of capacitance

Introduction

Capacitor is widely used in a variety of fields as it can store electric energy, such as Filtering, resonant circuit and moving phase. Different capacitors have different abilities to store energy, which is due to the difference of capacitance. Capacitance is the ability of a capacitor to store charge in an electric field, it is also a measure of the amount of electric potential energy stored (or separated) for a given electric potential. This report is going to investigate the capacitance of a capacitor made from the experiment by using different DC methods. Before the capacitor made from the experiment is measured, three DC methods will be tested to verify whether these methods are efficient by measuring the capacitance of the known capacitor. In addition, after measuring the unknown capacitor, the whole capacitors will be connected in parallel and the total size of capacitance will be measured.

Theory

Capacitance can be found by using:C??0??r?A. This is for two flat plates. dAs for the formula, C is the capacitance of a capacitor, A is the area of flat plates, d is the distance between the two flat plates, ?0 is the permittivity of vacuum, ?r is the relative permittivity. Permittivity is constant of proportionality

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

that relates the electric field in a material to the electric displacement in that material and relative permittivity is the ratio of the permittivity of a substance to that of free space or vacuum. Different materials have different relative permittivity, the behind table includes the relative permittivity of some different material:

Material Dielectric Constant Acetaldehyde Acetic Acid 6.2 Acetic Acid 4.1 Acetone Acetone 21.8 20.7 17.7 Source: (The Engineering Tool Box, 2011.)

When two capacitors are placed in series, the charge on each plate is of equal magnitude, so: C1?QQ; C2?, hence C1V1?C2V2(where Q is the amount V1V2of charges on plate and V is the voltage across the capacitor). When a capacitor is charged (V across capacitor): V?V0(1?e?tRC) and I?I0e?tRC(V0

is the initial voltage adding on the capacitor, e is a constant and it is 2.718, R is resistance, C is capacitance and I0 is the initial current flowing through the capacitor). Analogously, when a capacitor is discharged, it flows V?V0eand I?I0e

?tRC?tRC.

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Methods

Apparatus:

Power supply, leads, ruler, calipers, clips, known capacitor, aluminum foil, cling-film, paper, multi-meter, video camera.

Part A: using three different ways to measure the capacitance if the given capacitor.

Method1 of part A Diagram1:

Capacitor

Power supply

Resistor

Voltmeter

This method is measuring the increasing voltage of the given resistor while the capacitor is charged. Voltage of the resister is measured by a multi-meter, which is a tool that can measure many quantities such as voltage, current, and resistance. The given capacitor has an area(A) of1m2, and the distance(d) is

2?10?5m. The V changes very fast, so there needs a resister to slow it down

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

and a camera to record. The voltage of capacitor can be found by measuring the voltage of the resister, as voltage of the capacitor is equal to the output voltage subtracting the voltage of resistor: VC?Voutput?VR. When the loop is connected, using the camera to record the change of voltage. After recording, drawing a graph of the V (V should be the voltage of capacitor and it is equal to

Voutput?VR) and t (the time constant) , then using the equation in theory to find RC and C.

Table1: Result of method 1of part A

t(time)/s 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 V(voltage of resistor)/v 1.127 1.013 0.963 0.893 0.792 0.778 0.714 0.619 0.627 0.578 0.545 0.515 0.479 0.455 0.433 0.406 0.388 0.370 0.350 0.336 V(voltage of resistor)/v 0.373 0.487 0.537 0.607 0.708 0.722 0.786 0.881 0.873 0.922 0.955 0.985 1.021 1.045 1.067 1.094 1.112 1.130 1.150 1.164 V (output voltage)/v 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 4

English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

20.000 21.000 22.000 23.000 24.000 25.000 30.000 37.000 40.000 41.000 46.000 50.000 58.000 64.000 66.000 71.000 77.000 0.323 0.307 0.295 0.285 0.272 0.263 0.223 0.178 0.166 0.161 0.143 0.130 0.113 0.103 0.099 0.093 0.068 1.177 1.193 1.205 1.215 1.228 1.237 1.277 1.322 1.334 1.339 1.357 1.370 1.387 1.397 1.401 1.407 1.432 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500

Analysis for the method1

Graph 1: this graph is drawn from the result of method 1.

the change of Voltage of the capacitor V(voltage)/V2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000 t(time)/s0.000 10.000 20.000 30.000 40.000 50.000 60.000 70.000 80.000 5

Graph2: the standard graph.

