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Investigation: How length affects the resistance in a wire.

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Apparatus:

Wires with a very low, negligible  resistance

Power Pack (Max 8V)

Meter Ruler

Ammeter (2 d.p)

Voltmeter (2 d.p)

Wire Boards: Manganin (Width of 0.45),

Method:

In order to find the resistance I am going to use Ohm s law and use the voltage (V) and current (A) to find the resistance (W) - I have therefore set up a circuit which enables me to control the voltage using a rheostat and check it using a voltmeter. I can then find out the current using an ammeter.  I will measure the voltage across the resistance wire, all of the other wires have such a low resistance they can be said to have no resistance. After setting up the apparatus, in the circuit to the left, I began testing my first variable - length. Using the meter ruler, I measured and marked the lengths of 0.1m to 0.8m, marking every 0.1m on the boards, under the wire with the width of 0.45. I then used a crocodile clip on the points, taking readings of the voltmeter and ammeter for each length, on each wire. I repeated the experiment an additional two times, enabling me to comment on the reliability later on.

Safety :

In this experiment, I was dealing with electrical equipment and had to take various precautions, to ensure that my experiment is completely safe, as this is of up most importance.  A particularly crucial safety point I had to deal with during this experiment  was the heat that a wire can generate when exposed to currents with varying voltage. The wire can get very hot, glow and even catch alight, if the current isCHNKWKS >ÜøÖTEXTTEXTîqFDPPFDPPtFDPPFDPPvFDPPFDPPxFDPPFDPPzFDPCFDPC|FDPCFDPC~FDPCFDPC€FDPCFDPC‚FDPCFDPC„FDPCFDPC†FDPCFDPCˆFDPCFDPCŠSTSHSTSHŒSTSHSTSHŒ2SYIDSYIDPŒxSGP SGP ÈŒINK INK ÌŒBTEPPLC ÐŒ0o spot any oAim:

My aim is to investigate how resistance in a wire, is affected by the length.

Variables:

I am aiming to investigate the output variable (resistance) by changing my input variable.

Examples of input variables, in this experiment are:

The width of the wire

The length of the wire

Discussion of variables:

I am now going to suggest what I believe would happen to the resistance, if I were to change the input variable. A variable diameter can change the area that free electrons have to move within; if  the diameter increases there will be greater space for the electrons to flow in, consequently this causes a drop in the levels of resistance as it is harder to resist particles that have more room to flow in, as there will be a lower likelihood of collision . If one was to increase the length of a wire in the investigation, then the resistance would increase: this would be due to the free electrons having a higher chance of collision. This would thus lead to more energy being lost (resisted), as heat.

Accuracy:

Accuracy is the degree of conformity of a measured or calculated quantity to its actual value: therefore to get my results

as accurate as possible, I am going to use equipment that will measure the answers to two decimal places, this means that I can quite close to the true values. I am limited to two decimal places, as the ammeter and voltmeter I am using only measures to this degree of accuracy. My meter ruler measured to the nearest millimeter, which is very accurate, however the measurements may be inaccurate by around 0.5mm; this error is so small, in regards to the measurements I m taking, that it would not affect my results, by a significant amount.

Reliability:

Reliability characterises the degree of mutual agreement among a series of individual too high, this can present obvious danger to people. I knew that by using ALARA principle, in regards to the voltage, Ohm s law would dictate that I would have a much lower chance of getting the wire too hot. I therefore preformed a preliminary experiment, to find this desired voltage.

Input Variable:

In this experiment my input variable will be the length of the resistance wire. I will test the variable on a Manganin wire, with width 0.45cm.

Output Variable:

I will be measuring the outputs of both the wire s current and voltage throughout the experiment. Ultimately, I will use these two aspects to find out the resistance that the wire experiences, using Ohm s law of voltage divided by current equals resistance.

Prediction:

I predict that as I increase the length of my wire, the resistance will increase; there is greater distance for the current to travel through. Equally, there is greater distance for the resistance to the affect the flow of current during the flow. Therefore there is positive correlation as the length of the wire increases then the resistance increases too. I also predict that as I increase the width of the wire, the resistance will drop, as the electrons have a larger area to flow through, thus there will be a smaller ratio of resistance, tot area. This will mean there will be a negative correlation between width and resistance.

