• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Experiment: Decay of Charge in a Capacitor

Extracts from this document...

Introduction

Physics(AL) TAS Laboratory Report

Experiment: Decay of Charge in a Capacitor

Content

  1. Objectives
  2. Theories and Hypothesis
  3. Experimental Design
  4. Results and Data Evaluation
  5. Error Analysis
  6. Summary and Conclusions
  7. Possible Improvements

A. Objectives

The objective is to investigate the decay of charge in a capacitor when it discharges through a constant resistance. The discharge processes of two identical capacitors connected in series or parallel are also investigated. From the results obtained, determine the relations between discharge rate, capacitance and resistance.

B. Theories and Hypothesis

Theories about Decay of charge

Consider a capacitor with capacitance C charged up by a potential difference V, connected across a resistor with constant resistance R. (Figure 1)

image04.jpgimage00.png

At any time t, let VR and VC denote the potential difference across R and C respectively, I denotes the current through R, Q denotes the charge remained in C.

By Kirchhoff’s Laws,

image05.png

Hence,        image15.png

image23.png

When image30.png. Hence Q0 is the initial charge in capacitor.

Practically, the charge in a capacitor cannot be measured easily at any time. Therefore current, instead, can be measured.

At any time, image34.png

image35.png

Or,        image16.png,

where I0 is the initial current through the resistor.


        Therefore theoretically, it is known that the decay of charge through constant resistance follows an exponential decay pattern. That is, the discharge rate is always proportional to the charge remained.

The time constant image36.png

...read more.

Middle

3.        Open the switch so that the capacitor starts to discharge through the resistor and multimeter.

4.        Start the stop-watch when the multimeter reading reached 40μA, then record the time reading for every 5μA decreased. Stop timing after the reading reached 5μA.

5.        Repeat procedures 2, 3 and 4 twice to obtain the arithmetic mean value of time t.

6.        Plot a graph of current I against time t for the data obtained in procedure 5.

7.        Plot a graph of ln I against t.

8.        Repeat the experiment twice with the capacitor replaced by two identical capacitors connected in series or parallel.

9.        Plot the data obtained in procedure 8 on the same graph in procedure 6.

D. Results and Data Evaluation

Potential difference V across battery = 4.3image18.png0.05 V.

Current I through resistor after capacitor has fully charged up = 43image18.png0.5 μA.

Total resistance of resistor and multimeter = image19.png,

which agrees with the labelled value on the resistor. Also, the internal resistance of multimeter is not significant.

Current I/A

Logarithmic Scale

ln I/A

Time t/s

t1/s

t2/s

t3/s

mean t/s

40

3.69

0

0

0

0

35

3.56

6.25

6.35

6.23

6.28

30

3.40

13.57

13.63

13.67

13.62

25

3.22

22.47

22.60

22.35

22.47

20

3.00

32.97

33.04

32.89

32.97

15

2.71

46.97

47.01

47.01

47.00

10

2.30

66.97

66.92

66.97

66.95

5

1.61

99.88

99.67

99.26

99.60

Table 1

        Table 1 shows the data obtained in procedure 5. Using the data, graphs of I against t (Graph 1) and lnI against t (Graph 2) are drawn.

        Graph 1 shows an exponential decay curve and Graph 2 shows a straight line with negative slope.

...read more.

Conclusion

        Also, when two identical capacitors are connected together in series or parallel, their discharge processes still follow an exponential decay. In the case they connected in series, the time constant is approximately halved. And when connected in parallel, the time constant is approximately doubled.

        All of the above results agree with our experimental hypothesisimage14.png. Therefore we can conclude that the hypothesis is accepted by our experiment.

G. Possible Improvements

        The sources of error are mainly come from the reading of multimeter and the timing by stop-watch. Both of them are quite significant.

        To reduce the error from reading of multimeter, we can use a multimeter with more detailed scales or one with digital number displays and higher sensitivity.

        Reaction time of human is a random error. To reduce the error from timing, we can repeat the experiment a few more times. According to the Law of Large Numbers, the arithmetic mean of time can be more accurate as the number of timing increases.

        An alternative method to reduce the errors is using a data logger. A data logger can be connected to an ammeter to replace the multimeter, so that the change of current over time can be recorded more accurately. This increases the accuracy of reading ammeter/multimeter and at the same time avoids the effect of reaction time of human.


image33.pngimage32.png

/

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Electrical & Thermal Physics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Here's what a star student thought of this essay

4 star(s)

Response to the question

Layout - All the components of a good report is there, the layout is clear and the section headings helpful; but a better flow from one section to another would give an easier read. For example, you mentioned objectives at ...

