Resistance Of A Length Of Wire example essay topic

A deel Malik 11/g December 2002 Aim The aim of this experiment is to investigate how the resistance of a wire changes in relationship to its length. We will increase the length of the wire and measure the voltage and current, and then calculating the resistance. Prediction I think that as the length of the wire increases so will the resistance of it. I also believe that the rate at which the length of the wire is increased, the resistance of the wire will also increase in direct proportion to the length. The graph to show this should therefore look something like this: A graph to show the relationship between resistance of a wire and it's length. The resistance of the wire is directly proportional to the length of it.

Theory With electricity, the property that transforms electrical energy into heat energy, in opposing electrical current, is resistance. In a conducting material a property of the atoms 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 of all conductive atoms, the outer electrons are able to move about freely even in a solid. When there is a potential difference across a conductive material all of the free electrons arrange themselves in lines moving in the same direction.

This forms an electrical current. When current is passed through a conductor, the electrons move from areas of high potential (i.e. the negative terminal of the power source) to areas of low potential (i.e. the positive terminal of the power source. Flow of electrons from negative to positive Resistance is created when the negatively charged particles that make up the current, collide with other fixed particles in the material. As the resistance of a material increases so to must the force required to drive the same amount of current.

In fact resistance, in ohms (R) is equal to the electromotive force or potential difference, in volts (V) divided by the current, in amperes (I) - Ohm's law. R = V / I As the length of the wire is increased the number of collisions the current carrying charged particles make with fixed particles also increases and therefore the value for the resistance of the wire becomes higher. Resistance, in ohms (R) is also equal to the resistivity of the wire, in ohm-meters (~n) multiplied by the length, in meters (l) divided by the cross sectional area, in square meters (A). R = n x l / a Any solid material is made up of atoms, packed up closely together in a structure.

If electrons are flowing through the material (i.e. it is being used as a conductor) it is likely that all, of them will, at some point on their journey through the material, hit one or more of the atoms in the material, and so get slowed down. This effect is resistance. An electron passing through a cool material If the kinetic energy of the atoms in the material increases (i.e. the material is warmed up), the atoms will vibrate more, and thus take up more space. This means that it is more probable that electrons will hit the atoms, so the resistance increases. An electron passing through a warm material If you increase the diameter of a piece of wire, there is more room for the electrons to move in.

Effect of cross-sectional area on resistance The material and cross sectional area of the wire is constant throughout the experiment. Therefore it is clear from the formula that the resistance should be directly proportional to the length. Some use ful formulas I will need to use Diagram Apparatus. Power pack. Nickel Chromium Wire.

Connecting wires. Ammeter. Voltmeter. Crocodile clips. Heat proof mat Method 1.

Set up the circuit as shown on diagram. 2. Cut the wire in lengths of 5 cm, 10 cm, 15 cm, 20 cm, 25 cm and 30 cm. 3. Adjust the power supply to the lowest possible setting. 4.

Connect the 5 cm wire to the circuit. Take readings from the voltmeter and ammeter and record. The resistance can be calculated. 5. Increase the power supply gradually and take reading when the voltmeter reading is at; 0.1, 0.2, 0.3 up to 1.0.

Calculate the resistance. We will use an average reading. 6. Repeat the procedure for the with the following wires connected between the crocodile clips: - 10 cm - 15 cm - 20 cm - 25 cm - 30 cm 7. Use ohms law to calculate the resistance. We will use lengths starting from 5 cms up to 30 cms going up in 5 cm.

This is because then we can see a large enough difference to compare resistance. If we used a difference of only 1 cm then they wouldn't be hardly any difference in the readings, and if we used wires that were two long the resistance readings would be too far apart to plot on a graph. We are recording the results twice so this way we make sure are results are accurate. We used a heat proof mat because the wire gets hot as the more current is going through it. We will record our results in a table and then I will plot a graph of length against resistance.

