Experiment 05 Ohmic and non ohmic resistors in test By Christian Redeker 07.11.2007
Contents 1.) Hypothesis...3 2.) Diagram...5 3.) Method...5 4.) Errors...5 4.1) Systematic errors...5 4.2) Random errors...5 5.) Results...6 6.) Conclusion/Evaluation...7 7.) Bibliography...8 7.1) Note...8 2
1.) Hypothesis Electricity is one of the most important raw materials of the modern world. It builds the foundation of nearly all modern technology and has become an integral part of human life. Electricity is basically described by voltage and current. Electricity is thereby based on the attraction between charged particles. The most important charged particles in terms of electricity are the electrons (negatively charged) and the protons (positively charged). Oppositely charged particles attracted each other, in the way that they exert forces on each other which draw them together. Unequal distribution of charged particles leads to an electrostatic potential, which is a measure to describe how strong the attraction between the two regions of unequal charge is. The amount of electrostatic potential thereby depends highly on the distance between those regions and on the number of charged particle in those regions. The nearer the regions of unequal charge are and the higher the more charged particles are in the regions, the higher is the electrostatic potential, and the therefore the higher is the attraction between those two regions. The electrostatic potential is described by the term voltage. The higher the voltage, the higher is the electrostatic potential between two regions. An electric current is a transfer of charge from one place to another 1. In the simplest case an electric current is a movement of electrons. This is called a direct current. A direct electric current occurs when the electrons from a region of their high concentration flow to a region of their low concentration; in other words, it occurs between two regions of oppositely, unequal charged distribution to equalise the ratio of oppositely charged particles between region. However, the two regions must be connected in order to obtain an electron flow (i.e. an electric current) between those regions. The connecting medium must thereby be able to conduct electricity, which means it must have free electrons due to its intermolecular and intramolecular respectively arrangement. As soon as the two poles are connected with each other with a conductive material the positively charged pole draws in free electrons from the conductor, while on the other end, the negative pole releases electrons into the conductor as a reaction to the happenings on the positive end. Therefore an electron flow occurs. However, the movement of the electrons in the conductive material during the current flow is impeded by the molecules that make up the conductor. Thereby the electrons collide with those molecules, which in turn decreases the net flow of electrons. The amount of resistance of the material depends on the molecules of the material, and on the temperature of the material. The higher the temperature of the material is, the faster is the movement of the molecules within the material and therefore the higher is the likelihood of collision and the lower is the electric current. 3
An electric current can only flow within a closed circuit, i.e. when the two potential poles are connected by a conductor. Even air is a conductor of electricity, which is seen when a lightning (which is nothing more than a massive electric current) is created. However, air is a fairly poor conductor; for human made applications a better conducting material is needed to connect the two poles in order to get a reasonably electric current. A very good conductor is for example copper, from which the most cables are made of. The simplest man made circuit connects the two poles of the electric potential, with the help of a cable, through a resistor. The resistor is put into the circuit to obtain a reasonably small amount of electric current. This is due to the electric current (I) being defined as voltage (V) per resistance (R) or in mathematical terms as in the following equation: An increase in the overall resistance of the circuit goes therefore with a decrease in the electric current. However, the resistance a resistor delivers is not necessarily constant. The resistance of many resistors highly depends on their temperature. A resistor has in general a higher resistance at higher temperatures. Those resistors which have non-constant resistance are said to be nonohmic resistors. However, there are some resistors that are constant, even if their temperature changes; these resistors are called ohmic resistors. In this experiment three different resistors are tested in terms of being ohmic or non-ohmic. This is done by applying fixed voltages to three different resistors in a simple circuit and thereby measuring the resultant current of the circuit. Afterwards a current-voltage graph can be drawn which for an ohmic resistor should show a straight line and therefore a proportionality between those two quantities (see chapter 5 for a more detailed explanation). The three resistors which were tested were a constantan wire, a commercial resistor and a lamp. The constantan wire and the commercial resistor should be ohmic resistors. The alloy constantan is a very special material which does not change its resistance due to temperature changes, while commercial resistors are built in a way that they also do not change their resistance with temperature to maintain a stable current in any electronic application. However, the lamp should be a non-ohmic resistor. When a higher voltage is applied to the lamp, the lamp should shine brighter; the light which is emitted by the bulb is due to the heat created in the wire of the lamp. The brighter the light of the bulb the higher is the temperature of the wire. Due to the greater temperature of the wire when higher voltages are applied, the resistance of the lamp should also increase with higher voltages applied to it. 4