Strategy:

To ensure that I have accurate and reliable results, I have devised a strategy, to make sure everything is done/set up properly. Firstly, after setting up my circuit, I double checked it against my diagram to see that it was set up properly. If I had not done this, then the readings would misrepresent what the actual voltage/current was, leading me to the wrong conclusion. I  made sure that the voltmeter was set in series to the resistance board, whilst all the other components (the board, ammeter and DC Power pack) were in a single series circuit.

        I ensured that all my components, in particular the wire material and diameter remained the same throughout: changing these would result in an unfair test. I used repeats to lower the chances of errors being included; I repeated the measurement of each length three times to allow an average to be used instead of a single figure. This allows me to comment on the reliability later on. These are the strategies I considered during my experiment.

Preliminary Work:

To enable me to carry out the experiment properly, safely and accurately I must perform a preliminary experiment. During this experiment I found that a safe voltage to work at was 4V; I also found that despite what the power pack says, the voltage is very different thus I introduced a rheostat into my circuit. Two of my variables - material and width - were limited by the fact that I could only use the available equipment, thus I had to choose between three metals: Manganin, Constatan and Nichrome - I found that Manganin performed similarly to the other two materials, but didn t heat up as much. I was also limited to the widths: 0.28, 0.31 and 0.45. I found that the larger widths were less responsive at lower lengths, thus using 0.45 is safer. I did however have to come up with safe lengths to work at; I found that anything under 10cm was unsafe, as the wire became too hot and could therefore snap or set alight.

Interpreting Data:

Variable: Length

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Voltage: 4        Width: 0.45        Material: Manganin

Conclusion:

Trends and Patterns:

The obvious trend that I can decipher from studying my graph is that as the length of wire increases, so does the resistance: just as I predicted before the experiment.  

Comment on Graph:

My graph shows strong positive correlation between the two factors, the line also appears to come form the origin. The graph also appears to be very linear, this highlights the fact that the results they are very equally spaced. From these observations made, I can safely say that increasing length of wire is directly proportional to the increase of resistance. I believe I will be able to make a strong, steadfast conclusion from this graph.

Conclusion:

To prove the very strong positive correlation displayed in my graph I can provide a quantitative example. If one took the wire length of 0.4m and doubled this to 0.8m, they would find that the difference between the two output variables has doubled. The resistance of 0.4m is 1.06 Ohms, when comparing this to the 0.8m length of wire we see that the resistance has more or less doubled to 2.16 Ohms. The true doubled value is 1.12 Ohms. The proximity between these two resistances prove how direct the proportionality us between the two factors of length and resistance on my graph. This is because when one doubles the length of wire, it is effectively equivalent to two identical resistances in a series. Doubling the length of the wire is equivalent to having 2 lengths of wire half the size. Therefore the resistance will increase by x2 in both these cases as resistance is proportional to length. The following equation finds the resistance in a series circuit.

 R = r¹ + r²

R¹ and r² are the resistors. Adding them together finds the total resistance (R), this works in the same fashion for doubling one resistor as opposed to adding another equal one.

It is hard for me to construct a formula that will precisely connect both the input variable and output variable. This is because the voltmeter is not exactly consistent, as I have encountered during me experiment. The voltmeter often provided readings of around 0.01 or occasionally 0.002 outside of previous repeats. This could be because the temperature uncontrollably changes very slightly throughout the investigation. However, I can create a formula that will connect input variable (length of wire) to a close yet not precise resistance.

R = 0.27 x Lcm/10

In this formula:

R = Resistance (output variable)

Lcm = Length of wire in cm (Input variable)

I have decided to use the figure 0.27 as it is the modal resistance I encountered upon when I tested the wire at 0.1 m (10 cm). I decided to use the mode (0.27) instead of the mean (0.26), because the mode is more representative of what one test for resistance would reap. It is the most likely resistance to be encountered upon, purely because it occurs most commonly. (0.26 was the resistance on two out of three repeats). This will ensure that the results can be as close to the real resistance as possible. 0.27 is the resistance for the first length, it is number 1. This has much potential to intertwine into what we plug into the formula (For example: 0.27 x 100cm/10 = 2.7 Ohms).  I decided to use cm and then divide these by 10 to convert the figure to mm. If I had shortened the formula and used  Lmm , then things would complicate. For example, if the input length (mm) was less than 1m then the figure could be a large value (anything up to 999), when multiplying 0.27 by this, the number is decidedly larger than the value we require (Eg. 0.27 x 999mm = 269.73 Ohms). This is clearly wrong as my graph states that lengths of around 1m should only be 2.66 Ohms. Therefore using cm means that this problem can be overridden.

