Current
A long coil of wire has a high resistance, this is because it takes more current to travel down it than a short piece of wire, this is like a runner running a race; it takes more out of a runner running 1000m at the same speed as someone running a race of 10m. There are more atoms in a longer piece of wire and therefore more collisions must occur to pass on the electron flow, so for a longer length there will be more collisions, therefore higher resistance.
Resistors in series;
V= V1 + V2 as the current is the same throughout. I know R = V, and I want to know
I
what resistance could replace R1 and R2
Resistors in Parallel;
I know that: 1. in a parallel circuit the voltage across each branch is the same
2. total I = I1 + I2
3. Ohm’s law : V = IR
My independent variable is: charge
Dependant variable is: resistance
Control is: voltage
I predict that due to my scientific knowledge, as we increase the length of wire the resistance will also increase.
The Experiment.
To find a suitable range of voltages to use, I must do a preliminary experiment to see what works, using a piece of wire; 30cm long, in the following circuit;
Results;
I will therefore use a range of 0 to 0.70 volts for my main experiment.
However, when we set up the proper circuit for the main experiment, we found that the resistance would not go as low as 0, and went up to around 3,
So we decided to use a range of 0.5 to 1.50 for our experiment.
Apparatus:
Method:
1) Set up the apparatus shown above, making sure the ammeter is in series and the voltmeter is connected in parallel with the piece of wire.
2) Connect 1m of wire to the crocodile clips, making sure it is coiled to avoid a short-circuiting.
3) Using the variable resistor, change the voltage to the following values; 0.5, 0.75, 1.00, 1.25 and 1.50 using the voltmeter to get correct voltage readings. Each time read off the current from the Ammeter and record the results.
4) Repeat this 3 times in order to get accurate results.
5) Repeat steps 1 to 4, but each time changing the length of wire to 80 cm, 60 cm, 40cm and 20 cm, each time recording your results.
6) Take an average voltage for each length of wire and amount of voltage.
7) using Ohm’s law V=IR, we can work out the resistance for each value by rearranging the formula; R= V
I
Safety precautions:
Do not touch the wire, as it is very hot when current is passing through it and place it on a heatproof mat.
Results:
1m:
80cm:
60cm:
40cm:
20cm:
I can see that as voltage increases, current also increases: ie. They are proportional to each other. I can work out the resistance from the I/V graph by working out the gradients of each line.
1m: gradient = rise = 0.08 = 0.32 = 1 therefore R= 1 = 3.125
run 0.25 R 0.32
80cm: gradient = rise = 0.1 = 0.4 = 1 therefore R = 1 = 2.5
run 0.25 R 0.4
60cm: gradient = rise = 0.16 = 0.64 = 1 therefore R= 1 = 1.56
run 0.25 R 0.64
40cm: gradient = rise = 0.2 = 0.8 = 1 therefore R = 1 = 1.25
run 0.25 R 0.8
20cm: gradient = rise = 0.44 = 1.76 = 1 therefore R= 1 = 0.56
run 0.25 R 1.76
These gradients are all correct, proving that the ohm’s law is correct.
From my length/resistance graph, I can see that resistance increases when the length of wire increases. If they are directly proportional, y will equal mx where m is the gradient and x is the x co ordinate and y is the y co ordinate.
We can prove that length and resistance are directly proportional;
Gradient = rise = 0.6 = 0.03
run 20
if y=mx and m=0.03 and x= 40cm then the y co ordinate will equal
0.03 x 40 = 1.2 ohms
and true enough, we can read from our graph that when x=40cm, y=1.2ohms
since y = resistance, m= the gradient and x = length, we can construct the formula;
resistance = gradient x length
this information provides a solution to the electrician’s dilemma as it allows us to substitute in the resistance value and using the gradient found of 0.03 we can work out the length of wire required.
1.9ohms = 0.03 x length
length= 1.9 = 63.3 cm
0.03
For a resistance of 1.9 ohms the electrician will need a piece of 26 s.w.g. (the same as in out experiment as we are using out gradient) with a length of 63.3cm
28.5 ohms = 0.03 x length
length = 28.5 = 950
0.03
For a resistance of 28.5 ohms the electrician will need a piece of wire which is 950cm long.
From this information I can see that my prediction was correct, as resistance increases with the length of wire. We can see this from the graph and the mathematical formula. This backs up my scientific knowledge, which states that as There are more atoms in a longer piece of wire and therefore more collisions must occur to pass on the electron flow, so for a longer length there will be more collisions, therefore higher resistance. This is the main reason that resistance is directly proportional to length. If we have a piece of wire 40 cm long, and the resistance is 1.25 ohms, for a piece of wire 1m long, the resistance is double that: 2.5 ohms, as we have proved this in the experiment. This is sufficient evidence to further prove the equation, which relates to length being directly proportional to resistance.
Conclusion;
We can see that this procedure worked well enough to provide sufficient evidence to prove that the length of the wire affects resistance and to notice a mathematical relationship.
The experiment was quite accurate, as all the results seemed to be very accurate and reliable. However in the preliminary work we had a problem with the voltage, this is possible because we could have used a slightly different rheostat of a different s.w.g. of wire, however we were able to solve this problem by using a suitable range of voltages found immediately before the main experiment was carried out.
We could have made a couple of adjustments to get even more precise results. It is possible that temperature affects resistance, and as we were not measuring the temperature we cannot be sure that this wasn’t an influential factor. To solve this problem, we could have put the circuit in a vacuum, as this removes any air, therefore preventing convection, and it does not allow radiation to pass through and is not affected by conduction. It is very possible that out measuring of the wire was not exact, as it was hard to get the wire perfectly straight. This could be improved by carefully ensuring the wire is perfectly straight and greater care in the measuring and cutting of the wire.
We could extend the experiment by perhaps using much smaller and/or much bigger lengths of wire to see if the mathematical procedure works exactly the same. This experiment would be carried out in exactly the same way as the one above but using different values for the length of wire. This would create a greater range of results, therefore making the whole experiment more reliable. To improve the reliability we could use a larger rheostat, making it easier to get the exact voltage and therefore creating more accurate results. Using a wider range of voltages to further test the findings could also extend the experiment.