Title: Investigating the current – potential difference relationship for a metal wire. Aim: To design an experiment that will facilitate an I – V Graph to be ascertained of a metal wire and thus find the resistance of the wire by deriving the inverse of the gradient of the graph. Skill: Planning & Designing Theory: Resistance is a property of any object or substance to resist or oppose the flow of an electrical current. The quantity of resistance in an electric circuit determines the amount of current flowing in the circuit for any given voltage applied to the circuit. This is according to Ohm’s law. The unit of resistance is the Ohm which has the Greek letter ‘Omega (Ω)’. By default, that is, for electrical calculations, the inverse of Resistance is obtained and this is known as conductance. If conductance is calculated by dividing current by potential difference then from the preceding phrase it can be deduced that, Resistance is calculated by ascertaining the inverse of conductance.
The reasons for this will be provided within the Discussion/ Conclusion section. The resistance of an object is determined by the nature of the substance of which it is composed and this is known as the resistivity which are the dimensions of the object and the temperature. Resistance, however, is expressed in terms of the Ohm resistance per cubic centimeter at 20 oC (293 K). In its simplicity, before resistance is calculated, conductance is first obtained. Therefore: Current Conductance = Potential Difference Pooran (Rocky) Appadu Theory: Current -1 Resistance = Potential Difference Hypothesis: With reference to Ohm’s law, by varying the potential difference (using the rheostat), the current will increase linearly for the metal wire thus allowing an I – V graph to be ascertained. By deriving the gradient of the graph, the conductance of the wire will be obtained and finding the inverse of conductance, the resistance of the wire will be ascertained. Apparatus: 1. Voltmeter 2. Ammeter 3. 10 cm Metal Wire 4. 10 Cells 5. Conventional Wire 6.
Rheostat or Variable Resistor 7. Switch 8. Ruler Method: 1. Set up the circuit as seen in the diagram. 2. Using the variable resistor (or rheostat), vary the potential difference with eight different values. (The p.d. is varied be cause current is the independent variable, and according to the graph rules, the independent variable has to be placed on the x – intercept) 3. For each value, vary it three times at the same value, therefore collecting three readings for each value of current. 4. Tabulate the results on a table as can be seen under ‘Observations/ Results’. 5. Plot a graph of Current against Potential difference and derive the inverse of the gradient of the graph to ascertain the resistance of the wire. Variables Constant – The length of the metal wire used is kept constant. – The number of cells used are kept constant. – The different apparatus used remains the same. Changing – The p.d. through the metal wire is varied by the rheostat. Measured – The current from the ammeter is measured. – The potential difference from the voltmeter is measured. – The length of the metal wire is measured. Observations / Results: Table showing the results. Current (A) Uncertainty (A) Potential Difference (V) Uncertainty (V)
Expected Results: It is expected that the IV graph will be a linear graph, with similar increase in the magnitudes of both current and potential difference. Discussion / Conclusion: The experiment investigates the current – potential difference relationship for a metal wire. According to Ohm’s law which states that “at constant temperature, the potential difference across the ends of a conductor is directly proportional to the current through it”. Relating it to the experiment, it can be said that at room temperature, the potential difference (since this is varied) is directly proportional to the current that passes through the wire. This is assuming of course, that the temperature remains constant and the experiment, therefore, is considering the limits of experimental error. With reference to resistance, if an I – V graph is ascertained for a metal wire, then it is possible to find the resistance of the said wire since Resistance is equals to V/I. It can be deduced that the graph is the inverse of the formula of resistance. Therefore, if the graph is the inverse of the formula, then deducing the inverse of the gradient, logically suggests that the Resistance of the wire will be ascertained. In its simplicity, then, by deriving the inverse of the gradient of the I – V graph will give the resistance of the wire. Sources of Errors Like all experiments, random errors are inevitably predominant.
Parallax errors may be present when the values are read from the ammeter or voltmeter. This is however, rectified by the collation of consecutive readings and finding the average, thus reducing the error, and therefore facilitates an accurate reading to be collected. Direct current is not always consistent and the current provided will infact fluctuate. Because of this this, it is taken into consideration that the graph when plotted won’t be perfectly linear but will have points out of place. When the length of the metal wire used is found, there will be a numerical error of + 0.1 cm if a centimeter ruler is used. This will result in a small error of + 1 % and is therefore advisable that the centimeter ruler is used. The numerical uncertainties for the values obtained from the ammeter and voltmeter will not be very minute. One can only assume that by taking several readings that the percentage relative error will be smaller. Heat is lost to the surroundings because of the fact that the resistances of the test wire and conventional wire are different and will therefore oppose the potential difference across the wire.
Discussion / Conclusion: Limitations All experiments have its limitations and it doesn’t exclude this one. A few of these include but are not limited to: Only one type of wire is used. It would be better to obtain I – V graphs for varying wires which can allow comparisons to be made. Only room temperature is used rather than varying temperatures. Two temperatures would allow temperature affected I – V graphs to be collated for one wire or several wires to observe how temperature affects the resistance of the materials used. Direct current is utilized, alternating current could have provided a better means of power as it doesn’t ‘run down’ like a battery.
Assumptions It is assumed that the temperature of the surroundings remains constant. An increase or a decrease can alter the results enormously. It is also assumed that the current provided by the cells remain consistent throughout i.e. whilst the experiment is being implemented there was no adverse change in the current provided by the said cells. Conclusion With reference to the aim and hypothesis, it can be concluded that the ascertainment of an I – V graph for a metal wire will allow the resistance of the wire to be calculated as it has been explicitly stated many times. In addition the calculation of the resistance of the wire it provided a sketch of the said graph for the test wire and by deriving the gradient of the graph, the resistance of the wire will be ascertained.