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Extended Essay in Physics

Investigation of influence of the frequency of the electric current on the performance of transformer:

How does the frequency of current influence the input and output powers of the transformer and what is the effect on the efficiency of the transformer?
Word Count: 3025
Table of contents
Abstract......................................................................................................................3

1. Introduction..........................................................................................................4

1.1 Background.....................................................................................4

1.2 Objective..........................................................................................4

2. Equipment description and setup.................................................................4



2.1 General description.........................................................................4

2.2 Electric circuit.................................................................................5

3. Procedure..............................................................................................................5

3.1 Preparation......................................................................................6

3.1.1 Design of the electric circuit.......................................6

3.1.2 Gathering the data.......................................................6

3.1.3 The rate and amount of measurements.......................7



3.2 Conducting the experiment............................................................7

4. Data collection and processing...............................................................7

4.1 Graphs..............................................................................................7

4.2 Raw data..........................................................................................9

4.3 Processed data...............................................................................11

5. Data presentation and analysis............................................................13

5.1 Presentation....................................................................................13

5.2 Analysis...........................................................................................14

5.2.1 Uncertainties............................................................15



6. Conclusion and evaluation..........................................................................18

6.1 Conclusion.......................................................................................18

6.2 Evaluation.......................................................................................18

7. Bibliography....................................................................................................19

Abstract
This essay investigates how does the different frequency of electric current influence the performance of transformer. Essay investigates how does the change of frequency influence the input power, output power and efficiency of transformer. The research was done by applying the current of 10 volts to primary coil of the transformer and then measuring both the voltage and current in both primary and secondary coils of transformer. The product of voltage and current gave the power in primary and secondary coils. The ratio of power in secondary coil and power in primary coils gave the efficience of the transformer. The frequency was being controlled and being changed from 5 Hz to 1 000 Hz with the help of power amplifier and the data from ampere-meters and voltmeters were represented in a graphical way.
The investigation had not shown a significant change in the efficiency of transformer when the frequency of the current was being changed in increasing intervals from 5 to 100 Hz. By going to the frequencies higher than 100 Hz, the efficiency was decreasing in an increasing rates. Powers in both primary and secondary coils have been almost constant in the interval from 5 to 100 Hz, but were decrasing in linear relation starting from 100 and continuing till the 1 000 Hz. Even though the resistances of ammeters and voltmeters may have influenced the results of the investigation, it can be clearly seen from the graphs that the change of frequency had the biggest impact on the performance of transformer.
Word Count: 253
1. Introduction
1.1 Background

Transformers are not only being used in power lines in order to minizmize the heat losses when distributing the electricity, but also in a daily-used appliances. Many devices, for example, computers or mobile phones use transformers to change the voltage to the one that is needed to properly work with that device. One important aspect of transformers is that they are usually designed to be working in certain frequency of electric current. As there are different types of transformers, including those which work in an official electric frequency of Europe – 50 Hz, those that work in high frequencies (usually 440 Hz) and those that are designed to work in North America and other regions with the supplied current of 60 Hz, it would be interesting to investigate how do transformers perform in different frequencies of the current.


1.2 Objective

The objective of this study is to investigate how does the change of frequency influence the input power, output power and efficiency of the transformer. Therefore there are three research questions that are very closely related to each other and which require the same methods of investigation:



  • How does the change of frequency of the current influence the input power of the transformer?

  • How does the change of frequency of the current influence the output power of the transformer?

  • How does the change of frequency of the current influence the efficiency of the transformer?


2. Equipment description and setup
2.1 General description

The list of equipment:



  • Electric wires that connected the devices in electric circuit which is shown in Picture 1.

  • 2 Nova computers which were gathering the data from both ammeters and voltmeters.

  • 2 ammeters one of which was connected to the primary coild and the other – to the secondary.

  • 2 voltmeters one of which was connected to the primary coild and the other – to the secondary.

  • Power amplifier „Xplore GLX“ that produced a current of 10 volts and was able to change the frequency of it.

