# Introductory Theory

According to ?Calculations for A-Level Physics? by T.L. Lowe and J.F. Rounce, the resistance of a conductor is the opposition of the conductor to the current flowing through it, and is defined as the potential difference needed across the conductor per ampere of current. Resistance is measured in ohms (W), from ohms law stating the equation: R=V÷I Where R is resistance (W), I is current (amps), and V is voltage (volts). Resistance is virtually the negative electrons passing through the wire being attracted to the positive ions making up the metal that is the wire. Resistance is the heat given off when negative electron and a positive ion come together, thus the more positive ions the more resistance. So we could use the analogy of a corridor with people, who are the positive ions in the wire, trying so catch tennis balls, the volts passing through the wire.

If you throw lost of balls, high voltage, they will catch a few of the balls, but a lot more balls will pass through, low resistance. If you lengthen the wire, think of it as adding more people, then more balls will be caught, thus increasing the resistance. If you shorten the wire there will be a less people to catch the balls, allowing more current to pass through, thus decreasing the resistance. Other factors that could be investigated: width of cross-section of wire. length of wire. temperature. type of wire. Widening the wire should increase the amount of space for the electrons to pass through, thus decreasing the resistance, this means that the positive ions making up the wire would be more spread out, therefore leaving more space. I think that doubling the size of the cross section should halve the resistance in the wire, since more space inside the wire for the current to avoid the positive ions if kept at the same temperature. The length of the wire should increase the resistance since there will be more of a chance it will hit a molecule in the wire, which are usually single atoms and these are held together by electrical forces. These forces involve the sharing of electrons and these electrons are free to move at random within the metal. So we should think of a metal as consisting of ions rather than atoms. Therefore the further the current has to travel, the resistance should increase, using this theory I can predict that doubling the wire should double the resistance, again, in a fair test where the temperature does not change. Temperature will effect my results due to when metals are heated the expand(get bigger, since heating causes vibrations in the metal, this would cause the positive ions to move around in the wire, this would cause more resistance, and therefore decreasing the temperature less resistance. The type of wire should definitely effect my results. If I used copper wire, there would be low resistance, due to coppers lack of positive ions, in comparison to if I used lead, I would find that high resistance would be shown, as lead has many more positive ions to attract the electrons that copper does. I will investigate the length of the wire and how that will effect the resistance of the wire constantan at 28 swg. I will keep all the other factors measured above the same. I will repeat the experiment three times, I will measure 1m of constantan wire and record the voltage and amps, and therefore the resistance, every ten centimetres starting at 10 cm and finishing at 100 cm. Prediction I think that as the length of the wire increases so to will the resistance of it. I also think that the rate that resistance of the wire increases will be directly proportional to the length. With electricity, the property that changes electrical energy into heat energy, I can consider electrical current to be resistance. A property of the atoms of all conductors is that they have free electrons in the outer shell of their structure. All metals are conductors. With electricity, the property that transforms electrical energy into heat energy, in opposing electrical current, is resistance. A property of the atoms of all conductors is that they have free electrons in the outer shell of their structure. All metals are conductors and have an arrangement in similar form to this As a result of the structure that can conduct(all atoms are conductive), the outer electrons can move about freely, even in a solid. When there is a p.d (potential difference) across a material that conducts, all of the free electrons arrange themselves in lines to move in the same direction. This forms an electric current. Resistance occurs when charged particles that make up the current hit other particles in the material. As the resistance of a material increases, so to does the force required to push the same amount of current. In