IB Higher Physics
Internal Assessment

Candidate Name: Aleksei Kuryla
Candidate Number:

Title: resistivity of nichrome

|D |DCP |CE |
| | | |

DATA COLLECTION AND PROCESSING

| |Criteria |( |Mark |Comments |
|Aspect 1 |Raw results only shown | | | |
| |Correct units | | | |
| |Uncertainties shown | | | |
| |Uncertainties justified | | | |
| |Uncertainties to 1 sig fig | | | |
| |Decimal places consistent with uncertainty | | | |
|Aspect 2 |Processed results shown in separate table | | | |
| |All necessary values shown | | | |
| |Correct units | | | |
| |Uncertainties correct | | | |
| |Uncertainties to 1 sig fig | | | |
| |Data shown to correct number of sig figs | | | |
| |Sample equations shown for all calculations | | | |
| |Sample equations correct with units | | | |
|Aspect 3 |Graph fills whole page | | | |
| |Axis labelled correctly with units | | | |
| |Axes adjusted if necessary | | | |
| |Correct uncertainties shown on graph | | | |
| |Max and min gridlines drawn correctly | | | |
| |Lines drawn to calculate gradient clearly shown | | | |
| |Gradient uses at least half the line | | | |
| |Max and min gradients calculated correctly | | | |
| |Gradient calculations shown | | | |
| |Units shown for gradient | | | |
| |Sig figs correct for gradient | | | |
| |One sig fig for uncertainty | | | |
| |Processing for final value explained and shown | | | |
| |Units, sig figs and uncertainty correct for final value. | | | |
| | | |/6 | | |

CONCLUSION AND EVALUATION

| |Criteria |( |Mark |Comments |
|Aspect 1 |Answered the research question | | | |
| |Compared to referenced literature value | | | |
| |Discussed magnitude of uncertainties compared to calculated | | | |
| |value | | | |
| |Describe pattern of trend line and explain its shape by | | | |
| |linking to an equation | | | |
| |Discussed evidence of systematic errors and effect on | | | |
| |results | | | |
| |Discussed evidence of random errors and effect on results | | | |
| |Discussed reliability of results | | | |
|Aspect 2 |Identified all the main sources of error | | | |
| |For each source of error identified what caused it using | | | |
| |relevant physics | | | |
| |For each source of error state the significance relative to | | | |
| |other errors, referring to evidence | | | |
| |For each source of error state effect on final result (eg. | | | |
| |increased/decreased) | | | |
| |For each source of error state if error is systematic, | | | |
| |random or both | | | |
|Aspect 3 |For each limitation sensible improvement to method described| | | |
| |Describe how equipment may reduce random/systematic error | | | |
| |For each limitation sensible equipment and precision | | | |
| |described | | | |
| |For each limitation sensible range of independent variable | | | |
| |described (if applicable) | | | |
| | | |/6 | | |
| |
|What I have learned from this piece of work… |
| |
|The targets for the next piece should be… |
| |

Raw data:

Raw data table

This table shows the voltage and current measured while changing the length of a nichrome wire in a circuit. On the left is the length of wire used at which the measurements for current and voltage were taken and on the rest of the table are the three trials for voltage and current at the certain length. My uncertainty for length was 1 cm because that was the smallest unit in the ruler used to measure it, my uncertainty for voltage and current were 0.1 V and 0.01 A because that is how much the reading in the voltmeter and ammeter fluctuated. The reason why I determined the uncertainty for the diameter to be 0.00001 m is because that is the level of precision for the digital calliper I used.

Processed data:
[pic]

[pic]

To get value for the radius of the thickness of the nichrome wire, I divided the diameter in 2. To then determine the area of the cross section I used the formula [pic] and squared the radius and then multiplied that times 3.14.

I divided my values for length by 100 in order for the units to be in metres. I got the average for the voltage and current by using the formula (trial 1 + trial 2 + trial 3)/3 and then I divided voltage over current, in order to get the value for resistance, [pic]. After that, I multiplied my value for resistance times the area of the cross section.

In order to calculate the uncertainty for radius, I divided the uncertainty for the diameter by 2 and to calculate the uncertainty for the area of cross section I got the relative uncertainty by dividing the uncertainty for the radius by the value for the radius, multiplied the relative uncertainty times 2 and then multiplied it by the value for area. To calculate the uncertainty for the resistance, I got the relative uncertainties for voltage and current in the same way as I did for the radius and added the two values, after which I multiplied it times the value for resistance. Finally, to calculate the uncertainty for the area times resistance, I added the relative uncertainties for area and resistance and multiplied that times the value for area times resistance.

Graph:
[pic]
Calculations:
[pic]
[pic]
[pic]

Maximum gradient

Δy= 4.8 × 10-6

Δx= 0.98

[pic]

[pic]

p = 4.9 × 10-6 Ωm

Minimum gradient

Δy= 6 × 10-7

Δx= 1.1

[pic]

[pic]

p = 5 × 10-7 Ωm

Average value for resistivity

p= ((4.9 × 10-6)+( 5 × 10-7))/2

p= 2.7 × 10-6 Ωm

Uncertainty for resistivity

((4.9 × 10-6)+( 5 × 10-7))/2

Uncertainty = ± 2.2 × 10-6 Ωm
Conclusion:

My graph shows that resistance multiplied by area shares a linear relationship with the length of wire, they are directly proportional. They behave according to the formula [pic]or [pic]and that is why while plotting the resistance multiplied by area against the length of wire, you get the resistivity of nichrome of the wave for a gradient.

