Internal Resistance Investigation

Internal Resistance Investigation

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Internal Resistance Investigation

I will conduct the following investigation with the aim to find the
internal resistance of a lemon battery, which I will construct myself.

The variables that could affect my experiment are as follows:

· Size of lemon - I will conduct my experiment in no longer than an
hour, allowing me to use the same lemon for all results

· Size of metal electrodes - I will use the exact same electrodes
throughout the whole experiment

· Length of any connecting wires - I will use the exact same wires
throughout my experiment and will not break the circuit once I have
started collecting data

· Resistance in the circuit - I will vary this using a highly
sensitive variable resistor as shown in my method.

To make my experiment fair I will only vary the most relevant variable
to what I am investigating, which is the resistance in the circuit.
All the other variables will be kept the same throughout the
experiment as stated above.

In my experiment I will need to measure the terminal pd, V, and the
Current, I (in amps), for many values of resistance, R (in W), I will
measure these as I know that V=E-Ir so these are the values that I
need to know if I am to eventually calculate the batteries internal
resistance. I think that to make my graphs and conclusions accurate I
will need to take at least 10 measurements, covering the full range of
the variable resistor I have available to me.

To improve the accuracy of my experiment I will take my readings to
the most decimal places as my voltmeter and ammeter will allow me. To
do this I will need to make sure that I am using the milliamp/volt or
2 amp/volt setting on my meters. As I said before I will also do all I
can to ensure that no other variables other that the one I am
investigating are varied at any time during the experiment. It is hard
to determine the exact resistance that a variable resistor is set at

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but I will try to ensure that the resistances I use are equally spread
across the working range of the available variable resistor.

The apparatus that I will need available to me when conducting this
investigation is:

· A Lemon

· A Zinc electrode

· A Copper electrode

· Voltmeter

· Ammeter

· Variable resistor

· Crocodile clips

· Several insulated wires

· A sharp knife

Before I begin my investigation I will need to consider the following
safety aspects:

· Take care with knives when cutting the lemon

· Avoid contact of lemon juice with eyes (citric acid can irritate)

· Always handle electrical equipment with care



2




Method:

To complete my investigation I will use the following method:

1. Roll the lemon firmly on a tabletop to break up the small sacks of
juice inside the lemon

2. Make 2 slits, in either side of the lemon using a knife.

3. In one slit, insert the copper electrode, and insert the Zinc
electrode into the other.

[IMAGE]




4. Using crocodile clips to connect the electrodes to wires, set up
the following circuit:

[IMAGE]




5. Put the variable resistor on its highest resistance setting

6. Take a reading from the voltmeter and ammeter and record these
results.

7. Now change the setting on the variable resistor just slightly, to
give it a slightly lower resistance, and record the new readings shown
on the ammeter and voltmeter.

8. Repeat this 10 times (the variation of the resistance each time
will depend on the min. and max. resistance of the variable resistor I
have available)

When I have collected all my results I will need to analyse them. To
find the internal resistance I will draw a graph of Volts against Amps
and plot the points that I have found. I will then join these up with
a line of best fit and find the gradient. If, as hoped, my method has
been successful and my results are fair and accurate then the gradient
should be the internal resistance of my lemon battery. If there are
any apparent anomalies in my data I will do my best to detect and
explain them with regard to the relevant theory.

3




Background theory:

Lemon batteries: A small charge can be produced by putting two
dissimilar metal electrodes in either side of a lemon, and joining it
into a circuit, the charge produced is small but to give the largest
voltage possible the electrodes need to be largely different in
electrode potential. This is why I have chosen Zinc (E°= -0.76v) and
Copper (E°= +0.34) this gives a standard cell potential of: +0.34 -
(-0.76)

= 1.1v

A lemon battery because the copper atoms electrons more than do the
Zinc atoms, so if you bathe the two electrodes in a conductive
solution (Citric acid in a lemon) and connect them externally with a
wire, many electrons pass from the zinc to the copper, producing an
electrical current. The reactions between the electrodes and the
solution furnish the circuit with charges continually, this means that
the process that produces the electrical energy continues and becomes
useful. However, like any battery, this has a limited life. The
electrodes undergo chemical reactions that block the flow of
electricity. The electromotive force diminishes and the battery will
eventually stop working.

Internal resistance: Batteries are not perfect. Use them for a while
and you notice they get hot. Where is the heat from? It's from the
stored energy in every battery. So batteries turn some of their
available energy into heat inside themselves. Therefore, inside the
cell you get some energy put IN to the circuit by the cell (an e.m.f.)
some energy taken OUT of the circuit by the internal resistor (a pd)

So the pd, V, available to the rest of the circuit is:

V = E - Ir

Where: E = the e.m.f. of the cell

I = the current through the cell

And r = the value of the internal resistance

So Ir = the pd across the internal resistor

To find the internal resistance experimentally:

As V = E - Ir, if you plot a graph of terminal pd, V, against current,
I, the gradient of the graph will be equal to the internal resistance
of the cell.