English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

V (voltage)

t(time)/s

?tRCThe initial voltage (V0) is 1.45V. V?V0(1?e), when t=RC,

V?1?e?1?0.632,V0=1.45V, so V=0.91V, from the graph, t=9s when V=0.91V. V0Therefore, RC is equal to 9, as the resistance of resistor(R) is given and which is 390K?, C?t9??23uF. The capacitance of capacitor is4.5uF, but R390000here the result is23uF, so the experiment works not well. There are some reasons resulting to the big error between the real value and experiment value. First of all, comparing the standard graph with the result graph, When time is zero, the voltage also should be zero, however, the voltage of capacitor is not zero as t=0, this is due to the capacitor has some charges in it before the loop is connected. Second, as the data is gotten from the video by eyes, there exists the manmade error. Third, the voltmeter itself is a resistor, this also will cause the error. In addition, when the experiment is operated, the loop is not connected very well and the capacitor has been used.

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Method2 of part A Diagram2:

Capacitor Resistor

This method is measuring the current while the capacitor is charging. The way of method 2 is same as method 1and the resistor, power supply and capacitor are still the same. First, using the camera to record data. Then, drawing a graph according to these data. Last, calculating the capacitance according to the graph. For this method, the formula is I?I0eflowing through the capacitor).

Table2: Result of method 2of part A

t(time)/s 0.000 1.000 2.000 3.000 4.000 5.000 I(current)/A 5.510 2.650 1.340 0.687 0.420 0.222 7

?tRCPower supply A Ammeter (I0is the initial current

English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

6.000 0.140 7.000 0.098 8.000 0.064 9.000 0.043 10.000 0.027 11.000 0.019 12.000 0.014 13.000 0.011 14.000 0.009 15.000 0.007 16.000 0.006 20.000 0.004 26.000 0.002 34.000 0.001

Analysis for the method2

Graph 3: this graph is drawn from the result of method 2.

English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

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Investigation of capacitance

the change of current of the capacitorI(current)/A6.000 5.000 4.000 3.000 2.000 1.000 0.000 0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000 t(time)/s The relationship between the current and time isI?I0e?tRC. When t=RC,

I?I0e?1, the initial current(I0) is 5.51A, so I=2.03A. From the graph, the time (t) is

C?1.7s when I=5.52A. As t=RC, so RC=1.7,

1.71.7??4.36?10?6F?4.36uF. The capacitance of capacitor isR3900004.5uF. Comparing the result and the real capacitance, this method works well.

However, there are still some errors which are cannot be avoided. For example, the data gotten from the video is not accuracy.

Method 3 of part A Diagram3

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English Name: Vince Class: Eng1-1B Voltmeter Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Resistor Investigation of capacitance

Capacitor

This method is measuring the voltage while discharging. Similar to the method1 and 2, this method is also using camera to record the data and drawing a graph, then, using the graph and formula to get the capacitance of the capacitor.

Table3: Result of method 3of part A

t(time)/s 0.000 1.000 2.000 3.000 4.000 5.000 6.000 11.000 20.000 37.000 55.000 74.000 90.000 120.000 V(voltage of capacitor)/v 1.145 0.689 0.521 0.441 0.383 0.302 0.282 0.210 0.145 0.092 0.062 0.053 0.041 0.030 10

English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

160.000 200.000 0.021 0.012

Analysis for the method3

Graph 4: this graph is drawn from the result of method 3.

V(voltage)/V1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000 0.000 the change of Voltage of the capacitor20.000 40.000 60.000 80.000 t(time)/s100.000 120.000 140.000 When a capacitor discharged: V?V0e?tRC. V0=1.145V, When t=RC,

V?V0e?1?1.145?e?1?0.421V. From the graph, t=3s as V=0.421V, SO RC=3, C?33??7.7uF. The real capacitance is 4.5uF, comparing the result R390000with the real, the result is not accuracy. There are also some errors exist, the first is the there is some current flowing through the voltmeter which was ignored. The second is when the data recorded by eyes, there must be some manmade errors.

