Investigating The Effect Of Resistance On A Capacitor Circuit

Preliminary Work:

Before conducting the proper GCSE physics coursework experiment, we carried out a practise experiment on the discharge of a capacitor with a very similar method with the exception of using a data logger. By doing this, we were familiar with the apparatus and method and therefore we understood on what needed to be done for the proper experiment. By carrying out the practise experiment, I found out that a resistor with small resistance will not work as discharge will be too fast to measure and a resistor with too big resistance will take too long to record the discharge of a capacitor. The practise experiment was very convenient, as it helped me to arrive at my hypotheses.  

OBTAINING EVIDENCE

Results:

The table below shows the affect of capacitance on the rate of discharge. The rate of decay for 5 different capacitors using a 10k resistor is recorded. The table would be too big if the results were shown at every 0.1 seconds. Therefore I have shown my recording every 0.5 seconds.

This second table below shows the affect of resistance on the rate of discharge. It shows how fast a 470µf capacitor decays with 5 different resistors. The table would be too big if the results were shown at every 0.1 seconds. Therefore I have shown my recording every 0.5 seconds.

A summary grid for each of the two tables’ results can be seen below with the graphs in the analysis section.

ANALYSIS

Resistor- 10K

Capacitor- 470µf

I chose to stop my recordings for voltage at 90 seconds because that was the point where all my results were close to show complete discharge. The reason why my tables showing my recordings show the time taken for a 2200µf capacitor and a 47K resistor are over 90 seconds, is because they took a few more seconds to fully discharge, but in my method I chose to stop my recordings at 90 seconds only.

First Conclusion

By looking at the first graph, which shows how the capacitance affects the discharge of a capacitor through a resistor, it proves my first hypothesis to be correct. The graph clearly proves the statement: capacitance is directly proportional to the time taken to discharge a capacitor. This proof is shown by the much steeper curve caused by the 47µf capacitor than that caused by a 2200µf capacitor, which is flatter and longer lasting. This is for the reason that when the capacitor has fully charged up but then immediately discharged, the voltage begins to exponentially decrease. Yet when the store of charge in the capacitor increases, the voltage still decreases at a very rapid rate however it takes longer to discharge fully.

Second Conclusion

From the second graph above, I can again see that my second hypothesis proves to be correct as it is clear from the graph that as the resistance gradually increases, then the curve becomes less steep and carries on for a longer time. This is due to the fact that as resistance increases, current will decrease (flow of electrons slows down) and so will the discharge of a capacitor. Whereas for a very small resistance, the capacitor discharges fully exponentially and this is shown from the graph as the curve is very steep for a 1k resistor. Therefore resistance is directly proportional to the time taken for a capacitor to discharge.

To conclude with, I can say that when the resistance is higher, less charge (in coulombs) can pass through easily in the circuit, and therefore the rate of discharge will be slower too. We can relate the above to the equation: Q= IT

EVALUATION

Views on the Experiment:

The experiment went well and we were sure of what to do as we had a couple of practise test experiments building up to the main experiment for our coursework. With my hypotheses having been proved, the experiment was a success. The method was easy to follow once the circuit was set up, and from the experiment I obtained very good results which could help me draw up conclusions. The results were reliable as we had massive help from the data logging software, which recorded the voltage going down every millisecond which helped the results to be extremely accurate.  However, setting up the apparatus was rather difficult and it required much help by our teacher.

Improvements:

In carrying out the investigation, there are a few improvements which can be made for future purposes:

1. Collect more data to obtain more accurate results
2. Carry out a fair test by repeating the experiment at least 3 times, which can also provide averages for the results
3. Use more resistors and capacitors so that more data can be collected and also that the data becomes more reliable
4. Further practise of using and setting up the apparatus to avoid unreliable data
5. Measure more factors that could affect the rate of capacitor discharge with the two I have tested in this experiment

Reliability of Results:

Overall, the results which I acquired were very accurate. These were mainly due to the insight software on the laptop which collected results every 0.1 seconds and allowed me to access them straightforwardly. When plotting the results on the graphs, no obvious anomalies could be seen. Also, as there were 3 people in a group, this meant that there was more understanding of what had to be done in the experiment and each group member was given a specific role for the investigation.  

The results do support my conclusions, as it is very clearly shown on the graphs. The first batch of results show that the largest capacitor discharges for the longest amount of time while the smallest capacitor discharges for the smallest amount of time.

The second batch of results too supports my second conclusion, as it is visible from the graph that the 1k resistor allowed the 470µf capacitor to discharge fully within 10 seconds, but the 47k resistor allowed the 470µf capacitor to discharge over 90 seconds.  

Further Work:

If this investigation had been carried out on an industrial scale, then the experiment could be repeated except this time even smaller or larger sized capacitors. These could then be used for designing computers or even if producing a microchip.

I would repeat the investigation for a minimal of 20 times on a school scale for the investigation to be furthered. This would ensure that the results I can collect will be even more accurate and also the hypotheses would be proved further once these results have been collected and plotted on a graph.