# Experiment: Decay of Charge in a Capacitor

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

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

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,

Hence,

When . 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,

Or,        ,

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  reflects the time for the capacitor to discharge. The time required for the capacitor to discharge increases as the time constant increases. In an experiment, the time constant can be estimated by the equations above.

Consider the case when two capacitors are connected in series. (Figure 2)

By conservation of charge, the capacitors share the same charge Q.

Therefore for two identical capacitors, combined capacitance  is given by

.

Consider the case when two capacitors are connected in parallel. (Figure 3)

The potential differences across the capacitors are the same.

Total charge

Therefore for two identical capacitors, combined capacitance  is given by

When two identical capacitors connected in series or parallel discharge through constant resistance, the decay of charge still follow an exponential decay, but with different time constants.

When ...

#### Here's what a star student thought of this essay

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.

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.

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 Ã¢â‚¬Å“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.Ã¢â‚¬Â Putting things into context makes the report read better, as well as showing understanding.