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Part B: Making a capacitor

This part is describing the process of making a capacitor by using cling-film and aluminum foil. First of all, putting cling-film on the desk and spreading it. Second, laying the aluminum foil on the cling-film tidily. Then, putting the cling-film above the aluminum foil again. The next, letting the aluminum on the top and make sure the two aluminum cannot touch each other. At last, rolling them carefully and using multi-meter to test whether there is current between the two aluminum foils for one meter a time. After rolling, the capacitor was made. The length of materials is 4 meters with a wide of 0.25 meters, so the area (A) is 1 meter square. The distance (d) between two aluminum foils is

2?10?5m which is measured by a calipers. If the capacitor needs to store

more charge, the area should be larger and the distance should be smaller.

Part C: Measuring the capacitance of the capacitor made in class.

Method 1 of part C: Diagram4:

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Capacitor English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

This part is going to Estimate the size of the capacitor (capacitance) which was made in class by using four methods. This method is measuring the capacitance by using a known capacitor and let them in series. The formula is

C1V1?C2V2, C2?4.5uF, The voltage of capacitor 1 gotten from the experiment is 3.45v, the output voltage is 20v ,so V1?VOUTPUT?V2?16.55V, The result C1?C2V2A?0.938uF. In addition,C??0?r, ?0?8.85?10?12F, A

dV1Cd?2.11. This result is reasonable A?0is1m2 and d is 2?10?5m, therefore, ?r?and there are some errors exist. First, when the loop is connected, the capacitor will be charged and the data on voltmeter will change, so reading the initial data of the voltmeter(which was used as V2) is not accuracy. Second, the power supply has interval resistance, so the voltage of capacitor 1is not equal to VOUTPUT?V2 absolutely.

Method 2 of part C: Diagram5

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Capacitor

Power supply

Resister

Voltmeter

This method is using the same method as method 1 of part A. Table4: Result of method 2of part C

t(time)/s 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 13.00 24.00 65.00 100.00 V(voltage of resistor)/v 2.81 1.97 0.65 0.42 0.39 0.35 0.33 0.31 0.30 0.20 0.17 0.09 0.03 V(voltage of capacitor)/v 0.19 1.03 2.35 2.58 2.61 2.65 2.67 2.69 2.70 2.80 2.83 2.91 2.97 V (output voltage)/v 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00

Analysis for the method2

Graph 5: this graph is drawn from the result of method 1.

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

the change of Voltage of the capacitor 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00 20.00 40.00 60.00 80.00 ?tRCV(voltage)/Vt(time)/s100.00 The initial voltage (V0) is 2.98V. V?V0(1?e), when t=RC,

V?1?e?1?0.632,V0=2.98V, so V=1.88V, from the graph, t=1.7s when V0V=1.88V. Therefore, RC is equal to 1.7, as the resistance of resistor(R) is given and which is 390K?, C?C??0?rt1.5??3.8uF. so the result isC?3.8uF. R390000A, ?0?8.85?10?12F, A is1m2 and d is 2?10?5m, therefore, d?r?Cd?8.6. This result is not good, what results the bad result is errors of A?0this experiment such as the interval resistance of the voltmeter and the manmade error on reading the data from video. Method3 of part C Diagram6:

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Capacitor Resistor

Ammeter A

Power supply

This method is also using the same method as method 2 of part A

Table5: Result of method 3 of part C

t(time)/s 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 12.00 13.00 16.00 20.00 26.00 34.00 I(current)/A 4.21 3.02 1.55 0.89 0.42 0.32 0.28 0.25 0.23 0.22 0.18 0.17 0.15 0.14 0.13 0.10 Analysis for the method3

Graph 6: this graph is drawn from the result of method 3

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

the change of current of the capacitor3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 I(current)/At(time)/s The relationship between the current and time isI?I0e?tRC . When t=RC,

I?I0e?1, the initial current(I0) is 4.21A, so I=1.54A. From the graph, the time (t) is

C?1.9s when I=1.54A. As t=RC, so RC=1.9,

1.91..9A??4..9?10?6F?4.9uF. C??0?r, ?0?8.85?10?12F, A isR390000d1m2 and d is 2?10?5m, so ?r?Cd?11. This result is also not good. This A?0experiment works not well. As there are some errors. For example, the data gotten from the video is not accuracy and the power supply has interval resistance.