(From www.s-cool.co.uk/asphysics)

From this information I have predicted that a graph of my results
should look like this:

mV

Gradient (Dy/Dx) = internal resistance

[IMAGE]

[IMAGE]

mA

4

[IMAGE]




Results:


Experiment 1
------------


(mV)
----


Experiment 2
------------


(mV)
----


Average
-------


(mV)
----


Experiment 1
------------


(mA)
----


Experiment 2
------------


(mA)
----


Average
-------


(mA)
----

387

388

387.5

0.0350

0.0345

0.0348

374

376

375.0

0.0380

0.0370

0.0375

368

369

368.5

0.0395

0.0390

0.0393

357

357

357.0

0.0410

0.0415

0.0413

344

345

344.5

0.0435

0.0430

0.0433

317

319

318.0

0.0465

0.0465

0.0465

285

285

285.0

0.0505

0.0500

0.0503

251

255

253.0

0.0550

0.0550

0.0550

211

212

211.5

0.0620

0.0625

0.0623

165

168

166.5

0.0720

0.0720

0.0720

106

104

105.0

0.0880

0.0865

0.0873

As you can see, I repeated my experiment 2 times and took an average
of the results. This should make my graph more accurate. At this
stage, I cannot see any obvious anomalous results. I noticed straight
away as I was doing my experiment that as the volts increased, the
amps decreased and this remained consistent throughout. I did not need
to make any changes or modifications to my method during the
experiment as following my pre-recorded method seemed to work just as
I had planned.

Interpretation:

From my results I have used the average of each measurement to
construct a graph of voltage against current (see graph) I have drawn
a line of best fit and believe from the look of the graph and from the
background information I collected earlier that it is a straight line.
At first it appears to be a perfect straight line, it then starts to
curve slightly. This is because, after a while, all batteries start to
deteriorate. The electrodes undergo chemical reactions that begin to
block the flow of electricity. The electromotive force diminishes and
the battery stops working. Usually what happens is the production of
hydrogen at the copper electrode and the zinc electrode acquires
deposits of oxides that act as a barrier between the metal and the
electrolyte (lemon juice). This is referred to as the electrodes being
polarized.

From my straight line of best fit, I can see that as expected, as the
voltage increased, the current decreased. As expected from my
electrode potential calculations in my plan, the cell did not exceed
its potential off 1.1v, in fact, my results were all considerably
lower than this because that calculation was for a perfect experiment
which is almost impossible to achieve, as impurities in the
electrolyte or the electrodes and the fast rate of cell deterioration
mean that a lot less current is actually produced.

As I explained in my plan (background theory section) because V = E -
Ir, if you plot a graph of terminal pd, V, against current, I, as I
have done, then the gradient of the graph, Dy/Dx, will be equal to the
internal resistance of the cell. Using my line of best fit, I will now
calculate the internal resistance of my lemon battery:

400 - 75

0.088 - 0.033

5

= 325

0.055

= 5909.1 W

From this calculation I can conclude that the internal resistance of
this lemon battery was 5909.1 W This is a very large internal
resistance as the voltage produced was very high compared to the
current, and means that, of the energy produced by the battery, only a
small amount is put into the circuit, and a lot of energy is taken out
and converted to waste heat energy. A lemon has a high internal
resistance because the electrolyte (citric acid) is not a very strong
acid so there will not be many free ions to carry the electrical
charge through the whole lemon. Because of this, I think an
electrolyte of a higher PH would have a lower internal resistance.

Evaluation:

As my graph was a straight line, with no un-explainable anomalous
results, I think that my experiment went very well. The method that I
devised gave accurate enough results for me to do an accurate
approximation of the internal resistance and draw a conclusion. There
will have been some error in my results but because I measured each
result to 3 significant figures and repeated my experiment to get an
average to 4 significant figures this error will have been limited to
the best of my ability and the results should be exact to 4
significant figures. Next time I did this experiment I would try to
use more sensitive electronic measuring devices so that I could
measure the voltage and current to more decimal places and further
reduce the margin of error and improve the detail of my conclusion.

The only other problem I had with my experiment was the slight curve
in my graph due to the deterioration of the battery as I was
collecting my results. I could have avoided this by taking my results
more quickly so the battery had less time to deteriorate and repeating
the experiment more times to get a better average. This deterioration
must have also greatly affected the margin of error in my experiment
so I should have really thought about this more before I started
taking my results.

Because the battery deteriorates so quickly, this limits the amount of
time that you can collect data without the results becoming more
inaccurate, so repeating my experiment twice with the same lemon and
electrodes probably also limited the accuracy of my experiment.

Next time I would take more results more quickly and be more organised
to make my results and conclusions more accurate. I could also
investigate this topic further by using different substances for my
electrolyte like different fruit juices or acids. I could also try
using different materials for the electrodes and see how that affected
the internal resistance

I have completed my aim to find the internal resistance of my
self-constructed lemon battery and found the internal resistance to be
5909.1 W.
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