It is possible to work out the current that flows when a power source is connected to an external resistor, R. R and r are in series and given that the current flows through both, one after the other, their combined resistance can be written:

E=IR + Ir or E=I(R + r)

E cannot be directly measured because a voltmeter can only be connected across the entire cell, including the cells internal resistance, r. When a voltmeter is connected across the cell the result returned is the terminal p.d. V using this formula

V=IR

By examining the previous formula, this is less than the e.m.f by Ir, referred to as lost volts, and by combining the last two equations I get the following:

V=IR – Ir or V=E-Ir

As a word equation, this is written as terminal p.d = e.m.f – lost volts.

The e.m.f can also be calculated using another method, by plotting a graph of Voltage against Current. The graph should result in a straight line because the graph of V against I is proportional. The equation for a straight line is Y = MX + C, which can be applied to the e.m.f formula V = E-Ir, given that the voltage is on the Y-axis, the intercept (c) equals the electromotive force and the gradient (m) is equal to the internal resistance r.

Using these formulas and this newly acquired knowledge, I will be able to find the electromotive force, lost volts and internal resistance of a standard laboratory power pack.

### APPARATUS

- Power Pack – Standard Laboratory 12v
- Leads – Copper insulated wires
- Ammeter – 0-10A
- Voltmeter – 0-10V
- Rheostat – 5 amps, 20 Ohms max.

### PRELIMINARY WORK

As a preliminary experiment for this investigation, I was introduced to the principle of electromotive force, by being asked to measure the open voltage of a dry cell (1.5V battery). By only connecting a voltmeter to the dry cell, I could measure the e.m.f, as a voltmeter has a very high resistance, (around 1,000,000 ohms (1MΩ) minimum) it wouldn’t affect the voltage in any major way. The results were surprising, as the voltmeter returned a result that was higher that that stated on the battery! This lead me to discover that the actual output of the battery is higher than stated but is affected by a special type of resistance, internal resistance. This is basically another resistor located inside the power supply, (in this case it would be in the chemicals making the reactions and creating the power.)

### SAFETY

The experiments in this investigation are fairly safe in that not safety equipment (apron, goggles, etc.) need be worn, however, it should be noted that the rheostat will become very hot after power is put through it, and must be left to cool down before handling it.

### FAIR TEST

In order to make this experiment a fair test, several factors have been taken into consideration to make the experiment accurate. Firstly all of the same equipment will be used throughout the investigation, as this will affect the results from the power pack. The rheostat will be allowed to cool down in between experiment repeats, to make sure that the temperature is not affecting the results in any way, and finally, the same number of results will be taken from each repetition, as this will be used on the table to calculate the gradient and will be the basis of the results.

### DIAGRAM

### PREDICTION

I predict that, based on my initial research, the resistance will become reduced as the current is increased; this should not affect the internal resistance, which (hopefully) will remain the same. The e.m.f should also be slightly higher than the stated voltage on the power pack, as the e.m.f is the highest value for energy.

Method

- Set up the apparatus up as shown in the above diagram.

- Set the rheostat to it’s minimum value

- Make note of the results on both the ammeter and the voltmeter

- Increase the current using the rheostat and take at least 5 more readings.

(NOTE: the voltage on the power pack must remain the same for the whole process)

- To further the experiment, repeat the entire process using a different voltage on the power pack.

### RESULTS

By taking the gradients from the different graphs I have attained the following results for internal resistance and e.m.f.

### CONCLUSION

Looking at my results, I found that the voltage of the circuit was reduced as the current increased. This, as according to my graphs, leads to a decrease in resistance with a line of best fit following a straight line. My predication, based on background research and previous knowledge, was accurate and indicated the results. This reduction follows ohms law, as the decrease is proportional to the other calculated results. From the graphs I can calculate both the e.m.f and internal resistance for the power supply. The y-intercept gives me the value for E, and the gradient of the line of best fit gives me the value for -r, a negative value of the internal resistance, using this method gives a fairly accurate result even though the result was limited by the voltmeter’s2 decimal place display.

I also noticed that the internal resistance changed when using higher voltage reading on the power pack, this was due to an increase in current. Due to this observation, I have noticed that r cannot be simply described as an extra resistor located inside the power supply. The internal resistance is tiny in comparison to the external resistor, this allows for an efficient transfer of energy.

EVALUATION

In retrospect I have noted that the digital meters gave the most accurate results possible, the rheostat was the most accurate method of controlling the value of the current. The power pack kept the voltage in the circuit at a steady level before it is changed by the modification of the current, these features combined meant that the procedures taken during this experiment were suitable for this investigation.

The investigation showed no anomalous results, which can be attributed to the repetition of results in order to determine an average. This provides an evidential mark of consistency for this method of data collection.

I noticed during the collection of results there was instability in the voltmeter and ammeter of

± 0.2v and ± 0.1v respectively. This, obviously lead to certain mistakes being made through a simple case of choosing the wrong result, therefore leading to a error range of 4 volts and 2 amps. I have included a graph of current against potential difference, which includes error bars; this shows how the fluctuation on the voltmeter can have an effect on the results accumulated.

There was also an issue when trying to take reading at low temperatures; this was due to a reduced sensitivity on the rheostat. The result of this incident was that the accuracy of results at low voltages has a greater error range. This cannot be displayed on the graph as there is no direct indication as to the new error ranges. If I could get an opportunity to repeat this investigation in ideal conditions I would use a rheostat with a greater range of selections, this (hopefully) would reduce the error on lower voltages.

There were many limitations that I encountered during the conduction of this experiment; mainly this involved the equipment and digital readouts. Replacing these with significantly more accurate pieces of equipment would reduce the error range for the gradient, therefore giving more accurate final results. I would also spend a lot more time on taking many more results, especially in the lower voltages, as this would help in reducing the amount of error from the rheostat.