To measure voltage and current in the circuit and from that figure work out emf and internal resistance of the cell, to identify errors involved and deal with them in the most effective way and maintain a safe working environment at all times.
EMF (electromotive force) is a measure of work done per unit of charge and is measured in volts. Internal resistance is resistance in ohms of the cell. I will be using a 1.5V battery in the experiment. I will measure the voltage and current using multimeters.
I intend to rearrange the equation ‘ε=Ir+IR’ to form ‘V= -Ir +ε’ and then draw the y=mx+c graph equation to find EMF and internal resistanc`e. The y axis intercept measures EMF and the gradient gives you internal resistance.
Projected main sources of error
The multimeter has some inaccuracies: Resistance is accurate to 0.1 ohms (+/-0.8%), Current is accurate to 0.03 A (+/- 2%) and voltage is accurate to 1 mV (+/- 0.5%). These on their own are minor problems but may have a cumulative affect. The resistance of all the wires joined together is 0.6 ohms. But the biggest uncertainty after early testing is the fluctuations on the ammeter, the ammeter very rarely settles on a value which leads to an inaccuracy of 0.02 volts (+/- 0.01 volts) and 0.02 amps (+/- 0.01 amps). This uncertainty could be very high especially with lower values First experiment
I started with a simple experiment to get figures from which improvements could be achieved.
This is the circuit diagram of my first experiment
It was soon clear that the variable resistor didn’t have the necessary resistance to induce the current necessary for the experiment. I replaced the original variable resistor with a rheostat as the resistance could be changed in a more linear way rather than with the exponential increases of the variable resistor. There are few safety hazards in my experiment but to be sure I made sure there was no copper showing in wires, only touched the rheostat when it wasn’t connected to the cell and was wary of dangers associated with being near other experiments.
My initial results were very encouraging as the correlation was very strong. I repeated the same experiment but taking more time. These results form a clear negative correlation. However at the end of the experiment, the results went away from the line of best fit sharply showing there was a mistake that clearly occurred during the experiment. I originally thought this was a problem with the battery heating up over time so decided to measure resistance of rheostat in my next experiment so the battery would have a time to cool down.
See atatched graph (next page)
I also measured the voltage from my battery in between experiments and discovered my ‘1.5V’ battery to be producing 1.559V, a percentage error of 4%. To try and rectify this problem I tried new batteries until one with a very low percentage error was found, one with 1.503V which had negligible error.
As my initial first experiment brought back good results I thought no large scale changes were needed to my experiment. I decided to measure resistance of rheostat in between measuring voltage and current in the circuit, as at the time I believed the battery heating was the problem it would give it time to cool. The circuit diagram is the same as before with resistance on a side experiment measured. The results were initially good but then tailed off and the correlation even went in the wrong direction. Two attempts returned very similar results.
I thought this may have been as a result of the battery overheating as it had been on for a long time, as I initially struggled to get a reading as the resistance reading was very low. When the resistance on the rheostat is very low anomalies are produced. The battery produces a large fluctuating current, this is because if there is low resistance a high current is produced. The chemical energy in the battery isn’t quick enough to regenerate the power. I also used the same safety precautions as before as there was no new dangers associated with my slightly altered experiment
I changed my experimental method considerably for my third experiment. I worked out that the rheostat may have been overheating on its own or at the same time as the battery so I stopped taking resistance readings and introduced a switch into the circuit so the battery and rheostat are used for as little time as possible. I also did a final experiment without the switch as well as repeating the experiment with a switch.
Final circuit diagram
My best results were obtained from the final experiment with the switch, all of the final experiment results form a clear correlation. These are my final results. I did my final experiment again and have combined the results on to one graph to show the correlations.
My value for EMF is 1.45 volts with uncertainty +/- 0.1 volts. This is calculated using ‘V= -Ir +ε,’ at the x axis the ‘-Ir’ part of the equation =0 so ‘V=ε’ at that point so that is where the value is reads off from. If ‘V= -Ir +ε,’ is substituted into ‘y=mx+c’ the internal resistance is the gradient of the graph. My value for internal resistance is 0.1 ohms with uncertainty of +/- due to its lack of size. These results are taken from my final graph only. My error bars in both directions are combining all the uncertainties in the experiment.
My data points effectively fit a correlation. The emf value is the y intercept because when However as the current increases the data points get further apart. This is likely because they are combined from two different experiments and the battery or rheostat may have been heating up during the experiment, it is clear that to get the best correlation the various components must be ‘off’ as much as possible. I also made sure that there was no short-circuit results in my final results as that would have severely impacted the correlation making it inaccurate. If I was too do the experiment again I would have done these two sets of results directly after each other as the cell as clearly run down on the experiment between I took these readings. I would also take many more sets of data so I could be certain the correlation was correct and had the most accurate value of Emf and internal resistance.
I would use the switch from the start as much of the chemical energy may have been used up on the battery over time, especially when low resistance was short-circuiting it as its emf appears to have dropped from 1.503 volts at the start of the experiment to 1.45 volts at the end of the experiment. I would also have used more accurate multimeters to reduce the uncertainty in the experiment. I would also have tried batteries if different power ratings to see which batteries would give an emf value closest to its power rating. This experiment has very small errors as there is little possibility for human error, reaction time doesn’t come into it as the readings are given electronically. It is also a very safe experiment as there is very little possibility for injury but I still took every necessary precaution for my own safety and those around me.