Light Bulb
Please note that all data processing graphs are presented at the last page of this report.
Skill 5 Conclusions and Evaluations
Conclusions
To conclude from the V/I graphs, Resistor 1 (#8) has a resistance of 53.3Ω (±6Ω). Resistor 2 (#3) has a resistance of 20Ω (±2Ω). The uncertainty values here are deduced by using the min/max resistance error values, calculated from the graphs. On the other hand, the bulb has an approximate resistance value of 7.4Ω. However, as you can see from the graph, the line is not linear, but instead curved. Since this is the case, it is very hard to deduce the uncertainty value from the max/min gradients. However, an approximate value of (±2.5Ω) can still be deduced.
The fact that the graphs for the resistors are linear, and the graph from the light bulb is slightly exponential, indicates that the light bulb and the resistors have different properties. This property is known as an ohmic or non-ohmic conductor.
In short, because of the bulbs exponential shape, we can conclude and say that it is a non-ohmic conductor. On the other hand, because the resistors sloping linear V/I graph, we can say that it is an ohmic conductor. To explain why this is so, lets look at what an ohmic conductor really is.
An ohmic conductor is a conductor that follows the ohm’s law. The ohm’s law states that the current through a conductor is proportional to the potential difference across it provided its temperature remains constant. Because of the resistors sloping linear V/I graph, this indicates that current is surely proportional to the potential difference or voltage. It does not violate the ohm’s law; therefore it is called an ohmic conductor. However, for a bulb, the V/I graph is a curve, there is no constant relationship between current and voltage, they are not proportional, this implies that they do not comply with ohm’s law, hence the name; non-ohmic conductor.
All in all, as promised in the aim, the two resistors are both ohmic conductors, and the light bulb the non-ohmic conductor.
Evaluations
Error 1: non constant temperature change
As mentioned previously, ohm’s law states that the current through a conductor is proportional to the potential difference across it only when the temperature remains constant. It was observed in the experiment that the temperature, although aimed to be kept the same, still fluctuated a bit, as the air conditioner was switched on/off, sunlight shining in from the windows, increasing the temperature of the room. Since this was the case, temperature would no longer be constant, thus experimental values would not form the required V/I shape of the graph. This can be seen from the resistor graphs. Only when the errors are included and error bars are plotted that a linear sloping gradient occurred, indicating the proportionality of current and voltage, hence ohm’s law. Without taking into account the error bars and uncertainties, it would be impossible to plot a linear line, which may lead to a misinterpretation of an ohmic or non-ohmic conductor.
Error 2: Resistance in volt/amp meter
We could argue that the amp meter and volt meter itself would have an internal resistance. This would affect the final current and voltage displayed on the meter. Values would be smaller then the real value, as it would be used up in the resistance process. Furthermore, the internal resistance in the amp meter might be different from that of the volt meter. This would cause a false correspondence of current and voltage values and would create a significant error in the experiment, influencing the final shape of the V/I graph and adding to the error in the final resistance value.
Error 3: Graphs drawn and interpreted inaccurately
One of the major applications of the experimental results is to use them to calculate the resistance values from the V/I graphs. If the graphs were plotted inaccurately or even wrong on the first place then the resistance values would also bound to be wrong. A good example of this error in this experiment could be found in the V/I graph for the light bulb.
Here, it is completely up to interpreter to draw the max/min and normal tangents in order to calculate the resistance by change in voltage over change in current. If the interpreter has decided to draw the tangent steeper, then the resulting resistance value would be higher. If the interpreter has decided to draw the maximum tangent steeper and the minimum tangent shallower, then the resulting error value in resistance would also cover a much wider range.
As you can see, a slight error in graph plotting would cause the overall performance of the experiment to degrade. This is why the error is one of the key elements in controlling the accuracy of the experiment.
Improvement 1:
To ensure the temperature is constant simply turn off all air conditioners and don’t turn them back on during the experiment, shut all windows and curtains to prevent sunlight heating up the room, perform the experiment in a smaller room so that the temperature can be more easily monitored. In addition, a thermometer can also be used to record the temperature in the experimental area. If you find that the temperature has increased by a little, try turning the air conditioner to return to the original temperature. If you find that the temperature has decreased, then try opening the curtains and let sunlight warm the room a little. By attempting all these improvements, temperature would hopefully be constant, and would have minor effects on the final experimental conclusions.
Improvement 2:
Since we know that there is an internal resistance in the amp meter/ volt meter, we could test these apparatus in order to find the effects of this internal resistance on the final current and voltage values. To do this, we could connect the amp meter/ volt meter, to a known current and voltage and see how much the meter values are off by. We could then take this current and voltage correction and add them onto our experimental values. That way, we could easily correct the error the internal resistance in our apparatus has made towards our final results.
Improvement 3:
To improve on graph plotting and tangent drawing skills, we could use a computer to help us. Many computer software’s nowadays can help us draw tangents or even help us calculate the gradient directly. After the experimental results are obtained, simply copy them into the program and plot graphs of V/I. These graphs would be much more accurate then hand plotted ones, and resistance values would be calculated to the highest degree of accuracy.
Unfortunately, allowing the computer to do the job for you does not show any skill in data processing. Thus another improvement can be done by using calculus. Calculus is a good tool in mathematics to calculate the gradient of a known equation. Simply obtain the equation of the line/curve and perform differentiation, then you’ll get a gradient value that would possibly be even more accurate then a computer value!
By Clement Ng 12.6
Sunday, June 16 2002 03:37AM