I will now test the formula to find the approximate resistance on a 0.8m (80cm) wire. It is predicted that the resistance will be 2.16 for this length, in accordance with my graph

R = 0.27 x 80cm/10

This all amounts to R= 2.16 . This figure matches exactly with my graph and results table for 0.8m.

I will conclude this section by testing another length. For 1.1m length the formula stands at:

R = 0.27 x 110cm/10    

This all amounts to R =2.97 . When comparing this figure with the accumulation of my table of results, the 2.97 answer seems a realistic step up subsequent to 1.0m s 2.66 , with a difference of 0.31.

Evaluation:

Comment:

I believe that my procedure over my investigation has been well organised and monitored; this has led to an extremely promising set of results, which can be used with ease to make strong conclusions.

Quality of evidence and anomalies:

As mentioned previously, I believe that my work went very well. I came out with a good set of results and what I planned to achieve has been collected and completed. There was some miniscule variety within my results; this appeared often throughout my repeats. However the changes, could not be considered outliers or anomalous. They likely occurred due to slightly inconsistent conditions with regards to temperature. I can prove that there have been no anomalies occurring, as my graph contains error bars that barely stray from the line of best fit. In fact, on some of my points these bars are scarcely visible.

Suitability of technique and improvements:

The fact that I do accommodate error bars shows there cannot be complete precision. As I explained before, I believe that as resistance and temperature are proportional, that the temperature has been responsible for the minute variance in my repeats. Overall however, the results mainly show much accuracy. According to my research, the true values when it comes comparing resistance and length of resistor is that both factors increase at the exact same rate as each other. This idea was explained in my interpreting data conclusion. My results show very similar circumstances. As I showed in my above conclusion, my results approximately follow the course in accordance with the true theorem, but they are not fully precise as my variance in repeats has caused the occurrence of some slightly faulty averages, consequently detracting from full precision. My work does show traits of being very consistent, with my points being consistently spaced without any anomalous changes.

Reliability and reasons for anomalies:

The evidence here is reliable, and I have encountered only one apparent anomalies and this was expelled straight away and was not included in my averages or graphs. However, many aspects of the technique and surroundings could have caused my slightly inconsistent repeats, however this is usual and as they were very close together, I am still confident in my conclusion.

By Zak Arden          

Investigation:  How length affects the resistance in a wire.

Length

1

2

3

Mean

0.1- Voltage (V)

4.00

4.01

4.02

Current (A)

14.81

14.82

14.83

Resistance (W)

0.27

0.27

0.26

0.27

0.2- Voltage (V)

4.02

4.02

4.01

Current (A)

7.41

7.41

7.41

Resistance (W)

0.54

0.53

0.54

0.54

0.3- Voltage (V)

3.98

3.99

4.02

Current (A)

4.88

4.88

4.89

Resistance (W)

0.82

0.82

0.81

0.82

0.4- Voltage (V)

3.99

4.02

4.00

Current (A)

3.81

3.82

3.80

Resistance (W)

1.05

1.06

1.05

1.05

0.5- Voltage (V)

4.00

4.00

4.01

Current (A)

3.01

3.00

3.01

Resistance (W)

1.33

1.33

1.34

1.33

0.6- Voltage (V)

4.00

3.99

4.01

Current (A)

2.44

2.43

2.44

Resistance (W)

1.64

1.66

1.64

1.64

0.7- Voltage (V)

3.99

3.99

4.00

Current (A)

2.15

2.15

2.14

Resistance (W)

1.86

1.86

1.86

1.86

0.8- Voltage (V)

4.01

3.99

4.01

Current (A)

1.85

1.84

1.85

Resistance (W)

2.16

2.16

2.15

2.16

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""Ž""ø"FD


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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""]""Â",Ò

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""Ž""ø"FD


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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""Ž""ø"FD


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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""Ž""ø"FD


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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""]""Â",Ò

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

""""""ÿÿÿÿ "ƒigÿ!i""#"ƒigÿ$i%"&"'(")"*+",ÿÚ""Ž""ø"FD


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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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" ""8âÿ?ÿâ

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