Using my results I will plot a y = mx + c graph so that I can see the relationship between the current and the voltage. I predict that the graph and straight line will look like the one below:
The y-intercept on the graph will be the Emf and the gradient of the line will be the internal resistance of the cell.
For this experiment I will be using 5amp wire. I will not be using a high current, but if I were to use a current higher than 5 amps then there would be danger of a fire occurring.
From these results in the above table I am going to produce a
y = mx + c graph. From the graph I will calculate the internal resistance and the Emf of the dry cell in my circuit.
On the graph I have plotted the above results, but due to the sensitivity of the meters used there may have been some inaccuracy in the data. Consequently I have drawn error boxes around the results. The size of these is 0.1v big.
By using the error boxes I have been able to also draw on to the graph three lines of best fit: a maximum line, a minimum line and a normal line of best fit. These will enable to do my calculations later on.
As you can see on the graph, there are four anomalous results, these have been highlighted in the results table. These anomalous may have been down to a number of problems: human error when reading the meters, the cell running down and the sensitivity of the meters.
Analysis of results and graph
From the graph I can now calculate the internal resistance and Emf a dry cell.
Internal Resistance
The internal resistance of a cell can be calculate using the following formula:
r = Vr
I
Using the gradient of the line of best fit (grey line) I can substitute these values into the formula:
r =0.6
1.2
internal resistance =0.5
As there is an uncertainty with the accuracy of these results I will also use the maximum line of best fit (red line) and minimum line of best fit (blue line) to calculate the internal resistance + the error.
r max. =0.8
1.4
Max. internal resistance = 0.57
r min. =0.78
1.64
Min. internal resistance = 0.48
Due to the Maximum having a bigger difference to the normal line of best fit compared to minimum, I will use this result to calculate the internal resistance + the error.
The internal resistance = 0.57 – 0.05
= 0.07
r = 0.5 0.07
Emf
The Emf of a cell is the y-intercept of the line on the graph. Therefore:
The Emf of the line of best fit = 1.68v
Due to the uncertainty of the results I will use the line of best fit with the biggest difference to the normal line of best fit to calculate the Emf + the error.
Emf of the maximum line of best fit = 1.75v
Emf of the minimum line of best fit = 1.66v
Hence, the maximum line of best fit has the bigger difference.
Emf = 1.75 – 1.68
= 0.07
Therefore the Emf of the dry cell = 1.68 0.07
Conclusion
Even though not all my results on my graph are in a straight line, like I had previously predicted, you can expect this due to inaccuracies and human errors when reading the meters. Although, by using a line of best fit I could still calculate the Emf and the internal resistance of a dry cell. If you do not take into account the anomalous results then the results are in a straight line.
By using a maximum and minimum line of best fit as well as normal line of best fit I was able to also calculate the error of the results. This made my final calculations even more accurate than if I had just calculated the Emf and the internal resistance by using the y-intercept and the gradient of the normal line of best fit.
As you can see from the graph the voltage and current are inversely proportional to each other. You can tell this due to the negative slope of the straight line.