Method 4 of part C Diagram7

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Capacitor

Voltmeter Resistor

This method is using the same way as method 3 in part A. Table6: Result of method 4of part C

t(time)/s 0.00 1.00 2.00 3.00 4.00 5.00 6.00 8.00 11.00 16.00 21.00 30.00 45.00 60.00 V(voltage of capacitor)/v 3.12 1.75 1.27 1.08 0.95 0.83 0.71 0.61 0.56 0.36 0.28 0.18 0.08 0.05 Analysis for the method 4

Graph 7: this graph is drawn from the result of method 4.

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

the change of Voltage of the capacitorV(voltage)/V3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00 10.00 20.00 30.00 40.00 ?tRCt(time)/s50.00 60.00 When the capacitor discharged: V?V0e. V0=3.1V, When t=RC,

V?V0e?1?3.1?e?1?1.14V. From the graph, t=2.1s as V=1.14V, SO RC=2.1,

C?2.12.1A??5.3uF. C??0?r, ?0?8.85?10?12F, A is1m2 and d is R390000d2?10?5m, so ?r?Cd?11. There are some errors with the method. First of all, A?0the current will flow through the voltmeter but which was ignored. Second, the data gotten by eyes from the video cannot be very correct.

Part D: making a bigger capacitor Producing a capacitor in industry is complex and the main process is: The film-> evaporate gold-plated of layer-> cutting-> winding-> > fu spraying zinc-> welding wire can-> assembly->-epoxy or vacuum Baptist-> block-> oil testing

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

packaging (swordsky123, 2011,3,15.). This part is going to connect all of the capacitors made by the class in parallel to make a bigger capacitor and use three of the methods in part A to measure the total size. There are two capacitors made in class and they made in the same material with the same sizes. After finishing making the capacitors, the two capacitors were connected in parallel and then, measuring the total capacitance of the two capacitors by using the totally same three methods as part A. the results of the three methods are3.3uF, 2.1uF and 2.4uFrespectively, choosing the average value, so the total capacitance of the two capacitor is 2.6uF, the capacitance of one capacitor is

2.6?1.3uF(as the two capacitor are same). For this result, 2it is much more accuracy than the single connected capacitor. When two capacitors are connected together in parallel, the total capacitance will become bigger. Therefore, it is more accuracy. For example, when measuring the length of an object, if the length is only 1cm, it is not easy to measure, however, if the object has a length of 1m, it is easy to be measured.

Conclusion

This report has investigated the capacitance of the capacitor made from the experiment by using four DC methods. The known capacitor is also measured by using three ways as well as the big capacitor made up of two same

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

capacitors. Each method has a result, however, some methods work not very well and the result has a big difference with the real value. Among these methods, method 2 works better as the result is closest to the real value. To improve the method and make it more accuracy, there are some changes should be done. First of all, capacitance of the capacitor should be larger. Second, the capacitor should be charged longer. Third, the experiment should be done for several times and choosing the best result. Also, there are some other ways to measure the capacitance of a capacitor, constant-current method is a good way, the method is measuring the capacitance of a capacitor by the current and voltage, the relationship between them is Uc?I0t( Baidu CLibrary, 2011.5.12.). This method is simple but efficient and it is widely used in companies and research centre.

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

Investigation of capacitance

Reference list

The Engineering Tool Box (2011) Relative Permittivity - Dielectric Constant [Internet], Available from:

http://www.engineeringtoolbox.com/relative-permittivity-d_1660.html [Accessed 15th march 2012].

Swordsky123 (2011-3-15) Process of producing a Capacitor [Internet], Available from: http://zhidao.http://www.wodefanwen.com//question/229291304.html [Accessed 21th march 2012].

Baidu Library (2011) Communication and electronics [Internet], Available from: http://wenku.http://www.wodefanwen.com//view/eed239eff8c75fbfc77db2d5.html [Accessed 22th march 2012].

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English Name: Vince Class: Eng1-1B

Chinese Name: Wen Zheng Yang Student number: SBC-11-1025

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