  • 0,5 ohm resistor which served as a load in order not to have all the current flowing through the voltmeter so the voltage and current could me measured properly.

  • Step-down transformer that can step-down the voltage over 19 times.


2.2 Electric circuit
Figure 1.1


Figure 1.2


As it can be seen in Figure 1.2 the primary coil of transformer is connected to the polygon ACEBDF and the secondary coild is connected to the polygon GHJLKI.

Alternating current (later: AC) source in AB represents current of 10 volts that is being produced by power amplifier.

Ampermeters in BD and HJ parts are connected in series and they measure the current flowing through respectively primary and secondary coils.

Voltmeter in CD measures the voltage across the primary coil of tranformer.

Voltmeter in KL is connected in parallel with a resistor, because in other case voltmeter would be connected in series with ammeter and which would result in near to infinity equivalent resistance in secondary coil.
3. Procedure

3.1 Preparation

In the stage of preparation it was important to design how will the circuit look, how the data will be measured, analyzed and interpreted.



3.1.1 Design of the electric circuit

The most important was to decide how will the ammeters and voltmeters be arranged in a circuit so that the data could be measured accurately. I have put ammeter in part BD so that it would be in series with the AC source. Therefore, the voltmeter which is connected in parallel with the primary coil and the series of AC source will measure the coltage which is of course the same for parts CABD and EF as they are parallel.

Also, one change was made to the design of a circuit during the process. At first, the resistor was not put in part IJ. As the data was being gathered, it did not look realistic (the current value was near to zero) and thus I have made an assuption that the voltmeter is connected wrong in the circuit. As the voltmeter has to be connected in parrallel, it needed some kind of load in parallel with it, so that the current would almost not flow through the voltmeter. For that purpuse a resistor of value of 0,5 ohms was chosen..
3.1.2 Gathering the data

As my school did not have four different multimeters for measuring the voltages and current in both primary and secondary coild, I have decided to use Nova computers and its ammeter and voltmetrs for this procedure. Two voltmeters and two ammeters that were used in this investigation required to be connected to Nova computers so the data from them could be gathered and analyzed. As Nova computer has 4 ports, two voltmeters and two ammeters were connected to it. It was strange to see that the voltage from the secondary coil was zero. As it did not sound logical, assumption was made that there is a short connection in the Nova computer might have occured. Therefore another Nova computer was turned on. This time the ammeter and voltmeter from primary coil were connected to one computer and the ones from secondary coil to another computer. This time the data gathered seemed much more logical – the voltage was decreasing and the current was increasing, just like the step-down transformer should perform.


3.1.3 The rate and amount of measurements

It was also important to decide how much measurements should be taken with the Nova computers and what the rate of theirs should be. I have set the maximum 10 000 measurements per second, so that the graph which had to be produced would be as accurate as possible as that the peaks of sinusoids would be detected.


3.2 Conducting the experiment

The experiment was being conducted with in total 46 different frequencies (I have measured even more, but the accuracy after 1000 Hz has drastically decreased as the maximum rate of measurement was not as big). I first started with 5 Hz and was increasing the frequency by 5 Hz, but later the intervals between two frequencies were being increased as the changes were not as big.


4. Data collection and processing
4.1 Graphs

The Nova computers represented the gathered data in graphs – the sinusoids of voltage and current by time. After the experiment there were four sets of graphs:



  1. Voltage in primary coil

  2. Current in primary coil

  3. Voltage in secondary coil

  4. Current in secondary coil

To show how did it look, in Figures 2.1 and 2.2 the voltage and current in primary coil can be seen represented in the graph, when frequency is equal to 10 Hz.

Figure 2.1




Figure 2.2


One of the problems faced which that can also be seen in the graph was that there was an offset for both voltage and current (which has been changing every time and thus could not be automatically eliminated). Therefore, it was not enough just to look where the peak of sinusoid is. In order to the most accurate data for both voltage and current I decided to interpolate the data using Graphical Analysis program which when set to search for a sine function, finds the most accurate values for it. The way program interpolates the data can be seen in Figure 3.
Figure 3



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