In this column, several previous articles focused on mechanics experiments that can be analyzed using a mobile video motion analysis. However, the use of this method is also possible in completely different areas, which is the focus of this article.
In this column, several previous articles focused on mechanics experiments that can be analyzed using a mobile video motion analysis.1–5 However, the use of this method is also possible in completely different areas, which is the focus of this article.
Based on a high-speed recording of an incandescent light bulb, which shows periodic fluctuations in the brightness that cannot be perceived by the eye under normal conditions, the question is raised regarding the origin of these fluctuations. Here we show that the AC voltage of the power grid is the cause for these fluctuations, and careful observation allows a determination of the power line frequency.6 Since the brightness of an incandescent lamp in a simple resistive circuit is independent of the direction of the current, the bulb is equally bright whether the voltage is positive or negative. Therefore, to calculate the power line frequency, the determined flashing frequency must be halved (Fig. 1).
Why alternating voltage and determination of the power line frequency?
The main reason that alternating voltage is used in power grids for energy transmission is the transformability of the voltage. In order to avoid heat loss, the voltage of long-distance lines is transformed to high values. In common households, however, a significantly lower and less dangerous voltage is used. If there is a need for a higher voltage in a household, the voltage can be transformed using electrical transformers. The power line frequency in most parts of the world is 50 Hz and in Northern America it is 60 Hz. The frequency value is not arbitrary, but follows several criteria7: Higher frequencies allow smaller transformer cores (lighter and cheaper), but they also produce larger conduction losses due to the skin effect and cause larger phase shifts as the frequency is directly related to the number of rotations and poles of generators and motors (increase of centrifugal forces). Therefore, the choice of 50 or 60 Hz is a compromise of various factors.
Procedure
The investigated experiment has already been described in Ref. 9, but the authors used a digital camera with a frame rate of 1000 fps. In this work, we used a conventional smartphone, which allows students to perform the experiment at home without the need for additional equipment. New smartphone models typically feature a high-speed recording mode but the maximum frame rate is often limited to 240 fps. The significantly lower number of frames per second in comparison to the experiment in Ref. 9 requires an additional reduction in the playback speed for video analysis. This can easily be done directly in the smartphone using free apps.
In this experiment, we record an incandescent lamp (alternatively, LED lamps can be used if they are not operated via a stabilized DC voltage) in slow-motion mode (see Fig. 3 for a snapshot). The frame rate was set to the maximum value of 240 fps in the device settings of the iPhone 6s used here.
Two snapshots taken from the video (left at maximum brightness, right at a lower brightness level).
Two snapshots taken from the video (left at maximum brightness, right at a lower brightness level).
Analysis and results
When recording at 240 fps, the playback speed is 1/8 of the actual process speed. Here, the periodic changes in brightness are already clearly visible but they are still too fast for a quantitative evaluation. Therefore, we further reduce the playback speed with an appropriate app. In the example measurement described here, the application VivaVideo10 was used for this purpose. The app allows a reduction of the playback speed by a factor of 0.25. The output video was saved and its playback speed was additionally reduced by a factor of 0.25. Consequently, the actual process is 128 times faster compared to the playback speed of the slow-motion video. Finally, the slow-motion video was cut to a length of exactly one minute, which implies that the displayed process takes 60/128 < 0.47s in real time.11 In this video, the lamp lights up 47 times, which results in an actual blinking frequency of 100 Hz (= 47/60 3 128 Hz) and a power line frequency of 50 Hz, corresponding exactly to the frequency of the European power grid. Since the filament always “afterglows” a little, the lamp does not turn off completely. However, a complete turn off can be achieved using a light-emitting diode that is connected to a non-stabilized DC voltage source and operated slightly above the threshold voltage.12
Summary
The experiment described in this paper shows that video motion analysis could not only be used to described movements of objects but also in completely different areas. The analysis of periodic fluctuations of a light bulb can be used as an introduction to the theory of alternating current. For students, the flashing of the light bulb might be surprising at first and it can only be explained by a periodically changing voltage. The use of smartphones as experimental tool can be helpful during learning. As research shows, learning with mobile video analysis could increase conceptual understanding13,14 while decreasing irrelevant cognitive effort and negative emotions.13,15