fact resistance, in ohms? is equal to the electromotive force or p.d, in volts (V) divided by the current, in amperes (I) - Ohm?s law: R=V÷I. So in conclusion I believe that the longer the wire is the greater the resistance due to the more positive ions in the wire, this will create the heat and will cause more volts to be pushed through the circuit. This will cause greater resistance. So resistance is directly proportional to length of wire, When the wires length increases so does the resistance. Preliminary Results I first took some preliminary results to determine what sort of results I should be achieving in the actual experiement. Length of wire Current Voltage Resistance (ohms) 100 0.12 0.46 3.83 50 0.07 0.15 2.14 25 0.07 0.08 1.14 Method ? I set up a series circuit containing: battery pack(set at two volts for all experiments); ammeter; voltmeter; reastat; two crocodile clips(to attach to the wire every 10 cm(this was what I am investigating). ? To keep this experiment as accurate as possible we need to make sure, firstly, that the length of the wire is measured precisely from the inside edge of the crocodile clips, making sure that the wire is straight when we do this. ? I then placed a crocodile clip at 100 cm and moved the other crocodile clip at 10 cm intervals, starting at 90 then down to 0 cm, this was to eradicate any errors in length/width of wire, I noted the current and voltage, this was averaged to form 1 result. ? I placed the current, amps and length reading on a results table. ? I used the formula R=V/I (R-Resistance, V-Voltage, I-Current). This gave me the value of resistance for the lengths. I placed this on the results table also. I have devised a plan due to observing my preliminary results I will need quite a large range to show any significant change in resistance. This is why I will use a 90 cm range(from 10cm to 100 cm). Diagram [image] Results Tables Where the resistance values are in ohms and found using the equation Resistance=Voltage divided by Current. 1st time Length of wire Amps(I) Voltage(V) Resistance(ohms) 10 0.17 0.09 0.53 20 0.17 0.16 0.94 30 0.16 0.23 1.44 40 0.15 0.29 1.93 50 0.15 0.35 2.33 60 0.14 0.48 3.43 70 0.14 0.46 3.29 80 0.14 0.50 3.57 90 0.13 0.55 4.23 100 0.13 0.60 4.62 2nd time Length of wire Amps(I) Voltage(V) Resistance(ohms) 10 0.17 0.09 0.53 20 0.17 0.17 1.00 30 0.16 0.22 1.38 40 0.16 0.29 1.81 50 0.15 0.35 2.33 60 0.15 0.41 2.73 70 0.14 0.45 3.21 80 0.14 0.50 3.57 90 0.14 0.56 4.00 100 0.13 0.60 4.62 3rd time Length of wire Amps(I) Voltage(V) Resistance (ohms) 10 0.17 0.1 0.59 20 0.17 0.16 0.94 30 0.16 0.23 1.44 40 0.16 0.31 1.94 50 0.15 0.34 2.27 60 0.15 0.47 3.13 70 0.14 0.49 3.50 80 0.14 0.56 4.00 90 0.14 0.60 4.29 100 0.13 0.61 4.69 Average Length of wire Average Resistance(ohms) 10 0.55 20 0.96 30 1.42 40 1.89 50 2.31 60 3.10 70 3.33 80 3.71 90 4.17 100 4.64 Conclusion I found that as the length of the wire increases so does the resistance. So resistance is directly proportional to length, as one increases so must the other. I can say this since the line of best fit on my graph is very straight, I have no anomalies so none of my results can be mistake. I can show how length effects resistance in a diagram: [image] The diagram above shows that the negative current passes through the wire. My prediction supports my conclusion. In my conclusion I said that resistance would be directly proportional to resistance, this is true since it is backed up in my results, which I repeated three times and therefore any major and even minor errors were eradicated. This is because as the length of the wire increased the electrons that made up the current, had to travel through more of the fixed particles in the wire causing more collisions and therefore a higher resistance. Evaluation I believe my experiment and therefore results to be very accurate. All of my results lie close to the line of best fit, this is due to repeating the experiment 3 times, thus eradicating any anomalies. I had no anomalies. They support the definition of conclusion, my prediction that resistance is directly proportional to length. Since all my lines lie close or on to the line of best fit some errors must of occurred- any small errors in my experiment were encountered in the measuring of the wire. This is because it is not very practical to hold a piece of wire straight, whilst holding it next to a ruler and then trying to accurately fix crocodile clips to the right part on the wire. Calculative errors would have been hard to come by since in a simple calculation errors would been made obvious. Since I had no anomalous results a) I must have had a good method b) I must of carried my method out correctly.

Introductory Theory
9.2 of
10
on the basis of
3900 Review.