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# Investigating the E.m.f and Internal Resistance of 2 cells on different circuit Structures.

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Introduction

Khaled Hamid        Page

Investigating the E.m.f and Internal Resistance of 2 cells on different circuit Structures

Background Knowledge:

For this investigation the main variable will be the circuit structure and positioning of the two cells. Therefore I will discuss in brief the most relevant aspects of the electricity module regarding this investigation. These are the electrical circuits, the electromotive force and the internal resistance.

Circuits: According to Kirchoff’s first law, the series circuit is one in which the components are connected one after another, forming one complete loop.

Diag1:

The next circuit I will also be using is the parallel circuit. I am using these two circuits because the main aim from this investigation is see how the two circuits influence the e.m.f and the internal resistance.

The parallel circuit is one where the current can take alternative routes in different loops. The current divides at a junction, but the current entering the junction is the same as the current leaving it.

Therefore: I = I1 + I2 + I3

Diag1:

Electromotive force

The second factor involved in the investigation is the electromotive force. When charges pass through a power supply such as a battery, it gains electrical energy. The power supply is said to have an electromotive force (e.m.f). The electromotive force measures in volts, the electrical energy gained by each coulomb of charge that passes through the power supply. E.m.f is not actually a force however. The energy gained by the charge comes from the chemical energy of the battery.

e.m.f =        energy converted from other forms to electrical

charge

The electromotive force in a closed circuit is also equal to the sum of the potential difference. Therefore:

E = IR + Ir

R – external resistance                        r – internal resistance

Middle

The reason for the potential difference dropping could be due to more current flowing and causing chemical reaction in the cells therefore increasing the internal resistance which resulted in the potential difference dropping unusually.

There were fortunately not any other anomalous results which is very fortunate and this meant I had a reasonably more accurate result table compared to others in the group, as I had compared my results with others and I believe my results are extremely accurate to full human capabilities excluding other physical factors of cell heating up and creating resistance and the fact the resistors could also have been faulty and below or above the stated value they were given by the manufacturer.

Graph analysis

The graph showed a relatively straight line which corresponded to my graph hypothesis for each circuit.

In series circuit with two cells the graph showed a relatively straight line with the p.d across each resistor ranging form 2.5 – 3.0 volts. This is very close to the e.m.f 2.96. As the current was increasing the voltage was decreasing which obeyed ohms law of ohmic conductors but inversely proportional. I extended the line to calculate the e.m.f and substituted the value of x (I) for the current into the equation V = -rI + E to correspond to y = mx + c

In a parallel circuit the trend is exactly the same to the trend in the above circuit, however the values were halved. That was the only difference.

In a series circuit, the trend was exactly the same as the trend on the graph showing a V against I for parallel circuit with two cells, which meant is identical to the series circuit with two cells but exactly halved.

Results table for series circuit with two cells

Conclusion

Series circuit with two cells:

First range of line of best fit - +1.25

Second range of line of best fit -  -1.25

Therefore the error margin for original values is approximately plus 0.04% and minus 0.04% -> 0.04%+-

How could the investigation process be enhanced?

It is difficult to suggest major improvements fro this investigation. However below are some of my improvements that I would like to happen in any future investigation. These factors concentrate mainly on

• The value of resistor specified must be used. This should be checked before used
• Any faulty equipment should be checked and replaced. In my investigation I did not check for any faulty equipment. My results had a positive outcome but I believe many others using the equipment given had faulty equipment therefore it is fair to say that any faulty equipment would affect the result and cause inaccuracies and therefore should be avoided.
• The time should be recorded for each resistor in a closed circuit, or all circuits with different resistors should be in a closed circuit for a fixed time. This ensures that there is not excess current or voltage recorded and therefore not being part of the results and causing limitations to the investigation
• There should be more range of resistors and more repetitions should be taken for this investigation and the average should be used as the more the objective is conducted and the more results and pieces of data generated ensures that the investigation is far more accurate
• The investigation could also be carried out to check how different value e.m.f that cells have and how varied the internal resistance values are
• The e.m.f and internal resistance could also be investigated further to show if there is some sort of relationship between the connecting leads and the values of e.m.f and r.

This student written piece of work is one of many that can be found in our AS and A Level Electrical & Thermal Physics section.

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