Read full review

Response to the question

Layout - All the components of a good report is there, the layout is clear and the section headings helpful; but a better flow from one section to another would give an easier read. For example, you mentioned objectives at the beginning, but then went off to detailing the theory (and rightly so), and never went back to your objectives again - maybe try to incorporate your objectives into your procedure, it shows to the teacher/marker that you understand the relevance of each step.
The report is also good in the sense that there are no gaps in the explanation. It is very easy to jump from one step to the other while skipping a step, but that is not the case here - it is logical, with no gaps in the logic.
At the end of each section, there seems to be an abrupt end, and then you are tossed to the next section; this is A-Levels, so it doesn't have to read like a professional report, but as a practice to write better quality reports, always try to show how one section relates to another, or how one section flow into the other. Even just a simple line to say “Now that we know the theory behind a single capacitor, we will apply this to two capacitors, and then three. After, we will try to establish the general rule for capacity discharge for any number of capacitors.” Putting things into context makes the report read better, as well as showing understanding.

Level of analysis

Analysis and quality - The techniques, the theories, the calculations are all accurate, and the explanation given was good and logical - the section on the theory was particularly good. The author has made his objective clear at the start, and have followed a logical and comprehensive breakdown of the steps required to investigate it. There are no obvious errors in grammar or spelling.
One improvement maybe to have the graphs close to the text where it is mentioned from, so that people can see the graph as they read the text; otherwise, have captions with the graphs to explain what it shows. One of the best things I like about this report is that it shows the author understands - he/she knows the limitations of the experiments, taking into account errors and significance.

Quality of writing

Overall, this is a very good report. All the content is there, the major way of improving is to lay it out better, establish a flow in the report, and once in awhile refer back to the question.


Did you find this review helpful? Join our team of reviewers and help other students learn

Reviewed by superwiseman 01/03/2012

Read less
Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Electrical & Thermal Physics essays

  1. Marked by a teacher

    Internal Resistance of a cell

    5 star(s)

    the value of I with the internal resistance r and later subtracted it with the value of V in order to obtain the emf (the potential difference of the cell), this formula helped to calculate or to proof the variable of the unknown above symbols especially the emf.

  2. Single Phase Transformer (Experiment) Report.

    * I'2R1 is the voltage drop associated with the winding resistance and is in phase with I1. * I'2X1 is the voltage drop associated with the total leakage reactance and is in phase quadrature with I1. * Cos ?1 and cos ?2 are the primary and secondary power factors respectively.

  1. Physics - How Electric Eels Generate and Use Electricity.

    Three factors that are involved are: * Nerve fibers are closer to the head of the eel and are smaller near to the tail of the eel. * Slower chemical signals are implemented in nerve fibers closer to the head.

  2. The aim of my investigation is to determine the specific heat capacity of aluminium.

    At temperatures as great as this there is a large temperature gradient between the block and the air, because of this a lot of heat is lost into the atmosphere producing less reliable results and I will therefore record the time and temperature for a shorter time as the final

  1. Investigating the E.m.f and Internal Resistance of 2 cells on different circuit Structures.

    The e.m.f is also just below the correct or specified e.m.f of 3V. The 'lost volts' could be due to the internal resistor. The second trend is that in a parallel circuit with the same number of cells, the e.m.f and internal resistance is halved.

  2. Investigating Ohms law

    5 0.59 5 0.60 5 0.60 6 0.73 6 0.71 6 0.71 6 0.72 8 1.00 8 1.00 8 1.00 8 1.00 10 1.25 10 1.29 10 1.29 10 1.28 12 1.52 12 1.52 12 1.54 12 1.53 Thermistor Repeat 1 Repeat 2 Voltage (V) Current (mili amps) Voltage (V)

  1. The aim of this investigation is to study capacitors charging and discharging. A ...

    When looking a the results the discharging begins at 10 v but the charging ends a t 11.25v, the capacitor was not fully charged when Discharging.

  2. The purpose of this experiment was to measure the specific heat capacity (Cb) of ...

    The latent fusion would be compared to the known value. Introduction:- When a solid has reached its melting point, additional heating melts the solid without a temperature change. The temperature will remain constant at the melting point until ALL of the solid has melted.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work