I will draw a line of best fit if the results are slightly out. Safety This is not a very dangerous experiment but despite this you must always handle electricity with care, keep the current low, handle with dry hands. Since there are no high currents, voltages or temperatures being dealt with, and no hazardous radiation or chemicals, no special safety precautions need to taken beyond the usual necessary when dealing with electrical equipment... Always make sure your hands are dry when turning off the power switch... Turn off the power switch when increasing the length of wire so you don't get an electric shock... Don't turn the power pack above 4 v...

Never touch the wire when heating wires else you can seriously be burnt. Keep all bags under tables and all long hair tied. Key Factors Voltage- The voltage of the power pack should never go above 6 vs. as this can be dangerous an will probably melt the metal wire. Wiring- All the wiring should be connected properly to prevent any problems, this would also save time while doing the experiment. Temperature- The temperature of the wire is a key aspect. The hotter the wire gets the more it effects the resistance.

There is more flow of electrons therefore a smaller resistance. Length- Firstly, its length (l). If you make the length of conductor longer, you are increasing the number of atoms in the way of the electron flow, and so you are increasing its resistance. As the length of the wire is increased the number of collisions the current carrying charged particles make with fixed particles also increases and therefore the value for the resistance of the wire becomes higher. Ammeter- The ammeter measures the current in amperes which is important, all wires should be connected properly to the ammeter for accurate readings.

Voltmeter- The voltage is a key factor as it measures the voltage which is very important to the investigation. Area- Given a larger cross-sectional area for the wire, the electrons are not crammed into such a small space, so resistance is decreased. A good analogy is water in a pipe. If you increase the size of the pipe you can pump more water down it more easily. The resistance of a length of wire can be found by the formula: where l is its length and A is its cross-sectional area.

Crocodile Clips- The connecting leads and crocodile clips will have their own resistance. We need to compensate for this, so for each iteration of the experiment we will connect the crocodile clips together and take a reading before we take any readings with wire between the crocodile clips. Fair Test In this experiment we are only changing one factor - the length of the wire, the factors that we are going to keep the same are as follows: We must keep the surrounding room temperature the same or the particles in the wire will move faster (if the temperature is increased) and this will therefore have an effect on the resistance. The cross sectional area of the wire must be kept constant throughout as well. This is shown in equation where the cross sectional area is a factor that effects the resistance. The resistivity of the wire is kept constant.

If the experiment is to be a fair test, we need to keep all the variables other than the length of the wire constant. The temperature of the wire can be regulated by making sure that the current being passed through the wire is not excessively large. Since (at a constant temperature) voltage x current = constant, we can do this by setting the PSU to supply the smallest possible voltage, i.e. 2 V. We can also minimize the current by keeping the resistance high - so if we avoid testing any lengths of wire longer than about 35 m we should get rid of the problem. The material of the wire must also be kept the same as different materials have different conductivity.

The last two factors will be kept the same by using the same wire all of the way through the experiment. The current that we pass through the wire is to be kept the same, also. If this is changed the temperature of the wire might change in a way that is not constant making the results more confusing. Accuracy 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. We must also make sure that the wire is straight when we conduct the experiment.

If it is not, short circuits may occur and bends and kinks in the wire may effect the resistance, also. The reading that we take of the voltage should be done fairly promptly after the circuit is connected. This is because as soon as a current is put through the wire it will get hotter and we want to test it when heat is effecting it the least, i.e. at the beginning. Results These were the results for the nickel chromium wire at different lengths, with recordings for volts and current. I calculated the resistance using the formula Graph of results This is a graph to show the resistance plotted against the length of wire. Observation of results and graph A line of best fit was drawn on the graph, this is a good line as the results are very close to the line of best fit.

From the graph we can see one very clear trend, which is, as the length of the wire increases so does the resistance of it. Another, more significant thing is that the increase is constant. This is indicating by the fact that the line drawn is a straight one. The graph's line of best fit passes through the origin. This is to be expected, as zero length implies zero resistance.

The fact that the graph is a straight line through the origin shows that resistance is directly proportional to length.