With my experiment I could find out the value of the resistivity of nichrome, which was (2.7×10-6 ± 2.2×10-6) Ωm. The literature value for the resistivity of nichrome is p = 1.5×10-6 Ωm (Faughn, 2003). The established value is within the range of my value’s uncertainty, therefore, my value is accurate. My uncertainty was 81% of my value which I consider to be very large and therefore my experiment was widely imprecise. I believe the method was relatively effective because the value we got was accurate which allowed us to, even though it was not very precise, get a value for the resistivity of nichrome within the range of the uncertainty. There were large amounts of source of error in the experiment, both random and systematic. One of the main systematic sources of error being the increase in resistance as the temperature of the wire increases, giving the graph a very slightly curved shape. The experiment could have been more accurate and precise if the results would have been taken using an ATC (automatic temperature compensation) facility, which would have cancelled out the systematic error caused by temperature and used more precise equipment in order to reduce uncertainty.

|Limitation |Systematic/random |Effect on final result |significance |improvement |
|Increasing temperature in the wire|Systematic |Due to the temperature of the wire |As the temperature changed as the length of the |One way of improving this experiment could be|
|increases resistance | |increasing, the resistance in the wire |wire changed, each result was affected by how |to perform the experiment on a longer wire, |
| | |increases as well. This is because the |much temperature was on the wire. As the |for example a 3m long wire, along with a |
| | |charges in the wire collide against the |temperature affected the proportionality of the |wider range of results (30 results on 10 cm |
| | |particles beside the sea of delocalized |formula [pic], the shape of the graph, which |intervals) taken for the effect of |
| | |electrons, which when they have a high |should have been completely linear, became |temperature to be less drastic on the |
| | |temperature, the collisions in between |slightly curved and because of that, the maximum|results. The voltage provided to the circuit |
| | |these particles and the charges send the |and minimum gradient we took were imprecise. |could be lowered in order for the cable not |
| | |charges in all direction and not just in | |to heat up as much. Another, more precise way|
| | |the direction of the flow of charge, | |of not letting the temperature affect the |
| | |which causes there to be a higher | |final result as much could be to use an ATC |
| | |resistance. So the value for resistance | |(automatic temperature compensation) |
| | |changes depending on temperature. | |facility; a temperature probe, connected to |
| | | | |the ohmmeter, senses the temperature and the |
| | | | |resistance reading is corrected to a |
| | | | |reference temperature of 20°C. |
|The pressure being applied onto |Random |The force with which the pointed metal |I believe this would affect the final results as|This could be prevented by integrating the |
|the wire was different every time | |rod which we used to finish the circuit |another of the largest sources of error and as a|metallic rod into another insulating which |
|a result was taken | |for current and voltage changed every |very large cause for uncertainty because every |should have a flat base in order for the |
| | |time because the force applied by the |time the force with which the rod was placed on |person doing the experiment not to have to be|
| | |person holding the rod could not be |the cable varied and also every time the rod was|holding the rod every time a result was |
| | |exactly the same every time. When the rod|at a different angle to the cable, both of which|taken, the person would grab the insulating |
| | |was held down with more force, there was |inevitably happened every time, the resistance |material, which could be wood, with the rod |
| | |more pressure being applied on the wire |changed from what it should be if the contact in|inside it and place it on the place along the|
| | |and therefore the wire was deformed |between the rod and the wire was the same for |length of the wire were you wanted to take a |
| | |inwards (and stretched) and there is more|every result taken. |result and it would stand on its own so the |
| | |contact in between the metal rod and the | |same force (weight) would be applied onto the|
| | |wire. When there is more contact, there | |wire and therefore the same pressure and the |
| | |is less resistance because there is a | |same amount of contact in between the metals.|
| | |wider area through which the current is | |5 trials could also be done instead of 3, in |
| | |going through in that particular space. | |order for the uncertainties to affect the |
| | | | |final result less. |
|Dirty or rusted equipment cause a |Random and systematic |Equipment with dust, dirt or rust |If the resistance has been increased due to a |We could ensure that the equipment is on |
|change in resistance at that point| |covering can change the readings taken |partially insulating layer on either the rod or |perfect state every time we are going to use |
| | |because any of these can act as |the wire, the final result is altered because we|it and clean it before the experiment begins,|
| | |insulators while in contact. When the rod|are measuring the resistance through measuring |using alcohol. We could also buy new |
| | |touched the wire at a point at which |the voltage and current and if the resistance |equipment which is made of a metal of a less |
| | |either of the two had some sort of dirt |varies, the final result changes as well, giving|easily oxidizing metal and which still acts |
| | |or rust, the resistance increased because|an inaccurate and imprecise final answer. |as a good electrical conductor, such as gold.|
| | |the dirt and rust act as insulators in |However I believe this source of error did not |The equipment could be kept in a completely |
| | |the circuit. |affect the final result too much because there |clean and sterilized room while it is not |
| | | |was little rust and dirt on the wire and rod. |being used. |

Bibliography

Faughn, J. S. (2003). College Physics. California: Thomson Learning Inc.