2.) Diagram Figure 1: Schematic description of the electric circuit used in the experiment 3.) Method An electric circuit was set up as shown in figure 1. In the place of the resistor a lightning bulb was placed first. Afterwards different amounts of voltages were applied to the circuit one after another in increasing order. For each applied voltage the amount of electric current in ampere was read from the ammeter. The exact voltage which was applied to the circuit was read from the voltmeter. The same procedure was repeated with a constant wire and a commercial resistor in the place of the lightning bulb. 4.) Errors 4.1) Systematic errors The smallest sub-division of the voltmeter was 0.01 V. Therefore a systematic error of +/- 0.005 occurred during the voltage measurements. 4.2) Random errors The wires which made up the circuit had a resistance as well. The energy source had a small resistance too. The constant wire began to glow during the measurements using high voltage. The values of the current and the applied voltage had to be read very quickly because otherwise the wire would have burnt. Therefore the reading error for the measurements of the four highest applied voltages in the measurements using the constantan wire is likely to be more inaccurate as for the values obtained in the other readings. 5
5.) Results Aim of the experiment was it to find which of the resistors tested had ohmic and which had non-ohmic properties. A resistor is said to be ohmic if the value of the resistance of that object is constant independently from the applied voltage and current respectively. Voltage (V) is defined by the product of resistance (R) times the electric current (I). This is mathematically expressed by the following equation: Assuming that a resistor is ohmic, the resistance (R) in the equation is a constant. Therefore the voltage must be proportional to the current; the resistance is thereby the constant of proportionality. A voltage-current graph describing an ohmic resistor must therefore show a straight line. The value of the gradient of that line is the value of the resistance. To find out whether one of the tested resistors had ohmic or non-ohmic properties a voltage-current graph with the obtained values from the experiment had to be drawn for each of the three types of resistors. The resulting graphs are shown in figure 5 to 7. The values used are shown in figures 2 to 4. Whether an object is an ohmic or non-ohmic resistor can also be investigated by drawing a resistance-current graph and by calculating the resistances for each applied voltage respectively. A resistance of an ohmic resistor is constant independently from its temperature or the applied voltage. The resistance for each applied voltage should therefore be the same if the tested resistor was ohmic. Therefore a resistance-current graph of an ohmic resistor should be a straight line. With the help of the formula defining voltage shown above, the resistance for each applied voltage could be determined. Rearranging this formula to find the resistance gives the following equation: The resistance for each applied voltage was calculated for each of the three readings. In the following an example calculation for the lowest applied voltage of the measurement using the lamp as a resistor is shown. The other resistance values for each applied voltage were calculated in exactly the same way using the appropriate values which were obtained from the experiment: The lamp had therefore a resistance of 12 Ω when a voltage of 0.06 V was applied to it. With the help of the calculated values for resistance and the measured values for the corresponding electric current, resistance-current graphs were drawn for each of the three readings. They are shown in figures 8 to 10. The values used are shown in figure 2 to 4. 6
Current (A) Voltage (V) Resistance (Ω) 0.005 0.06 12.00 0.021 0.76 36.19 0.046 2.71 58.91 0.063 4.52 71.75 0.080 6.60 82.50 0.093 8.43 90.65 0.105 10.25 97.60 Figure 2: Measured values of current and voltage and calculated values of resistance in the experiment using the lightning bulb as a resistor Current (A) Voltage (V) Resistance (Ω) 0.0007 0.09 128.57 0.006 0.80 133.50 0.021 2.78 139.00 0.035 4.60 131.43 0.050 6.64 132.80 0.065 8.46 130.15 0.08 10.29 128.63 Figure 3: Measured values of current and voltage and calculated values of resistance in the experiment using the constantan wire as a resistor Current (A) Voltage (V) Resistance (Ω) 0.018 0.20 11.11 0.50 0.43 0.86 2.23 1.40 0.62 4.63 3.01 0.65 6.46 4.40 0.68 8.30 5.46 0.65 Figure 4: Measured values of current and voltage and calculated values of resistance in the experiment using the commercial resistor as a resistor 6.) Conclusion/Evaluation As predicted in chapter 1 the current-voltage graphs which were drawn with the help of the results of the experiment for the constantan wire and the commercial resistor showed almost a straight line. Therefore, those two resistors can be said to be ohmic resistors. However, the resistance-current graphs, which should have shown a straight line were fluctuating for both resistors. This was due to uncertainties which occurred during the measurements which were discussed in chapter 4. A line of best fit was drawn in the resistance-current graphs of the constantan wire and the commercial resistor. The line showed the resistances of the two resistors. The resistance of the constantan wire was approximately 0.64 Ω, while the resistance of the commercial resistors was approximately 132 Ω. The lamp was as expected a non-ohmic resistor. The voltage-current graph showed a parabola and therefore a exponential relationship between the voltage and the current. Due to the gradient of the graph being the resistance, the resistance was higher when higher voltages were applied. The light emission also increased with higher voltages which meant that the 7
temperature in the wire increased as well. Therefore it is likely that, as stated in chapter 1, the resistance of the bulb increased due to a temperature increase which was induced by the electric current. The experiment successfully showed that two of the tested resistors, namely the constantan wire and the commercial resistor, were ohmic resistors. Furthermore, it successfully identified the lightning bulb being a non-ohmic resistor. 7.) Bibliography 7.1) Note Note 1: Adams, Steve; Allday, Jonathan. Advanced Physics. (2000). Oxford University Press. pp. 639. 8