Preliminary Results
My results show me that as the length of the wire increases so does its resistance. In my actual experiment I will get 3 sets of results and calculate average in order to obtain precise readings. I found that I should use a low voltage in order to keep the heat generated as low as possible. Using a very high voltage could have burnt the wire or the lab unit. During the experiment the wire heats up, this causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons.
This increase in collisions means that there will be an increase in resistance. So to eliminate this ‘extra’ resistance I will have to turn the power pack off after a while to let the wire cool down. I would also need to ensure that the crocodile clips were placed in the exact positions on wire e.g. 10, 20… cm etc. this would ensure reliable and more exact results.
All these will have to be taken into account and will help me to minimize errors when calculating the resistivity of my unknown piece of wire.
Prediction
I predict that as the length of the wire increases, so too will its resistance. If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this the length increase should be proportional to the resistance increase.
So if the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. My graph should show that the length is proportional to the resistance.
Resistance means the property of anything to constrict the flow of electrons (a current). The electrons that carry the energy within the metal wire collide with "obstacles" (atoms) inside the wire and change direction. (The atoms in the wire are obstacles to the electrons.) This is known as scattering. This causes electrical resistance. Therefore, I can predict that the electrons will collide with the atoms, when the atoms have more energy, more often. The graph that I am expecting should look something like:
Theory
We define the resistance of a material as resistivity. 2 factors affect the resistance of a conductor are its length and its cross-sectional area.
Resistance α Length
(Doubling length doubles resistance)
Resistance α 1
Area
(Doubling the cross-sectional are halves the resistance)
Resistivity can be measured using ρ= AR
L
And R= ρL
A
Where:
R = resistance
Ρ= Resistivity constant
L= Length
A=Area
To find ρ I am going t plot a graph of R against L. The gradient of the graph will allow me to calculate ρ.
The equation of the straight line is y= mx + c
As the line will go through the origin c =o
Therefore y= mx
The Resistance will be the y-axis and Length will be the x-axis. Therefore:-
R= m×L
As R= ρL The gradient of this is ρ/A (excluding R and L)
A
So…..
m=ρ/A
ρ= mA
The area will be found by measuring the wires diameter and using the formula A=π (d/2)2
Section B- Results
The diameter of the wire was found using a micrometer.
Minimising Errors
To minimise errors the following precautions were taken:
- Method completed 3 times so that averages could be calculated.
- All results taken at same time so that temperature changes do not affect resistance
- Micrometer used to measure diameter of wire, as it can measure small distances accurately.
- Meter ruler used to measure wires length accurately.
- Power pack was turned off to cool inbetween readings so that the wire did not get hot and thus affect the reliability of my results at each value.
- I also tried to minimise human error in the experiment, such as putting the crocodile clips on the exact lengths and recording the readings on the ammeter and voltmeter accurately.
Section C- Analysis
Calculation
The cross sectional area of the wire is calculated using:
A= π (d/2)2
Therefore
A = 3.14 × (½ × 0.19 ×10-3)
= 2.8 ×10-8
The gradient (m) from my graph equals
m =13.8 cm
Therefore ρ = Am
= (2.8 × 10-8) × 13.8
=39 × 10-8
So my value for resitivity of the wire according to my results is 39 ×10-8
My prediction was correct because I got a straight line on my graph and this shows that the length is proportional to the resistance and as the length of wire increases so does its resistance.
I believe my experiment was good because
Section D- Conclusion
Analysis of errors
Error in the area of the wire
D = 0.19 ± 0.01mm
= 0.19 ± 5%
r= D/2 = 0.095 × 10-3 m ± 5%
A= πr2
As r is squared the % error is doubled
A= 2.8×10-8 ±10%
Error in the gradient
See the error graph
M = 14.1 ± 1.4
= 14.1 ± 10%
Error in the value of Resistivity of wire
ρ= Am
ρ = (2.8×10-8) ×14.1
= 39.4×10-8± 20%
= 39.4×10-8 ± 7.9
Possible sources of error
Systematic errors
- There may be inaccuracies in the measuring equipment. It’s possible that the micrometer may have been damaged and may not have read the thickness of the wire accurately.
- There may have been an error in measuring the location of the crocodile clips, and this may have lead to inaccurate results.
- The voltmeter takes a small amount of current from the wire
Random errors
- The temperature of the wire and the room may have lead to increased or decreased resistances.
- Thickness of the wire would not be constant, this would lead to different resistance values in different parts of the wire.
- Unknown material of wire
- The power supply may not have been constant.
Improvements
-
Errors in meters- use 3 different meters to check current, and voltage values
-
Location of crocodile clips- use pointers instead of clips to get accurate measurements
-
Some current flows through the voltmeter- I could have used an oscilloscope as it has a very high resistance so current will not go through voltmeter.
